MODEL TEST PAPERS - Sarkari Result Update€¦ · 4 Common Proficiency Test (CPT) Volume - II MODEL TEST PAPER - 1 23. Goodwill of the firm is valued at three year’s purchase of

Board of StudiesThe Institute of Chartered Accountants of India

MODELTESTPAPERSCommon Proficiency Test (CPT)Volume - II

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© The Institute of Chartered Accountants of India

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Reprint 40,000, September 2009

PREFACE

Under the New Scheme of Education and Training, thesimplified entry to the Chartered Accountancy Course has beendesigned through Common Proficiency Test (CPT). It is anobjective type test of 200 marks of four subjects, i.e.Accounting, Mercantile Laws, General Economics andQuantitative Aptitude with an objective to test basic knowledgein these subject areas. This test is of 200 marks. This test isdivided into two sessions of two hours each with a break inbetween. CPT is an objective type test with negative marking.Subjects to be studied in CPT are as follows:

SESSION – I (Two Sections – Two hours – 100 Marks)

Section A: Fundamentals of Accounting (60 Marks)

Section B: Mercantile Laws (40 Marks)

SESSION – II (Two Sections – Two hours – 100 Marks)

Section C: General Economics (50 Marks)

Section D: Quantitative Aptitude (50 Marks)

The CPT is treated as a single paper of 200 Marks. A studenthas to obtain 100 marks in aggregate to qualify CPT.

The Board of Studies has prepared comprehensive studymaterials covering the above mentioned subjects. There aregood number of objective type questions in the study materialswhich students should practice. To facilitate preparation ofthe students, a booklet on Model Test Papers (Volume-I) waspublished in October, 2006 , and a Self-assessment CD is alsoprovided.

In addition, this booklet on Model Test Papers (Volume-II) ispublished to strengthen the existing question bank providedto the students. It is to further state that the Board of Studieswill shortly release another CD using which the CPT studentswill be able to test their preparation subject-wise and chapter-wise. This book contains 10 Model Test Papers comprising of2000 objective type questions. Each Model test paper isdivided into four sections. Section A relates to Fundamentalsof Accounting carrying 60 marks. Section B relates to

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Mercantile Laws carrying 40 marks. Sections C and D relateto General Economics and Quantitative Aptitude carrying 50marks each. All the papers have been carefully designed so asto expose students to all types of questions such as one linestatement questions, fill in the blanks, numerical basedquestions, table based questions, paragraph based questionsand diagram based questions.

Students are advised to answer these each Test paper underexamination conditions. They should attempt Section A andSection B in first two hours and with a break; Section C andSection D should be attempted in next two hours. Then theanswer sheet should be assessed consulting the answers givenat the end of the Model Test Papers. They should deduct 0.25marks for each wrong answer. The same procedure should befollowed for all ten test papers. We are confident that studentswill be able to evaluate their performance by this process.

The Board acknowledge contribution of the faculty membersof the Board Studies, namely, Mrs. Prem J. Bhutani, DeputyDirector, CA. Seema Gupta, Assistant Director, CA. ShilpaAgrawal, Executive Officer, CA. Vikas Kumar, ExecutiveOfficer, CA. Ruchika Sabharwal, Executive Officer, ProfessorT. Mutthu Kumar, Assistant Director, Ms. Srishti Gupta,Management Trainee, Ms. Ginni Aggarwal, ManagementTrainee in the preparation of these Model Test Papers. TheBoard also acknowledge the contributions made by Mr. P.N.Kapur, Retired Vice-Principal, B.N.S.D Inter College, Kanpurwho developed question bank of Accounting, Mr. R.K. Gupta,Company Secretary, Kanpur and Dr. G.K. Pandey, ProfessorD.A.V. Degree College who developed question bank ofMercantile Laws, Dr. O.P. Shukla, Professor Arma Pur DegreeCollege, Kanpur, Dr. G.J. Srivastava, Professor D.A.V. DegreeCollege, Kanpur and Dr. Chamma Shukla, Teacher, VirendraSwaroop Inter College, Kanpur who developed question bankof Economics and CA. Atul Mittal, Kanpur and Mr. G.P.Bhargava, Retired Principal, P.P.N. Degree College whodeveloped question bank of Quantitative Aptitude.

Director of Studies

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The Institute of Chartered Accountants of India

COMMON PROFICIENCY TEST

Model Test Paper – BOS/CPT/VOLUME - 2

S. No. Test Paper Denomination Page No.

1. Model Test Paper – BOS/CPT-1/2007........................................................... 01 – 28



4. Model Test Paper – BOS/CPT-4/2007......................................................... 83 – 108

5. Model Test Paper – BOS/CPT-5/2007....................................................... 109 – 134





10. Model Test Paper – BOS/CPT-10/2007..................................................... 247 – 273

11 Answers ...................................................................................................... 275 – 294

12 Suggested Answers / Hints of Quantitative Aptitude................................ 295 – 443

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CONTENTS

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Recent Publications of the Board of Studies ............................................. 444 - 449

BOARD OF STUDIES

THE INSTITUTE OF CHARTERED ACCOUNTANTS OF INDIA

COMMON PROFICIENCY TESTModel Test Paper – BOS/CPT – 1 / 2007

Time : 4 hours Maximum Marks : 200

The test is divided into four sections.

Questions 1 to 200 have only one correct answer and carry + 1 mark for each correct answer and

– 0.25 mark for each wrong answer.

SECTION – A : FUNDAMENTALS OF ACCOUNTING (60 MARKS)

1. Which of the following is/ are current asset?

(a) Stock (b) Bill receivable(c) Prepaid Expenses (d) All of the above

2. Which of the following sets of expense are the direct expenses of business.

(a) Wages, Carriage Inward, Octroi(b) Postage, Wages, Carriage Inward(c) Purchase, Wages, Coal Expenses(d) Both (a) and (c)

3. Suspense Account in the Trial Balance will be entered in the :

(a) Manufacturing A/c (b) Balance Sheet(c) Trading A/c (d) Profit and Loss A/c

4. The accounting equation is based on

(a) Dual aspect (b) Business Entity(c) Going concern (d) All of the above

5. Different accounting policies can be adopted in the following area/areas

(a) Valuation of inventories (b) Calculation of depreciation(c) Valuation of investments (d) All of the above

1Common Proficiency Test (CPT) Volume - II

2 Common Proficiency Test (CPT) Volume - II

MODEL TEST PAPER - 1

6. Journal is a book of

(a) Original Entry (b) All cash transactions(c) Secondary Entry (d) All non-cash transactions

7. Normally, the following accounts are balanced

(a) Real A/c and Nominal A/c (b) Personal A/c and Real A/c(c) Only Nominal A/c (d) All accounts

8. Opening and closing entries are recorded in :

(a) Journal Proper (b) Purchase Book(c) Sales Book (d) Bill Receivable Book

9. Which of the following instruments is not a negotiable instrument

(a) Bearer Cheque (b) Promissory Note(c) Crossed Cheque (d) Bills of Exchange

10. Bank Reconciliation statement is

(a) A part of the cash book(b) A statement showing the causes of differences between the balance of cash book and

passbook.(c) A part of financial statement(d) None of the above

11. The Installation expenses for a new machinery will be debited to

(a) Cash A/c (b) Profit & Loss A/c(c) Machinery A/c (d) Installation expenses A/c

12. When obligation is not probable or the amount expected to be paid to settle the liabilitycannot be measured with sufficient reliability, it is called

(a) Contingent liability (b) Provision(c) Secured Loan (d) None of the above

13. A Trial Balance contains the balances of

(a) Only real A/c (b) Real A/c and Nominal A/c(c) Personal A/c (d) Both (b) and (c)

14. Error which affect only one account can be

(a) Error of omission (b) Error of posting(c) Error of principle (d) None of the above

15. Valuing the stock in trade at net realisable value or cost price whichever is lower, is anexample of the convention

(a) Conservatism (b) Consistency(c) Dual aspect (d) All of the above


16. In case goods are manufactured and segregated for specified consumers the best method forvaluation of inventory would be

(a) FIFO (b) Simple average(c) Base stock (d) Specific identification method

17. Fixed assets are

(a) Fictitious assets(b) Kept in the business for use over a long period(c) Meant for resale(d) Meant for conversion into cash as quickly as possible

18. Income earned but not received is shown in

(a) Asset side of the Balance Sheet(b) Liability of the Balance Sheet(c) Profit and Loss A/c (Dr. balance)(d) None of the above

19. Overriding commission is generally calculated on

(a) Cash sale only(b) Total sales exceeding invoice value/cost(c) Credit sales(d) None of the above

20. Claim of the retiring partner is payable in the following form

(a) Fully in cash(b) Fully transferred to loan A/c to be paid on with some interest on it.(c) Partly in cash and partly as loan repayment with agreed interest(d) Any of the above

21. As per Section 12 of Negotiable Instruments Act, which of the following is not a foreign bill?

(a) A bill drawn outside India and made payable outside India.(b) A bill drawn outside India and made payable in India.(c) A bill drawn outside India on a person resident in India.(d) A bill drawn in India on a person resident outside India and made payable outside India.

22. Kishan, the acceptor of the bill has to honour a bill on 31st March, 2006. Due to financialcrisis, he is unable to pay the amount of bill of Rs. 40,000. Therefore he approaches Karan,the drawer of that bill on 20th March, 2006 for extension of the bill for further 2 months.Karan agrees to extend the credit period by drawing a new bill for Rs. 42,000 together withinterest of Rs. 2,000 in cash. In this case old bill of Rs. 40,000 will be considered as

(a) Dishonoured (b) Retired(c) Cancelled (d) Discounted



23. Goodwill of the firm is valued at three year’s purchase of the average profit of the last fiveyears. The profits are as under

2006 16,0000 (Profit)

2005 20,000 (Loss)

2004 1,20,000 (Profit)

2003 1,00,000 (Profit)

2002 80,000 (Profit)

Goodwill amount will be

(a) Rs. 2,76,000 (b) Rs. 2,64,000(c) Rs. 2,60,000 (d) Rs. 2,28,000

24. Rama Ltd. forfeited 800 shares of Anil of Rs. 10 each fully called up for non-payment of finalcall of Rs. 2 per share and reissued to Ankit as fully paid up for Rs. 10 per share. Amounttransferred to capital reserve will be

(a) Rs.3,200 (b) Rs.4,600(c) Rs.6,400 (d) Rs.8,000

25. Dabur Ltd. forfeited 400 shares of Rs. 10 each fully called up, on which the holder has paidonly application money of Rs. 4 per share. Out of these 250 shares were reissued at Rs. 12per share fully paid up. Capital reserve will be credited

(a) Rs. 1,000 (b) Rs. 1,600(c) Rs. 4,800 (d) Rs. 3,000

26. On 1 Jan. 2007 Ankur of Delhi consigned 200 cases, cost price Rs. 3,750 at proforma invoiceof 25% profit on sales to his agent Mani of Manipur. Balance of Goods Sent on ConsignmentA/c transferred to General Trading A/c will be

(a) Rs. 5,000 (b) Rs. 3,750(c) Rs. 8,000 (d) None of the above

27. A manager gets 5% commission on net profit after charging such commission, gross profitRs. 58,000 and expenses of indirect nature other than manager’s commission are Rs. 16,000.Commission amount will be

(a) Rs. 2,900 (b) Rs. 2,000(c) Rs. 1,500 (d) Rs. 2,200


28. Particulars Amount Particulars Amount

Salaries 4,000 Interest on investment received 1,200Interest on loan 5,000 Freight inward 2,000Bad debts 1,200Wages 1,000Gross Profit 25,000Net Profit will be

(a) Rs. 15,300 (b) Rs. 13,000(c) Rs. 17,200 (d) Rs. 16,000

29. (i) Balance as per cash book on 31.03.2005 Rs. 10,000

(ii) Cheques sent to bank but not entered in cash book Rs. 2,200

(iii) Cheques issued and presented on 7th April Rs. 3,000

(iv) Bill payable by Bank not entered in the cash book Rs. 1,600

Balance on as per passbook will be

(a) Rs. 9,200 (b) Rs. 13,600(c) Rs. 10,800 (d) Rs. 6,400

30. Goods purchased Rs. 100000; sales Rs. 90000. If margin 20% on sales then closing stock willbe

(a) Rs. 25,000 (b) Rs. 35,000(c) Rs. 28,000 (d) Rs. 5,600

31. The total of wages for the month of Jan, 2006 amounting Rs. 6000 was not posted. Rectifyingentry for the same will be

(a) Suspense A/c Dr. 6000 ; To Labour A/c 6000(b) Wages A/c Dr. 6000 ; To Suspense A/c 6000(c) Wages A/c Dr. 6000 ; To Cash A/c 6000(d) None of the above

32. Anu and Anubhav are partners sharing profits in the ratio 5 : 3, they admitted Anup givinghim 3/10th share of profits. if Anup acquires 1/5th share from Anu and 1/10th share fromAnubhav, new profit sharing ratio will be

(a) 5 : 6 : 3 (b) 18 : 24 : 38(c) 17 : 11 : 12 (d) 4 : 3 : 2

33. Mr. Om sold goods worth Rs. 2,50,000 to Mr. Jai. Mr. Jai accepted a bill on 1.11.06, payableafter 2 months. Mr. Om discounted this bill @ 18% p.a. on 15.11.06. On the due date Mr. Jaifailed to discharge the bill. Later Mr. Jai become insolvent and 50 paise is recovered fromMr. Jai’s estate. How much amount of bad debts will be recorded in the books of Om.

(a) Rs. 1,25,000 (b) Rs. 1,36,500(c) Rs. 94,370 (d) Rs. 1,14,000



34. A, B and C are the partners sharing profits in the ratio 4 : 3 : 2. C died on 30.06.2005 andprofits for the accounting year 2004-05 were Rs. 72000. How much share in profits for theperiod 1st April, 2005 to 30th June 2005 will credited to C’s account

(a) Rs. 4,000 (b) Rs. 16,000(c) Rs. 18,000 (d) Rs. 12,000

35. A bill is drawn on 12th June for 2 months. The due date of the bill will be

(a) 12th August (b) 13th August(c) 14th August (d) 15th August

36. Goods costing Rs. 2,40,000 were sent on consignment basis. Goods are invoiced at cost +25%. The Invoice price and loading will be

(a) Rs. 2,40,000 and Rs. 60,000 (b) Rs. 3,00,000 and Rs. 10,000(c) Rs. 4,00,000 and Rs. 1,60,000 (d) Rs. 3,00,000 and Rs. 60,000

37. Which of these is not a part of double entry system?

(a) Memorandum Joint Venture A/c (b) Joint Venture A/c(c) Joint Bank A/c (d) Co-venturer A/c

38. Wright Ltd. issued 40000, 8% debentures of Rs. 10 each at par which are redeemable after8 years at a premium of 20%. The amount of loss on redemption of debentures to be writtenoff every year will be

(a) Rs. 60,000 (b) Rs. 50,000(c) Rs. 10,000 (d) Rs. 8,000

39. Chetan Ltd. recorded the following information as on March 31, 2004

Stock (1-4-03) Rs. 40000Purchases Rs. 80000

Sales Rs. 100000

It is noticed that goods worth Rs. 30,000 were destroy due to fire against this, the insurance companyaccepted a claim of Rs. 14000.The company sells goods at cost 33%. The value of closing inventory, after taking into account theabove transaction is

(a) Rs. 75,000 (b) Rs. 15,000(c) Rs. 25,000 (d) Rs. NIL

40. Riya and Piya are partners in a firm. During the year 2006, Riya withdraw Rs. 1000 p.m.and Piya withdraw Rs. 500 p.m. on the first day of each month for personal use. Interest ondrawing is to be charged @ 10% p.a. Total interest on drawings will be

(a) Rs. 975 (b) Rs. 650(c) Rs. 900 (d) Rs. 325


41. Mohan drew a bill on Gopal for Rs. 100000 for 3 months it proceeds are to be shared equally.Mohan got the bill discounted at 12% p.a. and remits required proceeds to Gopal. Theamount of such remittance will be

(a) Rs. 24,250 (b) Rs. 48,500(c) Rs. 50,000 (d) Rs. 97,000

42. R and S are partners sharing profits and losses equally. They admitted A for 1/3 share in thefirm. The new profits sharing ratio will be

(a) 3 : 2 : 1 (b) 1 : 1 : 1(c) 2 : 2 : 1 (d) Cannot be calculated

43. Gattu and Bittu entered into a joint venture where Gattu bought goods of the value Rs.100000 and consigned them to Bittu to be sold by them on joint venture, profits being dividedequally. Gattu paid Rs. 10000 for freight and insurance. Gattu draws a bill on Bittu for Rs.1,00,000. Gattu discounted at Rs. 95,000. Bittu sold the goods for Rs. 1,50,000. Commissionpayable to Bittu Rs. 5,000. The amount to be remitted by Bittu to Gattu will be

(a) Rs. 12,5,000 (b) Rs. 1,35,000(c) Rs. 1,30,000 (d) Rs. 1,40,000

44. 10000 litres of oil were consigned to a wholesaler the cost being Rs. 100 per litre by incurringfreight Rs.8,000. 10% of loss of oil unavoidable. 8,000 litres were sold by the consignee. Theremaining stock of 1000 litres will be valued at

(a) Rs. 1,12,000 (b) Rs. 1,11,111(c) Rs. 1,00,800 (d) Rs. 1,00,000.

45. Machinery costing Rs. 500000 was purchased on 1.4.2005. The installation charges amountingRs. 20000 were incurred. The depreciation at 10% per annum on straight the method forthe year ended 31st March, 2007 will be

(a) Rs. 5,00,000 (b) Rs. 50,000(c) Rs. 52,000 (d) Rs. 45,000

46. Credit balance as per passbook on 31.3.2006 is Rs. 22000. Cheques deposited but not clearedamount to Rs. 2000 and cheques issued but not presented of Rs. 8000. Balance as per cashbook should be

(a) Rs. 32,000 (b) Rs. 16,000(c) Rs. 28,000 (d) Rs. 18,000

47. A Company forfeited 2,000 shares Rs. 10 each held by Mr. Mohan for non payment ofallotment money of Rs. 3 per share. The called-up value per share was Rs. 8. On forfeiture,the amount debited to share capital will be

(a) Rs. 6,000 (b) Rs. 20,000(c) Rs. 1,000 (d) Rs. 16,000



48. Bill of Rs. 5000 accepted by Rajan was endorsed by Rohit to Raj on account of final settlementof Rs. 5200. The benefit of Rs. 200 earned by Rohit was

(a) Credited to discount received account by Rs. 200(b) Debited to discount allowed account by Rs. 200(c) Credited to rebate account by Rs. 200(d) None of the above

49. Ankur purchased goods costing Rs. 5000 at an invoice price, which is 50% above cost. Oninvoice price he enjoyed 15% trade discount and Rs. 375 cash discount on cash payment ofgoods in lump sum at the time of purchase. The purchase price to be recorded in the booksbefore cash discount will be

(a) Rs. 5,000 (b) Rs. 7,500(c) Rs. 6,375 (d) Rs. 6,000

50. Kapoor Ltd. issued 750000, 12% debentures of Rs. 100 each at a premium of 10% payableRs. 40 on application and balance on allotment. Debentures are redeemable at par after 6years. All money due on allotment was called up and received. The amount of premium willbe

(a) Rs. 3,00,00,000 (b) Rs. 75,00,000(c) Rs. 2,25,00,000 (d) Rs. 7,50,00,000

51. Gopi Ltd. purchased land and building from Mohan Ltd. for a book value ofRs. 200000. The consideration was paid by issue of 12% debentures of Rs. 100 each at adiscount of 20%. The debenture account is credited with

(a) Rs. 2,00,000 (b) Rs. 2,60,000(c) Rs. 2,50,000 (d) Rs. 1,40,000

52. A company offers to the public 20000 shares for subscription. The company receivesapplication for 24000 shares. If the shares are allotted on pro-rata basis the application for24,000 shares are to be allotted as

(a) 5 Shares for every 6 shares applied(b) 4 Shares for every 5 shares applied(c) 6 Shares for every 7 shares applied(d) None of the above

53. Arjun and Bheem are partners in the firm sharing profits and losses in the ratio 1 : 1. Theyhave invested capital of Rs. 80,000 and Rs. 50,000 respectively. As per partnership deed,they are entitled to interest on capital @ 2.5% p.a. before sharing the profits. During theyear firm earned a profit of Rs. 5000 before allowing interest. The net profit will beapportioned as

(a) Rs. 900 to Arjun, Rs. 900 to Bheem(b) Rs. 875 to Arjun, Rs. 875 to Bheem(c) Rs. 785 to Arjun, Rs. 785 to Bheem(d) Rs. 965 to Arjun, Rs. 965 to Bheem


54. Following figures have been taken from the trial balance of a traderGross Purchase Rs. 60,000 Gross Sales Rs. 1,00,000Purchase Returns Rs. 5,000 Sales Returns Rs. 7,000Duty Drawback Rs. 6,000 Sales Tax Rs. 12,000The amount of G.P. will be

(a) Rs. 32,000 (b) Rs. 38,000(c) Rs. 40,000 (d) Rs. 26,000

55. A debit note for Rs. 500 issued by Mr. Marshall to Mr. Fisher for goods returned by Mr.Marshall is to be accounted for

(a) Bill receivable Book (b) Purchases Return Book(c) Purchase Book (d) Journal Proper

56. A purchase of goods from Rahul amounting to Rs. 300 has been wrongly entered throughsales book, what will be the rectifying entry.

(a) Purchase A/c Dr. 300To Sales A/c 300

(b) Sales A/c Dr. 300To purchase A/c 300

(c) Rahul A/c Dr. 600To purchase A/c 300To sales A/c 300

(d) Purchases A/c Dr. 300Sales A/c Dr. 300

To Rahul 600

57. Original Cost = Rs. 63000. Salvage value = 3000. Depreciation for 2nd year @ units ofproduction method, If units produced in 2nd year was 5000 and total estimated production60000 units.

(a) Rs. 5,000 (b) Rs. 6,000(c) Rs. 5,250 (d) Rs. 5400

58. When drawing up a B.R.S. If you start with a debit balance as per the Bank statement, theunpresented cheques should be

(a) Not required to be adjusted (b) Subtracted(c) Added (d) None of the above

59. Purchase of Building from Bank

(a) Decrease in total liabilities (b) Increase in total assets(c) Decrease in total assets (d) No effect of total of assets.

60. Economic life of an enterprise is split into periodic interval as per

(a) Materiality (b) Going Concern(c) Accrual (d) Conservation



SECTION – B : MERCANTILE LAWS (40 MARKS)

61. What section of Indian contract Act, 1872 applies to a contract?

(a) 2(b) (b) 2(d)(c) 2(h) (d) 2(e)

62. Which of the following is correct?

(a) a promise is a contract(b) a set of promises is a contract(c) a proposal is a contract(d) agreements enforceable by law is a contract

63. A promise is defined in section

(a) 2(b) (b) 2(d)(c) 2(e) (d) 2(h)

64. Void agreements are

(a) Forbidden under law (b) Not forbidden under law(c) Punishable (d) Legal agreements

65. Where two parties make identical offers to each other, in ignorance of each other’s offer, theoffers are known as

(a) Cross-offers (b) An agreements(c) Contracts (d) Promises

66. In the case of specific offer, it can be accepted only

(a) by the person to whom it is made(b) by third party(c) by the stranger(d) by legal heir

67. A voidable agreements agreement is enforceable by

(a) None of the parties(b) Only one of the parties(c) All the parties to the contract(d) One or more but not by the other or others

68. An illegal agreement

(a) is void ab initio(b) becomes void(c) void abinitie as well as punishable(d) voidable


69. A minor is a person who has not completed

(a) 20 years of age (b) 21 years of age(c) 18 years of age (d) 19 years of age

70. A contingent contract is defined in section

(a) 32 (b) 31(c) 33 (d) 35

71. Where a certain amount is deposited as securing for performance of a contract, it is called

(a) Earnest money (b) Cash money(c) Hard money (d) All of these

72. Quantum merit means

(a) as much as is merited (b) as much as is credited(c) as much as is performed (d) None of these

73. The law in India relating to claim for damages is contained in section

(a) 75 (b) 71(c) 74 (d) 73

74. A contract of guarantee is defined in section

(a) 125 (b) 126(c) 128 (d) 129

75. A contract made by mistake about same foreign law, is

(a) Void (b) Valid(c) Voidable (d) Illegal

76. A partnership at will is one

(a) Duration not fixed(b) Duration fixed(c) Dissolved at any time(d) Can be dissolved only at the happening of an event.

77. The unpaid seller has the right against the goods

(a) Rights of lien (b) Right of stoppage in transit(c) Right of resale (d) all of these

78. Contract in which only one party has to perform his promise is known as

(a) Executed contract (b) Executory contract(c) Unilateral contract (d) Bilateral contract



79. When the performance of a contract becomes subsequently impossible or unlawful, thecontract becomes

(a) Illegal (b) Void(c) Invalid (d) Voidable

80. Contract for the sale of future goods is _______.

(a) Sale (b) Agreement to sell(c) Void (d) Auction sale

81. The Sale of Goods Act, 1930 deals with the _______.

(a) Movable goods only(b) Immovable goods only(c) Both immovable and movable goods(d) Tangible goods only

82. A party agrees to pay five lakhs to another party if first party brings to earth a star from sky,this is known as _______.

(a) Contingent contract (b) Quasi Contract(c) Implied contract (d) Wagering contract

83. _______ does not affect the free consent of the parties.

(a) Fraud (b) Coercion(c) incompetence (d) Undue influence

84. Consideration may be _______.

(a) Past (b) Present(c) Future (d) All of these

85. When the consent of a party is obtained by fraud, the contract is____________.

(a) Valid (b) Voidable(c) Illegal (d) Void

86. Registration means getting the partnership firm registered with _______.

(a) Registrar of firms(b) Registrar of co-operative society(c) Registrar of companies(d) All of these

87. An agreement to share earnings of a smuggling business is _______.

(a) Valid (b) Void(c) Voidable (d) Contingent


88. There can be a stranger to a _______.

(a) Contract (b) Consideration(c) Agreement (d) Promise

89. The authority of a partner to bind the firm is known as _________.

(a) Implied authority (b) Express authority(c) Contractual authority (d) None of the above

90. An actionable claim can always be _______.

(a) Assigned (b) Adjusted(c) Noted (d) All of these

91. Reciprocal promise means _______.

(a) A promise in return for a promise(b) A promise in return for a agreement(c) A promise in return for a contract(d) Accepted promise

92. When one of the parties to the contract has performed his part of the promise, it is known as_______.

(a) Consideration (b) Past consideration(c) Future consideration (d) Executory consideration

93. An agreement made without consideration is _______.

(a) Valid (b) Void(c) Voidable (d) Illegal

94. Acceptance in ignorance of the offer is _______.

(a) Valid (b) Invalid(c) Void (d) Voidable

95. An agreement to commit a crime is _______.

(a) Valid (b) Void(c) Voidable (d) Unenforceable

96. Communication of proposal is complete when it comes to the knowledge of _______.

(a) The proposer (b) The person to whom it is made(c) The Court (d) (a) or (b)



97. An offer made to a specific person is known as_________.

(a) Special offer (b) Separate offer(c) Specific offer (d) Standing offer

98. Advertising agent invites a tender it is known as _______.

(a) An offer (b) A counter offer(c) An agreement (d) An invitation to offer

99. A buys an article thinking it is worth Rs. 10,000 while it is actually worth Rs. 5,000 only.Decide what will be the remedy to A.

(a) The agreement can be avoided on the ground of mistake(b) The agreement cannot be avoid on the ground of mistake(c) A can sue for return taking back Rs. 5,000(d) A can sue for recovery of Rs. 2,000 only

100. A agrees to buy from ‘B’ a certain horse. It turns out that the horse was dead at the time ofthe bargain, though neither party was aware of the fact. Decide.

(a) The agreement is void(b) The agreement is valid(c) A can sue for purchasing new horse in place of dead horse(d) None of these

SECTION – C : GENERAL ECONOMICS (50 MARKS)

101. Monetary Policy refers to:

(a) Public Revenue and Public Expenditure Policy(b) Policy to control money supply(c) M1 and M2(d) Policy linked to banking

102. HYVP was restricted to the following crops:

(a) Wheat, Rice, Bajra, Jawar and Maize

(b) Wheat, Sugar, Bajra, Jawar and Maize

(c) Wheat, milk, Bajra, Jawar and maize

(d) Wheat, Banana, Bajra, Jawar and Maize

103. The Full form of ICICI is :

(a) Investment credit and Industrial Corporation of India

(b) Indian credit and Investment Corporation of India

(c) Industrial credit and Investment Corporation of India

(d) International credit and Investment Corporation of India


104. In the theory of demographic transition in the first stage :

(a) Both birth rate and death rate are high

(b) Both birth rate and death rate are low

(c) Birth rate is high and death rate is low

(d) Birth rate is low and death rate is high

105. Narrow money refers (as per latest RBI Working Group):

(a) Currency + Demand Deposits + other Deposits with RBI

(b) Currency + Demand Deposits + Post office saving deposits

(c) Currency + Demand Deposits + Money at call

(d) None of the above

106. In the case of a straight line demand curve meeting the two axes, the price elasticity ofdemand at y-axis of the line would be equal to

(a) 1 (b) infinity

(c) 3 (d) 1.25

107. A firm under perfect competition will be making minimum losses (in the short run) at apoint where:

(a) MC > MR (b) MR > MC

(c) MC = MR (d) AC = AR

108. In order to control Inflation in India RBI may:

(a) Increase CRR(b) Decrease CRR(c) Increase buying of Government Securities(d) None of the above

109. When the consumer is in equilibrium his price line is _____________ to indifference curve

(a) Parallel (b) At right angle(c) Diagonally opposite (d) Tangent

110. Which of the following is not the feature of Perfect Competition?

(a) Large number of buyers and sellers(b) Small number of buyers and sellers(c) Free Entry and Exit(d) Good is Homogeneous



111. In the long run under which competition a firm may earn super normal profits?

(a) Monopolistic competition (b) Perfect competition(c) Oligopoly (d) Monopoly

112. Nationalization means:

(a) Selling of government stake to private sector(b) Selling of government companies to private sector(c) Government purchasing 26% shares in private companies(d) Taking of full control and management from Private Sector

by the government

113. In April 2007, Bank rate was ——— percent

(a) 6 (b) 7(c) 5 (d) 8

114. In April 2007, the SLR was —— percent

(a) 5% (b) 15%(c) 25% (d) 20%

115. Economics is a Science which deals with wealth was referred by :

(a) Alfred Marshal (b) J. B. Say(c) Adam Smith (d) A.C. Pigou

116. Average fixed cost can not be:

(a) Less than one (b) One(c) Zero (d) Greater than

117. The number of Member Countries of WTO is :

(a) 184 (b) 149(c) 150 (d) 177

118. If as a result of 10% increase in price, the quantity supplied does not change at all, it impliesthat the elasticity of Supply is :

(a) Zero(b) Infinite(c) Equal to one(d) Greater than Zero but less than are

119. The Law of variable proportions examines the Production function with:

(a) One factor variable and only one factor fixed(b) One factor variable keeping quantities of other factors fixed(c) All factors variable(d) None of the above


120. In Law of negative returns (Third stage of Law of variable proportions):

(a) Total Product declines, M P is positive(b) Total Product declines, M P is Zero(c) Total Product declines, M P is negative(d) Total Product in constant, M P is constant

121. If GDP is 20% higher than last year and the rate of inflation is 9%, then production in theeconomy has grown by ———.

(a) 8% (b) 11%(c) 20% (d) 9%

122. Indifference Curve analysis is based on

(a) Ordinal utility (b) Cardinal utility(c) Marginal utility (d) None of the above

123. The demand curve is also known as:

(a) Marginal Revenue curve (b) Marginal utility curve(c) Average Revenue (d) Average utility curve

124. Supply of a good and its price have

(a) Negative relationship (b) Inverse relationship(c) No relationship (d) Positive relationship

125. MC curve cuts AVC Curve

(a) At its falling point (b) At its minimum point(c) At its rising point (d) At different points

126. TRYSYM stands for

(a) Training Regional Youth for Self Employment(b) Training Raipur Youth for Self Employment(c) Training Rural Youth for Self Employment(d) None of the above

127. PNB, SBI, Canara Bank are examples of:

(a) Semi Private banks (b) Public Sector banks(c) Private Sector banks (d) Semi Public Sector banks

128. Margin requirement for commercial bank refers to

(a) Profit margins(b) CRR and SLR(c) CRR(d) Difference between amount of Security to be given by the borrowers to the bank and the

amount of Loan.



129. Accounting profit is equal to:

(a) Total Revenue – Total variable cost(b) Total Revenue – Total direct cost(c) Total Revenue – Total cost(d) Total Revenue – Total Explicit cost and Total Implicit Cost.

130. RBI has ——— .

(a) Very few branches (b) One branch in each state of India(c) No branches (d) None of the above

131. If firm’s average cost curve is falling then marginal curve must be :

(a) Falling (b) Rising(c) below average cost curve (d) None of the above

132. Fiscal Policy in India is given by:

(a) RBI (b) Ministry of Finance(c) Prime Minister (d) None of the above

133. Which is not the aim of National Policy on Education?

(a) Universal access and enrolment(b) Universal retention of children upto 14 years of age(c) A Substantial improvement in the quality of education(d) None of the above

134. The goal of National Policy on Education is to make an expenditure of ——— of GDP.

(a) 5% (b) 7%(c) 6% (d) 8%

135. Gross Enrolment Ratio shows the proportion of children in elementary school in the agegroup of:

(a) 6-10 (b) 6-14(c) 6-8 (d) 4-10

136. VSAT stands far

(a) Very Small Aperture Terminals(b) Various Small Aperture Terminals(c) Very Small Application Terminals(d) Valuable Small Aperture Terminals

137. On an average, one post office serves:

(a) 18 Sq. Km area (b) 21 Sq. Km area(c) 31 Sq. Km area (d) 51 Sq. Km area


138. Airport Authority of India manages ——— airports

(a) 82 (b) 93(c) 92 (d) 103

139. India has ——— % of the world area

(a) 1.2 (b) 2.4(c) 16.7 (d) 7

140. What is the approximate life expectancy of the people living in India?

(a) 58 (b) 60(c) 65 (d) 50

141. Which of the following states has the highest percentage of literacy?

(a) Delhi (b) Kerela(c) Karnataka (d) Tamil Nadu

142. India’s share in world income is

(a) 5% (b) 16.7%(c) 1.2% (d) 2.4%

143. Every ——— poor person in the world is an Indian

(a) Sixth (b) Third(c) Fifth (d) Seventh

144. Density of Population refer to

(a) Number of person per square kilometer(b) Number of person per square kilometer of land excluding forest and river(c) Number of person per square kilometer of land excluding rivers and seas in the country(d) Number of persons per km of land

145. India’s present density of Population is

(a) 344 persons per square kilometer(b) 324 persons per square kilometer(c) 390 persons per square kilometer(d) 440 persons per square kilometer

146. Ginni Coefficient is often used to measure poverty in:

(a) Absolute Terms (b) Relative Terms(c) Both (a) and (b) (d) None of the above



147. Presently how many villages are not electrified?

(a) 25% (b) 5%(c) 10% (d) 15%

148. The ———— is defined as the number of persons in the labor force per 1000 persons

(a) WPR (b) LFPR(c) CWS (d) CDS

149. An expansion in the supply of a good is caused by a:

(a) Rise in the price of good(b) Fall in the prices of other goods.(c) Fall in the prices of factors of production(d) All of the above

150. Which of the following has the lowest price elasticity of supply?

(a) Luxury (b) Necessities(c) Salt (d) Perishable goods

SECTION – D : QUANTITATIVE APTITUDE (50 MARKS)

151. The value of ( ) (– )ο

⎛ ⎞ + +⎜ ⎟⎝ ⎠

41521

64 3264

(a) 171

8(b) 17

3

8

(c) 117

8(d) None of these

152. If a2 + b2 = 45 & ab = 18, then +1 1a b

is

(a)1

3(b)

2

3

(c)1

2(d) None of these


153. The value of

1 –1 –12 2 2a + a 1 – a

+1 – a 1+ a

(a)a

a –1(b)

a –1

2

(c)2

a –1(d)

2

1– a

154. If 2 625 16 10e x 10 elog , log = log , log , then x

(a) 7 (b) 5(c) 8 (d) None of these

155. The highest score in an innings was 2

9 of the total score and the next highest was

2

9 of the

remainder. These score differed by 8 runs. What was the total score in the innings?

(a) 162 (b) 152(c) 142 (d) 1132

156. The third proportional to 15 and 20 is

(a)80

3(b) 80

(c)80

7(d) None of these

157. The mean proportional between 9 and 25 is –


158. The ratio of the number of boys and girls in a school is 2:5. If there are 280 students in theschool, find the number of girls in the school.


159. A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If thetotal value is Rs. 35, how many coins of each type are there.




160. One-third of a number is greater than one-fourth of its successor by 1. Find the number.


161. The value of log3

1

81⎛ ⎞⎜ ⎟⎝ ⎠

is

(a) 4 (b) –4(c) 2 (d) –2

162. The value of ⎛ ⎞⎜ ⎟⎝ ⎠

2 2

1log

256 is

(a)16

3(b) –4

(c) 3 (d)–16

3

163. If logx3 1

215

= ; then value of x is

(a) 8 (b) 32(c) 16 (d) 64

164. If log4 [log3(log2x)] = 0; then value of x is


165. The value of logx(0.00001) = –5, then x is

(a) 10 (b) 102

(c) 100 (d) None of these

166. 1230 baskets of mangoes were loaded in three trucks. When unloaded, it was found that 5,10 and 15 baskets were rotten in the trucks respectively, but the remaining baskets were inthe ratio of 3:4:5. How many baskets were loaded initially in each truck?


167. Find the ratio x : y : z from 2x + 3y – 5z = 0 and –3x + 2y + 7z = 0

(a) 10:12:13 (b) 30:2:12(c) 31:1:13 (d) None of these


168. The value of loga n A

(a)1

n log

aA (b) a log

1/n A

(c) A loga

1

n⎛ ⎞⎜ ⎟⎝ ⎠

(d) None of these

169. The value of 10

10

log 4log 8

(a)1

3(b)

4

3

(c)2

3(d) None of these

170. If log10 12.45 = 1.0952 and log10 3.79 = 0.5786, Find the value of log10 124.5 + log10379

(a) 5.6738 (b) 4.6738(c) 6.6738 (d) None of these

171. Find the number of even numbers greater than 100 that can be formed with the digits 0, 1, 2,3?


172. How many numbers between 100 and 1000 can be formed with the digits. 2, 3, 4, 0, 8, 9?


173. In how many ways can the letters of the word “ALGEBRA” be arranged without changingthe relative order of the vowels?


174. How many words can be formed with the letters of the word “UNIVERSITY”, the vowelsalways remaining together?




175. In how many ways can the letters of the word “DIRECTOR” be arranged so that the threevowels are never together?

(a) 180 (b) 18,000(c) 18,002 (d) None of these

176. If f(x) = 1; if x < 3 , f(x) = ax + b; if 3 < x < 3 , f(x) = 7; if 5 < x.Determine the values of a & bso that f(x) is continuous.

(a) a=3 & b =– 8 (b) a = 3 & b=8(c) a–3 & b = 8 (d) None of these

177. Evaluate →

⎡ ⎤⎢ ⎥⎣ ⎦

2x 3

x 9lim –

x - 3 x – 3x


178. If f(x) = 4 –x2; then x 2

–→ −

f(2) f(x)lim

x 2 is

(a)2

5(b)

2–

5

(c) 2 5 (d) 4

179. Evaluate dydx

; if y = –

+1 x1 x

(a) 2

1

(1 x) 1– x )+ (b) 2

–1

(1 x) 1– x )+

(c) 2 2

1

(1 x ) 1– x )+ (d) None of these

180. If y =+x10 logx

x; then find

dydx

.

(a)

x10 (2 log10 –1) 2 – log x

2x x

× +(b)

x10 (2 log10 1) 2 – log x

2x x

× + +

(c)

x10 (2 –1) 2 – log x

2x x

+(d) None of these


181. Evaluate ∫x 22 x dx

(a)

x 2 x 1 x 1

2 3

2 x x2 2– c

2 (log 2) (log 2)

+ +

+ + (b)

x 3 2 x 1 x 1

2 2

2 x x 2 2– c

3 (log 2) (log3)

+ +

+ +

(c)

x 2 3 x x 1

3

2 .x x .2 2– c

3 3 (log 2)

+

− + (d) None of these

182. Evaluate ∫log x

dx3x

(a)1

log x c3

+ (b) ( )21log x c

3x+

(c) ( ) 21log x c

3⎡ ⎤ +⎣ ⎦ (d) None of these

183. Evaluate: 2∫log x

dxx

(a)1

(1 log x) cx

+ + (b)–1

log ex cx

+

(c)1 x

log cx e

⎛ ⎞ +⎜ ⎟⎝ ⎠

(d) None of these

184. Evaluate: ( )2

+∫

x 2e (x 1)dx

x +1

(a)x x –1

e cx 1

⎛ ⎞ +⎜ ⎟+⎝ ⎠(b)

x x 1e c

x –1

+⎛ ⎞+⎜ ⎟⎝ ⎠

(c)x x –1

–e cx 1

⎛ ⎞ +⎜ ⎟+⎝ ⎠(d) None of these



185. Evaluate ( )2∫xxe

dx1+ x

(a)xe

c1 x

++

(b)xxe

c1 x

++

(c) ( )x

2

ec

1 x+

+ (d) None of these

186. If y = ;+ 1x

x then

dy2x

dx is

(a)1

x –x

(b)1

xx

+

(c)1

x –x

(d) None of these

187. if y = –

– –

+ ++

2 2

2 2

x 1 x 1

x 1 x 1, then

dydx

is

(a)

3

4

2x2x –

x –1(b)

3

4

2x2x

x –1+

(c)

3

4

xx –

x –1(d) None of these

188. If y = –

34x x 2

log ex 2

⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟⎢ ⎥+⎝ ⎠

⎣ ⎦

then dydx

is

(a)2

2

x –1

x – 4(b)

2

2

x 1

x – 4

+

(c)2

2

x –1

x 4+(d) None of these


189. If y = xx, then dydx

is

(a) xx (2 + log x) (b) xx log (ex)

(c) xx loge

x⎛ ⎞⎜ ⎟⎝ ⎠

(d) None of these

190. If y = 2– xex then

dydx

is

(a)

22– x 2e – x 1– 2x log x

x

⎡ ⎤⎢ ⎥⎣ ⎦

x e (b)

3 22– x 2e – x2

1– 3x log x

x

⎡ ⎤⎢ ⎥⎣ ⎦

x e

(c)

22– x 1– 3x log x

xe

⎡ ⎤⎢ ⎥⎣ ⎦

(d) None of these

191. If the sum of first n terms of an A.P.’s Zero, then the sum of next m terms, where a is the firstterm of the A.P. is

(a)–am

(m n)(n –1)+ (b)–am(m n)

n –1

+

(c)am(m n)

n –1

+(d) None of these

192. First, Second and last terms of a finite A.P. are m, n and 2m respectively, then sum of theseries is

(a)3mn

2(n – m) (b)3mn

n m−

(c)3mn

2(n m)+ (d) None of these

193. The first and fifth term of an A.P. of 40 terms are –29 & –15 respectively. Find the sum of allpositive terms of this A.P.




194. If mth term of an A.P. is 1n

and nth term is 1m

, then sum of mn terms is –

(a) mn+1 (b)1

(mn –1)2

(c)1

(mn 1)2

+ (d) None of these

195. The sum of n terms of two A.P.s are in the ratio (7n+1) : (3n+2); find the sum of their 13th terms

(a) 6:7 (b) 16:7(c) 7:16 (d) None of these

196. If one Arithmetic Mean A and G.M.s G1 and G2 be inserted between any two numbers then3 31 2G + G is equal to –

(a) 2G1 G

2(b) 2A G

1 G

2

(c) 2AG1

(d) None of these

197. If ++

m+1 m+1

m m

a ba b

is the G.M. between the numbers a and b, then the value of m is

(a) –1

2(b)

1

2(c) 1 (d) 0

198. If the pth, qth, rth and sth terms of an A.P. are in G.P.; then p–q, q–r and r–s are in

(a) A.P. (b) G.P.(c) Cannot determine (d) None of these

199. The value of 1.4 is

(a)13

9(b)

10

9

(c)4

9(d) None of these

200. The value of 0.356 is

(a)356

999(b)

353

999

(c)353

990(d) None of these

❖❖❖

BOARD OF STUDIES








1. Present liability of uncertain amount, which can be measured reliably by using a substantialdegree of estimation is termed as

(a) Contingent liability (b) Liability(c) Provision (d) Reserve

2. Which one of the following statement is FALSE :

(a) There are many views about accounting principles(b) Accounting is based on accounting equation(c) Accounting is commonly treated as language of business(d) None of the above

3. For charging depreciation, on which of the following assets, the depletion method is adopted?

(a) Washing Assets (Mines) (b) Land(c) Goodwill (d) All of the above

4. Closing stock appearing in the trial balance is shown in

(a) The Profit and Loss Account (b) The Balance Sheet only(c) The Trading Account only (d) Both (b) and (c)




5. When the incoming partner brings his share of goodwill in cash, the amount of brought-inshare of goodwill is credited to

(a) Cash Account (b) Capital Account(c) Premium for Goodwill (d) Old Partner’s Capital Account

6. For shares issued to promoters for their services, account debited is

(a) Goodwill Account (b) Promotion Expenses Account(c) Promoters Account (d) Directors Account

7. According to Section 78 of the Companies Act, the amount in the securities premium A/ccan be used for the purpose of

(a) Issue of fully paid bonus shares (b) Writing off preliminary expenses(c) Both (a) & (b) (d) None of the above

8. Closing stock is valued at

(a) Cost price(b) Cost price or Net realisable value whichever is lower(c) Cost price or Net realisable value whichever is higher(d) Net realisable value

9. When the goods are returned to a supplier

(a) A Debit note is sent to him(b) An Account sale is sent to him(c) A receipt is sent to him(d) Either (b) or (c)

10. Bills receivable endorsed are debited to

(a) Bills Payable A/c (b) Debtor’s A/c(c) Endorsee A/c (d) Bills Receivable A/c

11. Capital Accounts of the co-venturers are of the nature of

(a) Nominal A/c (b) Personal A/c(c) Real A/c (d) None of the above.

12. Del-credere Commission is allowed to cover

(a) All types losses (b) Abnormal loss(c) Normal loss (d) None of the above

13. Entrance fee of Rs. 50,000 received by Shyam Cricket club is a

(a) Capital Expenditure (b) Revenue Receipts(c) Capital Receipt (d) Revenue Expenditures


14. Interest on Capital is ............... for the business.

(a) Revenue (b) Expense(c) Gain (d) None of the above

15. An amount of Rs. 5,000 received from Pankaj credited to Pooja would affect

(a) Pooja’s A/c (b) Pankaj’s A/c(c) Pankaj’s A/c and Pooja’s A/c (d) Cash A/c and Pooja’s A/c

16. Accounts payable has............... balance

(a) Credit (b) Unfavourable(c) Debit (d) Favourable

17. The concept that “an accountant shouldn’t anticipate profit, but must provide for all losses”is known as

(a) The conservatism concept (b) The consistency concept(c) The materiality concept (d) The reduction concept

18. Patents Accounts are

(a) Secured Loan Account (b) Nominal Account(c) Real Account (d) Debtors Account

19. If a bill is drawn on 24 November for 60 days, it will mature on

(a) 26 January (b) 25 January(c) 24 January (d) 21 January

20. Sales Tax payable is a

(a) Current Assets (b) Personal A/c(c) Nominal A/c (d) Real A/c

21. Jai Co. purchased goods for Rs. 30,00,000 and sold 70% of such goods during the accountingyear ended 31st March, 2007. The market value of the remaining goods was Rs. 7,00,000.Company valued closing stock at Rs. 7,00,000 and not at Rs. 900000 due to

(a) Periodicity concept (b) Cost concept(c) Conservatism concept (d) None of the above

22. Tata Communication invited applications for 50,000 equity shares of Rs. 10 each and received65,000 applications along with application money of Rs. 5 per share. Which of the followingis correct

(a) Refund the excess application(b) Make pro-rate allotment to all applicants, and refund the excess application money(c) Make pro-rate allotment to all applicants and adjust the excess money received towards

call money(d) All of the above



23. Goods costing Rs. 2,00,000 sent out to consignee at cost + 25%. Invoice price of the goodswill be

(a) 2,40,000 (b) 2,30,000(c) 2,10,000 (d) 2,50,000

24. A company wishes to earn a 25% profit margin on selling price. Which of the following inthe profit mark up on cost, which will achieve the required profit margin

(a) 33.33% (b) 20%(c) 30% (d) None of these

25. Ram of Raipur sends out goods costing Rs. 1,00,000 to Amar of Alwar. 3/5th of the goods weresold by consignee for Rs. 70,000. Commission 2% on sale plus 20% of gross sale less all commissionexceeds cost price. The amount of commission will be

(a) Rs.2,900 (b) Rs.3,333(c) Rs.2,833 (d) Rs.2,800

26. On 1.7.06, Ravi draws a bill on Raju for Rs. 10,000. At maturity Raju requests Ravi to renewthe bill for 2 months at 15% p.a. interest. Amount of interest will be

(a) Rs. 200 (b) Rs. 250(c) Rs. 300 (d) Rs. 325

27. Credit purchase of cotton by cotton dealer worth Rs. 10,000 will be entered in

(a) Sales Book (b) Bill Receivable Book(c) Purchase Book (d) None of the above

28. Goods worth Rs. 5,000 given as charity should be credited to

(a) Purchases A/c (b) Sales A/c(c) Capital A/c (d) None of the above

29. Anurag and Basu entered into a joint venture and agreed to share equal profits. Anuragpurchased goods costing 2,00,000, Basu sold 4/5th of the goods for Rs. 2,50,000. Balancegoods were taken over by Basu at cost less 20%. If same set of books is maintained, find outprofit on venture

(a) Rs.90,000 (b) Rs.85,000(c) Rs.83,000 (d) Rs.82,000

30. Brij Ltd. purchased a machine on 1.1.2004 for Rs. 2,40,000. Installation expenses were Rs.20000. Residual value after is estimated to be Rs. 5000. On 1.1.2004, expenses for repairwere increased to the extent of Rs. 5000 depreciation is provided under straight line method.Depreciation rate is 10%. Annual depreciation will be

(a) Rs.20,000 (b) Rs.26,500(c) Rs.26,000 (d) Rs.23,000


31. J, K and L are partners sharing profits and losses in the ratio of 3 : 2 : 1. They look a jointlife policy of Rs. 60000. On the death of L, what amount will be payable to each partner.

(a) J = Rs.15,000, K = Rs.30,000, L = Rs.15,000(b) J = Rs.10,000, K = Rs.20,000, L = Rs.30,000(c) J = Rs.30,000, K = Rs. 20,000, L = Rs.10,000(d) J = Rs.30,000, K = Rs.30,000

32. Sale of office furniture should be credited to

(a) Furniture A/c (b) Sales A/c(c) Cash A/c (d) Purchase A/c

33. Pankaj Ltd. issued 500 equity shares of Rs. 100 each as fully paid up in consideration ofpurchase of plant and machinery Rs. 40000. What will be the amount of discount an issue ofshares

(a) Rs. 15,000 (b) Rs. 10,000(c) Rs. 5,000 (d) Rs. 1,000

34. Omega Ltd. issued 5000 shares of Rs. 20 each. The called up value per share was Rs. 16. Thecompany forfeited 400 shares of Mr. Ajay for non-payment of 1st Call money of Rs. 4 pershare. He paid Rs. 12 for application and allotment money. On forfeiture, the share capitalA/c will be

(a) Debited by Rs. 6,400 (b) Credited by Rs. 1,600(c) Debited by Rs. 1,600 (d) None of the above

35. Sundry debtors on 31st March, 2005 are Rs. 1,05,000. Further bad debts are Rs. 5,000, salesreturn recorded in the books Rs. 10,000. Old provision for bad debts is Rs. 4,000. Provisionfor doubtful debts is to be made on debtors @ 10% and also provision of discount is to bemade on debtors @ 3%. What will be the amount of bad debts charged in Profit and Loss A/c after considering provisions for bad debts?

(a) Rs.2,700 (b) Rs. 10,000(c) Rs.12,700 (d) Rs. 6,000

36. In the bank reconciliation statement, when balance as per cash book is taken as the startingpoint, the direct deposits from customer of Rs. 10,000 in the bank will be

(a) Subtracted (b) Added(c) Ignored (d) None of the above

37. The profit of the M/s JPH, a partnership firm before charging managerial commission is Rs.84,000. The managerial commission is charged @ 5% on profit after charging suchcommission. The amount of managerial commission will be

(a) Rs. 4,200 (b) Rs 8,400(c) Rs. 4,000 (d) Rs. 8,000



38. Naveen of Nagpur sends out 1,000 boxes costing 1,00,000 to Deepak of Delhi at cost +20%consignor’s expenses were:Freight Rs. 6,000Insurance Rs. 2,000Consignee’s expenses were :Loading and Unloading charges Rs. 10,000Salesman salary Rs. 6,000 andCommission 2% on Gross sale.What will be the amount of profit if 3/4th goods sold by consignee at Rs. 1,00,000

(a) Rs. 5,500 (b) Rs. 6,500(c) Rs. 7,500 (d) Rs. 3,500

39. Manish sold goods to Kamal for Rs. 25,000. Manish will grant 2% discount to Kamal. Kamalrequested Manish to draw a bill. The amount of bill will be

(a) Rs.25,000 (b) Rs.24,750(c) Rs.24,500 (d) Rs.24,250

40. Edward Motors Ltd. a dealer in cars has the following five vehicles of different models andmakes in their stock at the end of the financial year 2005-06

Car Cost (Rs.) Market Price (Rs.)

(i) Zen 2,00,000 2,10,000

(ii) Fiat 3,50,000 3,70,000

(iii) Esteem 3,25,000 3,20,000

(iv) Honda City 6,00,000 6,30,000

(v) Optra 7,25,000 7,00,000

The value of stock included in balance sheet of the company as on 31 March, 2006 was

(a) 21,70,000 (b) 22,00,000(c) 22,30,000 (d) 22,60,000

41. Mr. Anuj sent 2000 units costing Rs. 1800 each to Mr. Mahipal. The goods were to be soldas to yield a gross profit of 20% on sales. Mr. Mahipal sold 1200 units @ 2050 per unit oncredit and 650 units @ Rs. 2300 per units on cash. Mr. Mahipal is entitled to a commissionRs. 300 per unit. The amount of commission will be

(a) Rs. 5,55,000 (b) Rs. 5,70,000(c) Rs. 5,90,000 (d) Rs. 6,10,000

42. Vimal and Vishal are partners sharing profits and losses in the ratio of 2 : 1. On 1st Jan2005, Vasu is admitted with 1/4th share in profits with guaranteed amount of Rs. 25,000.The profits for the year ended 31 Dec, 2006 amounting to Rs. 76,000. The share of Vishal inthe profits should be

(a) Rs. 19,000 (b) Rs. 17,000(c) Rs. 15,000 (d) Rs. 13,000


43. Rohit and Raja enter into a joint venture to sell cotton, sharing profit, and losses equally.Rohit provides cotton from stock Rs. 1,00,000. He pays expenses amounting Rs. 10,000.Raja incurs further expenses on carriage Rs. 10,000. He received cash on sale of cotton Rs.1,50,000. He also takes over goods to the value of Rs. 20,000. Profit on venture will be

(a) Rs. 30,000 (b) Rs. 40,000(c) Rs. 45,000 (d) Rs. 50,000

44. The profits of last three years are Rs. 58,000, Rs. 55,000 and Rs. 61,000. Capital employed isRs. 500000 and normal rate of return is 10%. The amount of goodwillcalculated on the basis of super profit method for three years of purchase will be

(a) Rs. 8,000 (b) Rs. 16,000(c) Rs. 24,000 (d) Rs. 32,000

45. “Inventories should be out of godown in the sequence in which they arrive” is based on

(a) FIFO (b) Weighted average(c) LIFO (d) None of the above

46. The following information pertains to Sethi Ltd.

(i) Equity share capital called up Rs. 10,00,000

(ii) Call in advance Rs. 90,000

(iii) Call in arrear Rs. 1,10,000

(iv) Proposed Dividend 12%

Amount of dividend for the year will be

(a) Rs. 1,17,600 (b) Rs. 96,000(c) Rs. 1,06,800 (d) Rs. 1,20,000

47. A transaction is

(a) Profit and Loss A/c and Balance Sheet(b) Language of business(c) A base for accounting(d) Business performance of trading activities

48. The weekly or monthly total of the purchase book is

(a) Posted to the debit of the purchase A/c(b) Posted to the credit of the purchase A/c(c) Posted to the credit of the bill payable A/c(d) None of the above

49. Revenue from sale of product ordinarily is reported as part of earning in the period

(a) The planning takes place (b) The sale is made(c) The product is manufactured (d) The cash is collected



50. Mr. Yogesh was the holder of 700 shares of Rs. 100 each in KFC Ltd. upon which 50 pershare had been called up but he had paid only Rs. 25 per share thereon. The companyforfeited his shares and afterwards sold them to Kamlesh, credited as Rs. 50 per share paidfor Rs. 25,000. The amount to be transfer to capital reserve is

(a) Rs. 7,500 (b) Rs. 25,000(c) Rs. 35,000 (d) Rs. 70,000

51. DBM Ltd. issued 7,000, 5% debentures of Rs. 100 each at a discount of 6%, redeemable at apremium of 5% after 5 years payable as Rs. 50 on application and Rs. 44 on allotment. Totalamount of discount/loss on issue of debenture will be

(a) Rs. 42,000 (b) Rs. 35,000(c) Rs. 77,000 (d) Rs. 1,22,000

52. From the following figures ascertain the gross profit/lossOpening stock = Rs. 60,000Cost of good sold = Rs. 2,20,000

Freight on purchase = Rs. 1,20,000Sale = Rs. 3,00,000

(a) Rs. 80,000 (b) Rs. 8,000(c) Rs. 20,000 (d) Rs. 68,000

53. Abhi draws a bill on Ravi for Rs. 1,00,000 for 3 months. At maturity, the bill returneddishonoured, noting charges Rs. 1,000. Ravi was declared insolved and only 30 paise in arupee was recovered from his estate. The amount of deficiency to be recorded on insolvencyin the books of Ravi will be

(a) Rs. 30,300 (b) Rs. 29,400(c) Rs. 35,500 (d) Rs. 70,700

54. M, N and O are partners sharing profit and losses in the ratio of 3 : 2 : 1. P joins the firm andgets 2/10th of share in the ratio of 1 : 1 from M and N calculate new ratio

(a) 24 : 14 : 5 : 6 (b) 12 : 7 : 5 : 6(c) 12 : 7 : 10 : 12 (d) 24 : 10 : 14 : 12

55. Original cost = Rs. 2,52,000 Salvage value = 12000.Depreciation for 3rd year @ 5% p.a. under W.D.V method

(a) Rs. 12,600 (b) Rs. 11,382(c) Rs. 11,372 (d) Rs. 11,970

56. Tarun Ltd. purchased building from Varun Ltd. for a book value of Rs. 400000. Theconsideration was paid by issue of 12% debentures of Rs. 100 each at a discount of 20%.The debenture account will be credited

(a) Rs. 5,00,000 (b) Rs. 4,00,000(c) Rs. 1,00,000 (d) None of the above


57. Goods sold for cash Rs. 50000, plus 10% sales Tax. Sales will be credited by

(a) Rs. 45,000 (b) Rs. 50,000(c) Rs. 55,000 (d) Rs. 60,000

58. Ram and Shyam enter into a joint venture sharing profits and losses in the ratio 3:2. Rampurchased goods casting Rs. 200000. Other expenses of Ram Rs. 10000. Shyam sold goodsfor Rs. 180000. Remaining goods were taken over by Shyam at Rs. 20000. The amount offinal remittance to be paid by Shyam to Ram will be


59. Net realisable value means :

(a) Sales less cost incurred necessarily to make the sale(b) Sales less sales return(c) Sales less cost of purchase(d) Sales less gross profit margin

60. In the absence of a partnership deed, the allowable rate of interest on partners loan accountwill be

(a) 4% (b) 7%(c) 6% (d) 12%


61. A general offer may be accepted by

(a) Any person (b) Promisee only(c) Legal representative only (d) Any of these

62. Moral pressure is involved in the case of

(a) Coercion (b) Undue - influence(c) Misrepresentation (d) Fraud

63. An unpaid seller is bound to resell the goods

(a) False(b) True(c) Unpaid seller can sue for compensation(d) Unpaid seller can force to pay the price

64. Communication of acceptance, as against the proposer, is complete.

(a) When the letter of acceptance is put into a course of transmission(b) When the letter of acceptance reaches the proposer(c) When the proposer has actually learnt the contents of the letter of acceptance(d) None of the above



65. In a unilateral contract

(a) Only one of the parties makes a promise(b) One of the parties has already performed his part of the promise(c) Both the parties have to perform their respective promises(d) Not a contract at all

66. Standing offer means

(a) Offer allowed to remain open for acceptance over a period of time(b) After made to the public is general(c) When the offeree offers to qualified acceptance of the offer(d) Offer made to a definite person

67. Performance to the contract, is provided in the Indian contract Act, 1872 in

(a) Section 35 (b) Section 36(c) Section 37 (d) Section 40

68. Offer of promise to perform must be made

(a) at the proper time (b) at the proper place(c) at the proper form (d) All of the above

69. A promisor can perform the promise

(a) Through his representatives irrespective of the competency of that representative(b) Through his representative component to perform(c) Himself(d) None of the above

70. Assignment of contract may be by

(a) Operation of law (b) The act of parties(c) (a) or (b) (d) None of the above

71. Reasonable time for a performance of a contract is a

(a) Question of fact (b) Question of prudence(c) Question of law (d) Mixed question of fact and law

72. Whether time is essence of the contract depends on the

(a) Provisions of law(b) Intention of the parties(c) Facts and circumstances of each separate case(d) All of the above

73. Contract can be discharged by agreement between parties by the way

(a) Remission (b) Waiver(c) (a) or (b) (d) (a) and (b)


74. The damage awarded by way of punishment is

(a) Vindictive damages (b) Special damages(c) Nominal damages (d) Ordinary damages

75. Anticipatory breach may be

(a) Express (b) Implied(c) (a) or (b) (d) (a) and (b) both

76. Specific performance may be ordered by the court in the following cases

(a) When the damages are an adequate remedy(b) When defaulting party is not ready to pay damages(c) When damages are not an adequate remedy(d) When the contract is voidable

77. A finder of lost goods can be treated as

(a) Thief (b) Bailor(c) Bailee (d) True owner

78. Claim for necessaries supplied to an incompetent person is provided in the Indian ContractAct, 1872, in


79. Price consideration in a contract of sale can be

(a) Only by way of money(b) Only by way of goods in return(c) Party by way of money or partly by way of goods return(d) No consideration is required at all

80. An agreement to sell is _______ contract.

(a) Executed (b) Executory(c) Implied (d) Unilateral

81. Consideration in _______ passes from both parties to each other.

(a) Sale (b) Gift(c) Transfer (d) None of these

82. In agreement to sell buyer _______ goods on insolvency of seller.

(a) Cannot claim (b) Can claim(c) Can conditionally claim (d) None of the above



83. As per section 20, where there is an unconditional contract for sale of _______ , the propertypasses to the buyer at the time when contract is made.

(a) Unascertained goods(b) Specific goods in a deliverable state(c) Specific goods to be put in a deliverable state(d) Specific goods in a non-deliverable state

84. Partnership is created by _______ among the partners.

(a) Mutual status (b) Agreement(c) Understanding (d) Birth

85. Every partner has the right to _______.

(a) Take part in the business of the firm(b) To share exclusive profits(c) To use the property of the firm for personal purposes(d) Pay taxes

86. Section _______ of the partnership Act, 1932 deals with ‘’Particular Partnership’’.

(a) 6 (b) 7(c) 8 (d) 9

87. The partner who does not take part in the conduct of the business is known as _______.

(a) Sub partner (b) Nominal partner(c) Sleeping partner (d) All of the above

88. Each partner of a firm is _______.

(a) Principals as well as agents (b) Only agents of the firm(c) Only representative of the firm (d) Only Co-partners of the firm

89. A partnership firm is _______.

(a) Judicial person(b) Not a distinct legal entity from its partners(c) A distinct legal entity from its partners(d) Either (a) or (c)

90. The members of a club or associations have _______ of the club or association.

(a) Interest in the property (b) Mutual agency(c) Membership (d) Both (a) and (b)

91. In all the joint Hindu family firms, their _______ are personally liable to third parties.

(a) Kartas and major members (b) Kartas only(c) All major members (d) All the members


92. Where seller resells the goods after giving notice to the buyer, the _______ shall not beentitled to any profit which may occur on resale.

(a) Buyer (b) Seller(c) Bailee (d) Buyer and seller

93. Goods which are in the existence at the time of the contract of sale is knownas ________.

(a) Present goods (b) Specific goods(c) Ascertained goods (d) Existing goods

94. A _________ is a stipulation collateral to the main purpose of the contract. The breach ofwhich gives rise to a claim for damages but not a right to reject the goods and treat thecontract repudiate.

(a) Warranty (b) Condition(c) Implied condition (d) None of the above

95. In a contract of sale of goods, breach of condition may be treated as breach of _______.

(a) Guarantee (b) Term(c) Warranty (d) Promise

96. ___________ signifies that the parties are not further bound under the contract.

(a) Discharge of a contract (b) Breach of a contract(c) Waiver of a contract (d) Recission of a contract

97. When a contract expressly provides for the order of performance of reciprocal promises,the promises shall be performed in ___________.

(a) Any reasonable order(b) Any appropriate order(c) Any order(d) The order mentioned and not otherwise

98. Section __________ of the Indian Contract Act mentions three exceptions when an agreement,even though without consideration, is enforceable.

(a) 25 (b) 26(c) 28 (d) 30

99. ‘A’ is a minor, who broke his right leg in a cricket match. He engaged, a doctor, to set it. Doesthe doctor have a valid claim for his services? Decide.

(a) Minor will be personally liable.(b) Minor’s parents will be liable.(c) Minor’s properties, if any, can be held liable for necessary services rendered to a minor .(d) Nobody will be liable.



100. ‘A’ lends a horse to ‘B’ for his own riding only ‘B’ and ‘C’, his wife, to ride the horse, ‘C’,rides with care, but the horse accidentally falls and is injured. Decide the liability.

(a) A will not be liable. (b) A’s wife will be liable.(c) A is liable to make compensation. (d) Nobody will be liable.


101. In Economics, the central economic problem means:

(a) Output is restricted to the limited availability of resources(b) Consumers do not have as much money as they would wish(c) There will always be certain level of unemployment(d) Resources are not always allocated in an optimum way

102. The other names of ———— method are abstract, analytical and priori method.

(a) Inductive method (b) Economic method(c) Deductive method (d) Name of the above

103. All points on PPC show that goods and services are produced at:

(a) Least cost and some resources are wasted(b) High cost and no resources are wasted(c) Least cost and no resources are wasted(d) Moderate cost and no resources are wasted

104. Which of the following is a cause of an economic problem

(a) Scarcity of Resources (b) Unlimited wants(c) Alternative uses (d) All of the above

105. Calculate income elasticity for the household when the income of a household rises by 10 %,the demand for Rice rises by 5%.

(a) - .5 (b) + .5(c) - 2 (d) + 2

106. When two goods are perfect substitutes of each other then

(a) MRS is falling (b) MRS is rising(c) MRS is constant (d) None of the above

107. The Law of Scarcity

(a) Does not apply to rich, developed countries(b) Does not apply to poor, under developed countries(c) Implies only to socialist economies.(d) Implies that all consumer wants will never be completely satisfied.


108. Scarcity definition of economics is given by

(a) Alfred Marshall (b) J B Say(c) Allen and Hicks (d) Robbins

109. In case of a Giffin good, the demand curve will be:

(a) Horizontal (b) Downward- sloping to the right(c) Vertical (d) Upward – sloping

110. Which of the following statements is incorrect?

(a) The services of doctors, lawyers, teachers etc are termed as production(b) Man cannot create matter(c) Accumulation of capital does not depend solely on income(d) None of the above

111. Which is the other name given to Average revenue curve?

(a) Profit curve (b) Demand curve(c) Indifference curve (d) Income curve

112. Which of the following is not the function of RBI?

(a) Issue of currency (b) Bankers’ bank(c) Controller of credit (d) Banker to general public

113. The IMF was set up in:

(a) 1945 (b) 1946(c) 1947 (d) 1950

114. M1 is defined by RBI (as per latest definition) as

(a) Currency + Deposits + other deposits with RBI(b) Currency + Demand Deposits + other deposits with RBI(c) Currency + Fixed Deposits + other deposits with RBI(d) Currency + Time Deposits + other deposits with RBI

115. Nationalised Banks include:

(a) SBI (b) Citibank(c) American Express Bank (d) All of the above

116. Two Nationalized banks were merged in the year:

(a) 1991 (b) 1975(c) 1980 (d) 1993

117. Out of 5.6 lakh villages in India, only _______villages are being served by commercial banks:

(a) 56,000 (b) 10,000(c) 5,000 (d) 50,000



118. 100 percent privatization has taken place in:

(a) VSNL (b) Hindustan Zinc(c) IBP Company (d) Centaur Hotel

119. The disinvestment programme was started in:

(a) 1990-91 (b) 1991-92(c) 1995-96 (d) 1997-98

120. TRIPs stand for:

(a) Trade Related Intellectual Property Rights(b) Transaction Related Intellectual Property Rights(c) Trade Related Intelligence Property Rights(d) Trade Related International Property Rights

121. 100% FDI is Permitted is:

(a) Oil Refineries (b) Banking(c) Insurance (d) Defense

122. Duty Free Export Credit Scheme has been revamped and re-cast into:

(a) Made in India model (b) Served from India Scheme(c) India’s Shining Scheme (d) EPCG Scheme

123. Export Promotion Capital Goods scheme was abolished in:

(a) 1991 (b) 2002(c) 2005 (d) False, it is still continuing

124. Financial sector reforms mainly relate to:

(a) Banking sector reforms (b) Capital reforms(c) Insurance sector reforms (d) All of the above

125. FDI has been allowed in defense upto:

(a) 74% (b) 49%(c) 26% (d) 100%

126. Administered prices means

(a) Prices fixed by private sector under the guidance of government(b) Prices fixed by consumer forums(c) Prices fixed by the Government and private sector(d) Price level fixed by the Government


127. Price support policy means:

(a) Prices at which government would be buying agricultural products from farmers(b) Prices at which farmers will be selling goods to the private sector(c) Subsidy received by farmers from government(d) None of the above

128. Stagflation:

(a) means prices are falling and purchasing power is increasing(b) is in the form of a low rate of growth combined with the general price level increase(c) means high rate of growth combined with rise in the general price level(d) means that due to increase in the cost of products, prices of final products are increasing

129. NPE stands far

(a) National Policy on Education (b) Nuclear Policy on Electronics(c) National Policy on Electronics (d) National Policy on Elections

130. Sarva Shiksha Abhiyan was launched in the year

(a) 2000-01 (b) 2001-02(c) 2002-03 (d) 2004-05

131. Secondary education prepares students in the age group of:

(a) 14-16 years (b) 14-18 years(c) 12-18 years (d) None of the above

132. National Literacy mission was launched for:

(a) Primary education (b) Secondary education(c) Adult education (d) All of the above

133. Postal system was started in India in the year:

(a) 1837 (b) 1847(c) 1857 (d) 1867

134. Which is not the problem faced by Indian ports?

(a) Inadequate dredging and container handling facilities(b) Inefficient and non optimal deployment of port equipment(c) Proper coordination in the entire chain(d) Operational constraints such as frequent break down of cargo handling equipment due to

obsolescence

135. GRT stands for

(a) Gross Registered Tonnage (b) Gross Regular Tonnage(c) Gross Regulated Tonne (d) Gross Registered Tollage



136. Pawan Hans Helicopters Ltd provides helicopter support services to:

(a) Petroleum sector(b) State and Union Territory government(c) Public sector undertaking(d) All of the above

137. India has a long coastline of:

(a) 7517 Km, 12 major ports and 187 minor ports(b) 7518 Km, 12 major ports and 87 minor ports(c) 7517 Km, 11 major ports and 187 minor ports(d) 7577 Km, 12 major ports and 187 minor ports

138. For the prices- taking firm:

(a) Marginal revenue is less than price(b) Marginal revenue is equal to price(c) Marginal revenue is greater than price(d) The relationship between marginal revenue and price is indeterminate

139. A monopolist is able to maximize his profits when:

(a) His output is maximum(b) He charges high price(c) His average cost is minimum(d) His marginal cost is equal to marginal revenue

140. In Imperfect competition:

(a) Excess capacity always exists(b) Excess capacity never exists(c) Excess capacity may or may not exist(d) None of the above

141. In long run, in perfectly competitive market there will be:

(a) Normal profit (b) Super normal profits(c) Losses (d) None of the above

142. In perfect competition utilization of resources is

(a) Partial (b) Moderate(c) Full (d) Over

143. Which of the following statements is false?

(a) For equilibrium the main condition is MC=MR(b) AR curve and Demand curve are same(c) MC and AC curves are U-shaped in every market(d) None of the above


144. Product differentiation is the most important feature of:

(a) Monopolistic Competition (b) Monopoly(c) Oligopoly (d) Perfect Completition

145. MC=MR and MC cuts MR from below is a true equilibrium condition in:

(a) Short run (b) Long run(c) Both in short run and long run (d) None of the above

146. Price discrimination occurs when:

(a) Producer sells a specific commodity or service to different buyers for the same price(b) Producer sells specific commodity or service to different buyers at two or more different

prices due to differences in cost(c) Producer sells a specific commodity or service to different buyers at two or more different

prices for reasons not associated with difference in cost(d) Producer under perfect competition sells different goods to consumers at different prices

147. MR curve under Monopoly lies between AR and Y-axis because, the rate of decline of theMR is

(a) Just half of the rate of decline of A.R.(b) Just equal to the rate of decline of A.R.(c) Just triple the rate of decline of the average revenue(d) Just double the rate of decline of the average revenue

148. Relationship between AR, MR and Price elasticity of demand is

(a) MR = AR + E 1

E

−⎡ ⎤⎢ ⎥⎣ ⎦

(b) MR = AR x E 1

E

−⎡ ⎤⎢ ⎥⎣ ⎦

(c) AR = MR x E

E 1⎡ ⎤⎢ ⎥−⎣ ⎦

(d) MR = AR x E

E 1⎡ ⎤⎢ ⎥−⎣ ⎦

149. In a perfectly competitive firm, MC curve above AVC is the_____Curve of the firm

(a) average cost (b) marginal revenue(c) demand (d) supply

150. In the long run, normal profits are included in the ______ curve.

(a) LAC (b) LMC(c) AFC (d) SAC




151. If (P+1)th term of A.P. is twice the (q+1)th term; then the ratio of (P+q+1)th term and(3P+1)th term is:


152. If the common difference of an A.P. equals to the first term, then the ratio of its mth termand nth term is:

(a) n:m (b) m:n(c) m2:m2 (d) None of these

153. If the mth term of A.P. is 1

n and the nth term is

1

m, then its mnth term is:

(a) 1 (b) –1(c) 0 (d) None of these

154. Sum the series upto n terms 1 1 1

+ + + ............2.5 5.8 8.11

(a)n

2(3n 2)+ (b)n

2(3n 2)

−+

(c)n

2(3n 2)− (d) None of these

155. Which term of the series 0.004 + 0.02 + 0.1 + ……………… is 12.5


157. Find the compound interest on Rs. 2,000 at 5% per annum, compounded yearly for 2½years.

(a) Rs. 250 (b) Rs. 250.50(c) Rs. 260.12 (d) None of these

158. At what rate percent s upto n terms 1 1 1

+ + + ............2.5 5.8 8.11

(a)n

2(3n 2)+ (b)n

2(3n 2)

−+

(c)n

2(3n 2)− (d) None of these


159. If the compound interest on a certain sum for 2 years at 3% be Rs. 101.50, what would bethe S.I.?

(a) Rs. 100 (b) Rs. 200(c) Rs. 300 (d) None of these

160. The difference between the compound interest and the Simple Interest on a certain sum ofmoney at 5% per annum for 2 years is Rs. 1.50. Find the sum.


161. A batsman in his 17th innings makes a score of 85 and thereby increases his average by 3.What is his average after 17th innings?


162. A person travels from A to B at the rate of 20 km/h and from B to A at the rate of 30 km/hr.What is the average rate for whole journey?

(a) 20 km./hr. (b) 24 km./hr.(c) 30 km./hr. (d) None of these

163. A person divides his journey into three equal parts and decides to travel on three parts atthe speeds of 40, 30 and 15 km/hr respectively. Find his average speed during the wholejourney.

(a) 30 km./hr. (b) 24 km./hr.(c) 35 km./hr. (d) None of these

164. A person covers 12 km at 3 km/hr, 18 km at 9 km/hr and 24 km at 4 km/hr. Find the averagespeed in covering the whole distance.

(a) 4.5 km./hr. (b) 5 km./hr.(c) 10 km./hr. (d) None of these

165. A person runs the first 15

th of the distance at 2 km/hr, the next one half at 3 km/hr and the

remaining distance at 1 km/hr. Find his average speed.

(a)15

17km./hr. (b)

30

17km./hr.

(c)17

30km./hr. (d) None of these



166. The mean of 100 observations is 50. If one of the observations which was 50 is replaced by40, the resulting mean will be

(a) 40 (b) 49.90(c) 50 (d) None of these

167. The combined mean of three groups is 12 and the combined mean of first two groups is 3. Ifthe first, second and third groups have 2, 3 and 5 items respectively, then the mean of thirdgroup is

(a) 10 (b) 21(c) 12 (d) 13

168. Mode is

(a) Least frequent value (b) Middle most value(c) Most frequent value (d) None of these

169. If the arithmetic mean of two numbers is 10 and their geometric mean is 8, the numbers are

(a) 20,5 (b) 16,4(c) 15,5 (d) 12,8

170. A frequency distribution can be presented graphically by a

(a) Pie diagram (b) Histogram(c) Pictogram (d) Line diagram.

171. In co - variance method the sum of difference of rank is

(a) 1 (b) –1(c) 0 (d) Cannot say

172. The relation between the production of Pig iron and Soot content in a factory is

(a) Positive (b) Negative(c) 0 (d) None of these

173. If the relation between two random variables x and y is 2x + 3y = 4, then the correlationcoefficient between them is

(a) –2/3 (b) 1(c) –1 (d) None of these

174. For a two way frequency table having (m×n) classification the total number of cells is

(a) m (b) n(c) m + n (d) mn


175. For a m×n two way or bivariate frequency table, the maximum number of marginaldistributions is

(a) 1 (b) 2(c) m+n (d) m.n

176. The correlation coefficient r is the ………….. of the two regression coefficients.

(a) G.M. (b) H.M.(c) Arithmetic Mean (d) None of these

177. Each and every index number is independent of Unit of measurement.

(a) True (b) False(c) Both (a) & (b) (d) None of these

178. For factor reversal test: ∑× =∑

1 101 01

0 0

P QP Q

P Q = True Value Ratio (T.V.R.) This is

(a) False (b) True(c) Both (a) & (b) (d) None of these

179. Factor Reversal test is satisfied by

(a) Fisher’s Ideal Index Number (b) Laspeyre’s Index Number(c) Paasche’s Index Number (d) All of the above

180. During a certain period, the cost of living index number goes up from 110 to 200 and thesalary of the worker is also raised from Rs. 3,250 to Rs. 5,000. Does the worker really gain?

(a) No (b) Yes(c) Cannot determine (d) None of these

181. Ticket numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is theprobability that the ticket drawn bears a number which is multiple of 3 or 7?

(a)1

5(b)

2

5

(c)3

5(d) None of these

182. A card is drawn from a pack of playing cards at random. What is the probability that thecard drawn is neither a king nor a heart?

(a)4

13(b)

9

13

(c)2

13(d) None of these



183. A bag contains 3 red, 5 yellow and 4 green balls. 3 balls are drawn at random. Find thechance that balls drawn contain exactly two green balls.

(a)12

55(b)

10

55

(c)13

55(d) None of these

184. A husband and a wife appear in an interview for two vacancies in the same post. Theprobability of husband’s selection is 3/5 and that of wife’s selection is 1/5. Then the probabilitythat only one of them is selected is

(a)16

25(b)

17

25

(c)14

25(d) None of these

185. A bag contain 4 white balls and 2 black balls. Another contains 3 white and 5 black balls. Ifone ball is drawn from each bag. Then the probability that one is white and one is black is

(a)11

24(b)

13

24

(c)15

25(d) None of these

186. Poison distribution is a biparametric distribution. This is

(a) True (b) False(c) Either (a) or (b) (d) None of these

187. Binomial distribution is a biparametric distribution. This is


188. If x and y are two independent variance follow poison distribution in the parametersm1 & m2 respectively. If z = x + y and also follows the poison distribution then theparameter of Z is

(a) m1 – m

2(b) m

1. m

2

(c) m1+ m

2(d) None of these


189. If x and y are two independent variables such that x ~ B (n1, P) and y ~ B (n2, p) then theparameter of Z = x + y is

(a) (n1+n

2), P (b) (n

1–n

2), P

(c) (n1+n

2), 2P (d) None of these

190. The Binomial or poison distribution could be uni–modal or bi–modal. This is

(a) False (b) True(c) Either (a) or (b) (d) None of these

191. If x be a normal variate with mean 3 and variances 16, find the value of t such that:P (3 < x <t) = 0.4772 (Given: P(Z < 2) = 0.9772, where Z is N (0, 1) variate)


192. A bag contains 5 red and 4 blackballs. A ball is drawn at random from the bag and put intoanother bag contains 3 red and 7 black balls. A ball is drawn randomly from the second bag.What is probability that it is red,

(a)32

99(b)

1

3

(c)74

99(d) None of these

193. A committee of 4 persons is to be appointed from 3 officers of the production department, 4officers of the purchase department, two officers of the sales department and 1 CharteredAccountant. Find the chance there must be one from each category.

(a)4

35(b)

3

35

(c)1

7(d) None of these

194. A committee of 4 persons is to be appointed from 3 officers of the production department, 4officers of the purchase department, two officers of the sales department and 1 CharteredAccountant. Find the chance that it should have at least one from the purchase department.

(a)4

35(b)

39

42

(c)42




195. A committee of 4 persons is to be appointed from 3 officers of the production department, 4officers of the purchase department, two officers of the sales department and 1 CharteredAccountant. Find the chance that the Chartered Accountant must be in the committee.

(a)4

35(b)

39

42

(c)42


196. Six boys and five girls are to be seated in a row such that no two girls and no two boys sittogether. Find the number of ways in which this can be done.

(a) 86,400 (b) 85,000(c) 85,400 (d) None of these

197. A six faced die is so biased that it is twice as likely to show an even number as an odd numberwhen it is thrown. What is the probability that the sum of the two numbers is even.

(a)4

9(b)

5

9

(c)3

8(d) None of these

198. A and B select a digit at random from 0, 1, 2, 3, ………….. 9 independently. Find the chancethat the product of the two digits chosen is Zero.

(a)1

5(b)

2

5

(c)4

5(d) None of these

199. In the sequence (xn) where ( )!

+= −+

33

n

n P195x

4n! n 1 & nEN, the set of natural numbers. The

number of positive terms is

(a) 1 (b) 2(c) 4 (d) 5

200. If , ,1 1 1

x + y 2y y + 2 are in A.P., then x, y, z are in

(a) A.P. (b) G.P.(c) Cannot determined (d) None of these

❖❖❖

BOARD OF STUDIES



Model Test Paper – BOS/CPT – 3 / 2007



Questions 1 to 200 have only one correct answer and carry + 1mark for each correct answer and



1. ............... is recorded in purchase book.

(a) Credit purchases of goods dealt in by firm

(b) Cash purchases of goods dealt in by firm

(c) All purchases of goods dealt in by firm.

(d) None of the above.

2. When will the bill mature if the date of maturity of a bill is a holiday.

(a) Holiday itself (b) Other agreed day

(c) Preceding working day (d) Next working day

3. Under Bank reconciliation statement while adjusting the cash book

(a) All the errors and omissions in the passbook are taken into consideration

(b) Delays in recording in the passbook due to difference in timing are taken into consideration

(c) All the errors and omission in the cashbook are taken into consideration

(d) All of the above

4. Memorandum joint venture account is a

(a) Personal A/c (b) Real A/c

(c) Nominal A/c (d) None of the above




5. .................. is not required in Promissory Note

(a) Acceptance (b) Noting(c) Discounting (d) None of the above

6. Loss leads to a reduction in

(a) Capital (b) Income(c) Liabilities (d) None of the above

7. Transaction between business and owner are recorded following ________ concept

(a) Periodicity (b) Business Entity(c) Prudence (d) Going Concern

8. One of the Fundamental accounting assumption is

(a) Materiality (b) Going Concern(c) Business entity (d) Dual aspect

9. Bhagat Ltd. depreciate machinery by written down value method year after year due to

(a) Consistency (b) Comparability(c) Convenience (d) All of the above

10. Contra-entries are passed only when

(a) Double column cash book is prepared(b) Three-column cash book is prepaid(c) Simple cash book is prepared(d) None of the above

11. Petty cash balance is

(a) Liability (b) Income(c) Expense (d) An asset

12. Dividends are usually paid as a percentage of

(a) Net profit (b) Authorised share capital(c) Called-up capital (d) Paid-up capital

13. A proforma invoice is sent by

(a) Consignee to consignor (b) Consignee to Debtors(c) Debtors to consignee (d) Consignor to consignee

14. A ............... is sent to a customer when he return the goods

(a) Cheque (b) Proforma invoice(c) Credit note (d) Debit note


15. Commission to promote credit sale by consignee is known as

(a) Del-credere commission (b) Over riding commission(c) Ordinary commission (d) Special commission

16. Generally, when the size of the venture is............... the co-venture keep separate sets of accountfor joint venture transactions

(a) Big (b) Medium(c) Small (d) None of the above

17. The Petty cashier generally works on............... system

(a) Imprest (b) Balancing(c) Accrual (d) None of the above

18. The amount due to the retiring partner on account of goodwill is debited to the continuingpartners in their........

(a) Gaining ratio (b) Capital ratio(c) Sacrificing ratio (d) None of the above

19. When money is withdrawn from the bank, the bank............... the account of the customer

(a) Debit (b) Credit(c) Either (a) or (b) (d) None of the above

20. The Cash discount allowed to a debtor should be credited to

(a) Sales account (b) Discount account(c) Customer’s/Debtors account (d) None of the above

21. Closing capitals of Amit, Sumit and Vineet were Rs. 50,000, Rs. 45,000 and Rs. 30,000respectively. Their drawings during the year were Rs. 10,000, Rs. 5,000 and Rs. 12,000respectively. Amount of net profit earned during the year was Rs. 18000 which was distributedin the ratio of 3:2:1. Opening capital of Vineet will be

(a) Rs.45,000 (b) Rs.39,000(c) Rs.56,000 (d) Rs.44,000

22. Ryan Ltd. issued 20,000, 8% debentures of Rs. 10 each at par, which are redeemable after 5years at premium of 20%. The amount of loss on redemption of debenture to be written offevery year will be

(a) Rs.8,000 (b) Rs.40,000(c) Rs.20,000 (d) Rs.10,000



23. Ram and Shyam are partners sharing profits and losses in the ratio 5:3. On admissionMohan brings Rs. 70,000 cash as capital and Rs. 48,000 against goodwill. New profit sharingratio between Ram, Shyam and Mohan are 7:5:4. The sacrificing ratio between Ram andShyam will be

(a) 2:1 (b) 5:4(c) 3:1 (d) 4:2

24. Nikhil of Delhi sent out goods costing Rs. 45,000 to Shyam of Kolkata at cost +33 1/3%. 1/10th of goods were lost in transit and 2/3rd of the goods are sold at 20% above IP. Theamount of sales value will be

(a) Rs.36,000 (b) Rs.60,000(c) Rs.54,000 (d) Rs.43,200

25. Debit balance as per cash book of Shyam enterprises as on 31.3.2006 is Rs. 1,500. Chequesdeposited but not cleared amount Rs. 100 and cheque issued but not presented of Rs. 150. Thebank allowed interest amounting Rs. 50 and collected dividend Rs. 50 on behalf of ABCenterprises. Balance as per pass book should be

(a) Rs.1,650 (b) Rs.1,600(c) Rs.1,850 (d) Rs.1,450

26. A business purchased goods for Rs. 10,00,000 and sold 60% of such goods during the financialyear ended 31st March 2005. The market value of the remaining goods was Rs. 3,00,000.They valued the closing stock at cost. He violated the concept of

(a) Periodicity (b) Cost(c) Conservatism (d) Money Measurement

27. A Company forfeited 2,000 shares of Rs. 10 each (which were issued at par) held byMr. John for non-payment of allotment money of Rs. 4 per share. The called-up value pershare was Rs. 9. On forfeiture the amount debited to share capital Account will be

(a) Rs.18,000 (b) Rs.8,000(c) Rs.10,000 (d) Rs.2,000

28. Ram and Rahim are partners in a firm sharing profits and losses in the ratio 5:3. The firm’sprofit or loss of last four years amounting Rs. 18,000, Rs. 8,500 (loss), Rs. 30,000 and Rs.16,500 respectively. The value of goodwill on the basis of one and a half year’s purchase ofaverage profits of last four years will be

(a) Rs.14,000 (b) Rs.6,000(c) Rs.17,000 (d) Rs.21,000


29. A cheque of Rs. 1,000 received from Ratnesh was dishonoured and had been posted to thedebit of sales return account. The rectifying journal entry will be.

Rs. Rs.(a) Sales return A/c Dr 1,000

To Ratnesh 1,000(b) Ratnesh A/c Dr 1,000

To Sales return A/c 1,000(c) Ratnesh Dr 1,000

Sales return Dr 1,000To Suspense A/c 2,000


30. If sales revenue are Rs. 3,00,000; cost of goods sold is 2,00,000 and operating expenses areRs. 50,000 the gross profit is

(a) Rs.50,000 (b) Rs.1,00,000(c) Rs.1,50,000 (d) Rs.2,50,000

31. Rs. 5,000 spent on the overhauling of machines purchased second hand is

(a) Deferred revenue expenditure (b) Capital expenditure(c) Revenue expenditure (d) None of the above

32. Our acceptance to Mr. Ram for Rs. 8,000 renewed for 3 months on the condition thatRs. 2000 is paid in cash immediately and the remaining balance to carry out interest at 18%.p.a. The amount of the renewed bill of exchange will be

(a) Rs.6,270 (b) Rs.8,000(c) Rs.6,370 (d) Rs.6,000

33. Shyam bought a Guitar of Rs. 1870 by cheque. It has been wrongly posted in the cashbookas Rs. 1,780. This has the effect of

(a) Decreasing the bank balance by Rs. 180 in the cash book(b) Increasing the bank balance by Rs. 180 in the cash book(c) Increasing the bank balance by Rs. 90 in the cash book(d) Decreasing the bank balance by Rs. 90 in the cash book

34. Mohan, Sohan and Rohan share profits and loss in the ratio of 4:4:2. They have a Joint LifeInsurance Policy of Rs. 1,00,000 whose premium is paid by the firm. Surrender value of thepolicy at the beginning of the year 2007 is 80,000. On the death of Mohan on 2nd Jan 2007the amount to be credited in Rohan’s account will be

(a) Rs.40,000 (b) Rs.16,000(c) Rs.30,000 (d) Rs.20,000



35. Books of Ram shows on 1st January 2006 furniture Rs. 20,000. During the year a part of thefurniture whose book value on 1st January 2006 is Rs. 1,200 has been exchanged with anotherfurniture by paying additional Rs. 500. Ram charge depreciation @ 10% p.a. The net amountof the furniture to be shown in the balance sheet will be

(a) Rs. 18,478 (b) Rs. 18,600(c) Rs. 18,504 (d) Rs. 18,784

36. X, Y and Z takes a joint life policy their profit sharing ratio is 2:2:1. On death of B, A and Cdecides to share profits equally. They had taken a Joint life policy of Rs. 2,50,000 with thesurrender value Rs. 50,000. What will be the treatment in the partner’s capital account onreceiving the JLP amount if joint life policy is maintained at surrender value along with thereserve?

(a) Rs. 2,50,000 created to all the partners in old ratio(b) Rs. 2,00,000 credited to all the partner in old ratio(c) Distribute JLP reserve account in old profit sharing ratio(d) Both ‘b’ and ‘c’

37. Mohit Ltd. had 9,000, 10% redeemable preference shares of Rs. 10 each, fully paid up. Thecompany decided to redeem these preference shares at par by the issue of sufficient numberof equity shares of Rs. 10 each fully paid up at a discount of 10%. The number of equityshare issued should be

(a) 11,000 (b) 9,000(c) 7,000 (d) 10,000

38. Goods costing Rs. 2,00,000 were sent on consignment basis. These goods are invoiced togive a gross margin of 20% on invoice price. The amount of loading is :

(a) Rs.50,000 (b) Rs.40,000(c) Rs.60,000 (d) Rs.55,000

39. A lease is purchased on 1st January 2005 for 4 years at a cost of Rs. 1,00,000. Lease is to bedepreciated by the annuity method charging 5% interest. Annuity of Re. 1 over 4 yearscharging 5% interest is Re. 0.282012. The amount of annual depreciation will be

(a) Rs.26,405 (b) Rs.27,612(c) Rs.28,201 (d) Rs.28,000

40. Ashok Ltd. purchased land and building from Vivek Ltd. for a book value of Rs. 2,00,000.The consideration was paid by issue of 12% debentures of Rs. 100 each at a discount of20%. The debenture account is credited with

(a) Rs.2,50,000 (b) Rs.2,40,000(c) Rs.2,70,000 (d) Rs.1,90,000


41. Debit balance as per cash book of ABC enterprises as on 31.3.2006 is Rs. 15,000. Chequedeposited but not cleared amount to Rs. 1000 and cheque issued but not presented of Rs.2,000. Balance as per pass book should be

(a) Rs.15,000 (b) Rs.16,000(c) Rs.14,000 (d) Rs.17,000

42. Goods purchased Rs. 2,00,000. Sales Rs. 1,10,000. Margin 25% on sales. Closing stock is

(a) Rs.90,000 (b) Rs.75,000(c) Rs.1,17,500 (d) Rs.1,50,000

43. Sohan runs a department store. He renovates his shop to increase its space. The amount ofRs. 75,000 was incurred on renovation. The amount to be charged to Profit and Loss A/c is

(a) Rs. 75,000 (b) Rs. 10,000(c) NIL (d) None of the above

44. X of Kolkata sends out goods costing Rs. 3,00,000 to Y of Delhi. Commission agreed is 2%on sales + 3% on sales as del-credre commission. The entire goods is sold by consignee forRs. 4,00,000. However consignee is able to recover Rs. 3,95,000 from the debtors. The amountof profit to be transferred to P/L as net commission by consignee will be

(a) Rs.16,000 (b) Rs.15,500(c) Rs.15,000 (d) Rs.17,000

45. Alok and Rohit were partners in a joint venture sharing profits and losses in the proportionof 3/5th and 2/5th respectively. Alok supplies goods to the value of Rs. 60,000 and incursexpenses amount Rs. 6,000. Rohit supplies goods to the value of Rs. 16,000 and his expensesamount to Rs. 3,000. Rohit sells goods on behalf of the joint venture and realises Rs. 1,20,000.Rohit is entitled to a commission of 5% on sales. Rohit settles his account by bank draft.How much amount Rohit will pay to Alok as final settlement.

(a) Rs.93,600 (b) Rs.82,000(c) Rs.83,400 (d) Rs.40,000

46. Ram, Mohan and Sohan are partners in a firm sharing profits and losses in the ratio of5:3:2. The firm took separate life policy of Rs. 50,000, Rs. 1,00,000 and Rs. 1,50,000 forRam, Mohan and Sohan respectively. The share of Mohan in the policy will be

(a) Rs.45,000 (b) Rs.90,000(c) Rs.80,000 (d) Rs.70,000

47. Rs. 7,000 paid as rent to Sohan, the landlord was debited to Sohan’s personal account. Theerror will

(a) Not affect the trial balance(b) Affect the suspense account(c) Affect the trial balance(d) None of the above



48. Which one of these is not a cause of difference in balance as per pass book and as per cashbook

(a) Errors in cash book(b) Errors in pass book(c) Cheques deposited and cleared(d) Cheques issued but not presented for payment.

49. If average stock = Rs. 20,000. Closing stock is Rs. 4,000 were than opening stock then thevalue of closing stock will be

(a) Rs.16,000 (b) Rs.18,000(c) Rs.20,000 (d) Rs.22,000

50. If sales is Rs. 10,000 and the rate of gross profit on cost of goods sold is 25%, then the cost ofgoods sold will be

(a) Rs. 2,000 (b) Rs. 8,000(c) Rs. 2,500 (d) Rs. 10,000

51. Rajesh of Ramnagar sends out goods costing Rs. 2,00,000 to Gopal of Gujarat.3/5th of the goods were sold by consignee for Rs. 1,50,000. Commission 2% on sales plus10% of gross sales less all commission exceeds cost price. The amount of commission will be

(a) Rs. 4,545.45 (b) Rs. 5,454.54(c) Rs. 6,363.63 (d) Rs. 7,272.72

52. Ankit, Anu and Anurag are partners sharing profits in the ratio 4:3:2. On retirement ofAnu, goodwill was valued Rs. 90,000. The contribution of Ankit and Anurag to compensateAnu will be

(a) Rs. 20,000 and Rs. 10,000(b) Rs. 10,000 and Rs. 20,000(c) Rs. 8,700 and Rs. 97,000(d) Rs. 10,800 and Rs. 18,200

53. Jai Ltd. purchased machinery from Om Ltd. for Rs. 8,00,000. The consideration was paidby issue of 15% debentures by Rs. 100 each at a discount of 20%. Number of debenturesissued by Jai Ltd. will be

(a) 8,000 (b) 10,000(c) 12,000 (d) 15,000

54. Ankur purchased a computer costing Rs. 24000. Repairing expenses Rs.1,500 & other charges(loading & unloading) Rs. 1500 were incurred by him. He sold the computer at 25% marginon selling price. The profit on sale will be

(a) Rs. 8,500 (b) Rs. 9,000(c) Rs. 10,000 (d) Rs. 11,500


55. Mr. Rakesh Roshan is a partner in a firm. He withdraws Rs. 500 at the beginning of eachmonth. If the rate of interest is @ 5%, then interest on drawings is

(a) Rs. 55.50 (b) Rs. 157.50(c) Rs. 160.50 (d) Rs. 162.50

56. Mr. Bajaj who was the holder of 200 Equity shares of Rs. 100 each of Canny Ltd., on whichonly Rs. 75 per share has been called up, couldn’t pay his dues on allotment and first classeach at Rs. 25 per share. The director forfeited the above shares and reissued 150 of suchshares to Mr. Birla at Rs. 65 per share paid up as Rs. 75 per share. The amount to betransferred to capital reserve account will be

(a) Rs. 1,500 (b) Rs. 2,250(c) Rs. 2,750 (d) Rs. 3,250

57. On 1.4.07 Mr. Rahul draws a bill of one month on Mr. Sachin for Rs. 1,00,000. At maturityMr. Sachin request to accept Rs. 20,000 in cash and noting charges Rs. 1,000 and for thebalance Mr. Rahul draws a bill on Sachin for 2 months at 12% p.a. Interest will be

(a) Rs. 1,200 (b) Rs. 1,300(c) Rs. 1,400 (d) Rs. 1,600

58. Opening stock of material is Rs. 12000, purchases Rs. 30,000 carriage Rs. 5,000, Sales valueRs. 40,000, closing stock 14,000 & other indirect expenses Rs. 2,300. Amount of Gross Profitwill be

(a) Rs. 7,000 (b) Rs. 4,700(c) Rs. 6,300 (d) Rs. 5,000

59. A promissory note does not require

(a) Discounting (b) Acceptance(c) Noting (d) All of the above

60. Errors are .................. mistakes

(a) Intentional (b) Undetected(c) Unintentional (d) None of the above


61. Which Section of the Partnership Act, 1932 deals with “Minor admitted to the benefits ofpartnership”.


62. The reconstitution of the firm takes place in case of

(a) Admission of a partner (b) Retirement of a partner(c) Expulsion or death of a partner (d) All of the above.



63. Which of the following is not an essential feature of partnership?

(a) Result of an agreement(b) Organised to carry on business(c) Carried on by all any of them acting for all(d) Separate legal entity

64. Which of the following is not the right of unpaid seller?

(a) To resell(b) To stop the goods in transit(c) Of lien(d) To demand back the goods.

65. Breach of contract may be

(a) Actual breach of contract(b) Anticipatory breach of contract(c) (a) or (b)(d) (a) not (b)

66. An anticipatory breach does not give any right to claim

(a) Damages (b) Compensation(c) Either (a) or (b) (d) Both (a) and (b)

67. A contract can be discharged by operation of law in which of the following ways

(a) Death of Promisor (b) Insolvency of Promisor(c) Merger of Rights (d) All of the above

68. Acceptance is complete for the offer

(a) When it is posted(b) When the offer thinks to accept the offer(c) When it is re-posted(d) None of these

69. In a bilateral contract, obligations are outstanding

(a) An offeror (b) An offeree(c) On Both (d) On none

70. Fine may be made the essence of a contract by self sequent notice also. Statement is

(a) True (b) Partly true(c) False (d) Partly false

71. When a partner declared insolvent he ceases to be a partner from the date of its

(a) Insolvency (b) Birth(c) Appointment (d) None of the above


72. It is the duty of the finder of goods to trace the true owner of the goods, and if does not do so,he shall be guilty of

(a) Theft(b) Extortion(c) Criminal misappropriation of property(d) None of the above

73. A person who supplies “necessaries” to a minor is entitled to be reimbursed from the propertyof the minor on the basis of a

(a) Valid contract (b) Voidable contract(c) Quasi contract (d) Contingent contract

74. Which of the following constitute responsibility of finder of lost goods?

(a) He shall take reasonable steps to trace the owner(b) He shall take care of the goods(c) If the goods are in a deteriorated or wrong condition, sell them off and remit the proceeds

to the owner(d) All of the above

75. Where price of goods sold is to be fixed by a third party and the third party refuses to fix theprice, the contract becomes

(a) Void (b) Voidable(c) Illegal (d) Void and illegal

76. Where seller delivers to the buyer a quantity of goods less than the contracted to sell, thebuyer

(a) May reject them(b) Should not reject them as more quantity might be supplied(c) May resell them(d) Give less price for them

77. Section 60 of the Sale of Goods Act, 1930 applies where the contract of sale is repudiated byeither party

(a) Before the date of payment of price(b) Before the date of delivery of goods(c) (a) and (b)(d) (a) or (c)

78. Delivery of goods to the carrier would not pass the property in the goods to the buyer wherethe seller

(a) Reserves the right to disposal(b) Does not reserve the right to disposal(c) (a) or (b)(d) None of the above



79. A contract to do or to abstain from doing a certain thing on the happening of an event

(a) Cannot be enforced(b) Can be enforced when the event has happened(c) Can be enforced at any time(d) Can not be lawful

80. A person having possession of goods under voidable contract can sell the goods before_________ of the contract by the agreed party.

(a) Confirmation (b) Execution(c) Rescission (d) Ratification

81. When the seller gives physical delivery of the goods to the buyer it is called ________ delivery.

(a) Systematic (b) Actual(c) Construction (d) Symbolic

82. Section 41 of the Sale of Goods Act, deals with examination of goods by the ________.

(a) Buyer (b) Seller(c) (a) or (b) (d) (a) and (b)

83. The right of lien is lost by the unpaid seller, under the situation stated in Section _________of the Sale of Goods Act.

(a) 50 (b) 49(c) 48 (d) 47

84. If the changes taking place in a registered firm are not registered with the registrar of firms,it is _________.

(a) No more a registered firm(b) Needs to be re-registered(c) Cannot file suit against other party(d) Can not claim its statutory rights

85. The public notice is not required if partner __________.

(a) Retires (b) Expelled(c) Dies (d) Either (a) or (b)

86. Expulsion of a partner is dealt with under Section ________ of the Partnership Act, 1932.

(a) 23 (b) 32(c) 33 (d) 43

87. ____________ means a claim to any debt or any beneficial interest in movable property notin possession and which can be enforced through the court of law.

(a) Actionable claim (b) Auctionable claim(c) Default claim (d) None of the above


88. Where a buyer neglects to accept delivery of the goods, the seller may sue for ________.

(a) Payment of price(b) Damages for non acceptance(c) Damages for non acceptance and charges for care and custody of the goods(d) All of the above

89. Where in an auction sale, the seller appoints more than one bidder, the sale is_________.

(a) Void (b) Illegal(c) Conditional (d) Voidable

90. A ___________ is a right to retain the possession of goods until the payment of the price ofsuch goods.

(a) Capture (b) Lien(c) Surrender (d) Sue

91. Knock-out agreements are generally _________ in auction sale.

(a) Unlawful (b) Not unlawful(c) Void (d) Required

92. A buyer can sue for specific performance of the contract if the goods are _______.

(a) Specific (b) Future(c) Contingent (d) Perishable

93. Section 52 deals with the rights when partnership contract is rescinded for _______.

(a) Fraud (b) Misrepresentation(c) (a) or (b) (d) (a) nor (b)

94. A partner may be expelled by a _______ decision.

(a) Unanimous (b) Managing partner’s(c) Majority (d) Senior partner’s

95. The Registrar of firms is deemed to be a _______ under Section 21 of the Indian Penal Code.

(a) Government servant (b) Civil Servant(c) Public servant (d) None of the above

96. Partnership property vest in the ________.

(a) Firm (b) Partner of the firm(c) Continuing partners of the firm (d) Retiring partners of the firm

97. Which one of the following is not an implied warranty?

(a) Agreement to sell (b) Sale(c) Hire purchase (d) Installment to sell



98. Whether a given contract is one of sale or same other kind of contract in respect of goods, isa matter of _________.

(a) Terminology (b) Law(c) Agreement (d) All of the above

99. ‘A’ leaves a cow in the custody of ‘B’ to be taken care of. The cow gives birth to a calf. Decidethe liability of ‘B’.

(a) B is not bound to deliver the cow as well as to calf to A(b) ‘B’ is bound to deliver the cow as well as the calf to ‘A(c) ‘B’ is bound to deliver only the calf to A(d) ‘B’ is bound to deliver the cow only to A

100. ‘B’ agrees to buy the entire crop of wheat that would yield in ‘A’s farm, at the rate of Rs.1,000 per quintal. Decide the subject matter of goods.

(a) This is an agreement of sale of future goods(b) This is an agreement of sale of present goods(c) This is a contract of sale(d) None of the these


101. The definition “Science which deals with wealth” was given by:

(a) Alfred Marshall (b) A.C. Pigou(c) Adam Smith (d) J. B. Say

102. Questions like what should be the level of national income, what should be the wage rate fallwithin the scope of:

(a) Positive Science (b) Normative Science(c) Both (a) and (b) (d) None of the above

103. The shape of PPC is concave due to:

(a) Falling opportunity cost between two goods(b) Rising opportunity cost between two goods(c) Constant opportunity cost between two goods(d) None of the above

104. Which of the following is not one of the features of capitalist economy?

(a) Right of private property(b) Freedom of choice by the consumers(c) No profit, No Loss motive(d) Competition


105. Calculate Income-elasticity for the household when the income of a household rises by 10%the demand for T.V. rises by 20%

(a) + .5 (b) - .5(c) + 2 (d) - 2

106. In case of necessaries the marginal utilities of the earlier units are large. In such cases theconsumer surplus will be:

(a) Infinite (b) Zero(c) Marginally positive (d) Marginally Negative

107. Which is not the assumption of Indifference curve Analysis?

(a) The consumer is rational and possesses full information about all the aspects of economicenvironment

(b) The consumer is not capable of ranking all combinations(c) If consumer prefers combination A to B, and B to C, then he must prefer combination A to C(d) If combination A has more commodities than combination B, then A must be preferred to B.

108. The horizontal demand curve parallel to x-axis implies that the elasticity of demand is

(a) Zero(b) Infinite(c) Equal to one(d) Greater than zero but less than infinity

109. Which of the following is not the characteristic of Labour?

(a) Labour is highly ‘Perishable’ in the sense that a day’s labour lost cannot be completelyrecovered

(b) Labour is inseparable from the labourer himself(c) Labour has a strong bargaining power(d) The supply of labour and wage rate are directly related in the initial stages

110. Indicate which of the following is a variable cost?

(a) Payment of rent on building(b) Cost of Machinery(c) Interest payment on Loan taken from bank(d) Cost of raw material

111. Marginal costs are closely associated with:

(a) Variable cost (b) Total fixed cost(c) Average cost (d) Total cost

112. The present cash reserve ratio as in (May 2007) is:

(a) 5% (b) 5.5%(c) 6% (d) 6.5%



113. Population per Bank Office at present is:

(a) 5,000 (b) 55,000(c) 16,000 (d) 18,000

114. The Highest Deposit Mobilisation is in:

(a) Delhi (b) Gujarat(c) Maharashtra (d) Punjab

115. Total bank lending was just ——— in June, 1969

(a) 9,933 crore (b) 3,399 crore(c) 1,000 crore (d) 10,000 crore

116. ————— means integrating the domestic economy with the world economy

(a) Disinvestment (b) Liberalisation(c) Privatisation (d) Globalisation

117. In World Trade Organization, each member country has:

(a) One vote(b) Depends upon National Income of the nation(c) Depends upon UNO ranking(d) Depends upon whether the country is developed, developing or underdeveloped

118. NRIs are allowed to remit upto ——— per calendar year out of their Non - resident ordinaryaccounts / sale proceeds of assets.

(a) $ 25,000 (b) $ 25 million(c) $ 1 million (d) $ 5,000

119. India achieved full convertibility on current account in:

(a) 1994 (b) 1991(c) 2001 (d) 2005

120. Current account convertibility means freedom to buy and sell foreign exchange for thefollowing transactions except:

(a) All payment for purchase and sale of goods and services(b) Payment due as interest on loans(c) Moderate remittances for family living expenses(d) Purchase of immovable property abroad

121. Which one of the following is not a method of disinvestment?

(a) Equity offer (b) Cross holding(c) Warehousing (d) None of the above


122. Cash compensatory scheme was abolished in:

(a) 1992 (b) 1999(c) 1991 (d) False. It is still continuing

123. Export promotion capital goods scheme was liberalized in April 1992 to:

(a) To encourage Export of Capital Goods(b) To encourage Import of Capital Goods(c) Both (a) and (b)(d) None of the above

124. As per RBI recommendations Basel II framework has to be operationalised by:

(a) March, 2008 (b) March, 2009(c) March, 2007 (d) March, 2010

125. The Securitisation and Reconstruction of Financial Assets and Enforcement of SecurityInterest Act, was passed for assisting banks:

(a) In the recovery of their loans(b) To give more loans on lesser security(c) To give loans by taking more security(d) None of the above

126. Which of the following is not the problem of India’s Education System?

(a) Unplanned expansion of higher education(b) Neglect of primary education(c) Large number of unemployed uneducated people(d) Large scale migration of educated people to the developed western countries

127. VPT stands for:

(a) Village Public Telephone (b) Value Public Telephone(c) Various Public Telephone (d) Valmiki Public Telephone Yojna

128. Which of the following is not the factor for poor growth of coastal shipping?

(a) High transportation costs (b) Port delays(c) Over - aged vessel (d) Fast handling of the cargo at ports

129. Price discrimination is not possible:

(a) Under Monopoly (b) Under Monopolistic competition(c) Under perfect competition (d) Under any market form

130. Most of the unemployment in India is:

(a) Voluntary (b) Structural(c) Frictional (d) Technical



131. Which of the following has not been a part of the land reforms programme in India?

(a) Ceiling an holding (b) Consolidation of holding(c) Abolition of zamindari system (d) Agricultural holding tax

132. Disguised unemployment in India is maximum in:

(a) Agricultural Sector (b) Secondary Sector(c) Tertiary Sector (d) Both (a) and (c)

133. Which of the following is an economic activity?

(a) Seeing T.V.(b) Teaching one’s own son at home(c) Medical Facilities rendered by a charitable hospital(d) A housewife preparing food for the household

134. The cost incurred on the factor of production is known as:

(a) Accounting cost (b) Economic cost(c) Marginal cost (d) Implicit cost

135. Which of the following is considerered as economic cost?

(a) The normal return on money capital invested(b) Salary of entrepreneur(c) The interest on capital invested(d) All of the above

136. Economic cost means

(a) Accounting cost + Implicit cost (b) Accounting cost + Marginal cost(c) Cash cost + Opportunity cost (d) Implicit cost

137. When is average product at its maximum point

(a) When A.P. intersects M.P. (b) When A.P. intersects T.P.(c) When M.P. is highest (d) At the point of inflexion

138. When is TP maximum?

(a) When AP becomes Zero(b) When MP becomes Zero(c) At the interesting point of AP and MP(d) When MP is highest

139. Variable cost includes the cost of

(a) Buying land and building(b) Hire charges of machinery(c) Insurance premium(d) Material bought



(a) Marginal cost is always less than the average cost.(b) Marginal cost is always more than the average cost.(c) Marginal cost is always equal to the average cost at its minimum point.(d) Marginal cost is always equal to the average cost

141. When average cost curve is rising then, marginal cost

(a) Must be decreasing (b) Must be above the average cost curve(c) Must be constant (d) Must be equal to average cost

142. Which among the following is NOT a cause of sickness of industrial units in India?

(a) Outdated Technology (b) Labour Problems(c) Faulty Location (d) Lack of capital account convertibility

143. Which of the following is not a factor payment?

(a) Free uniform to defense personal(b) Salaries to the member of Parliament(c) Imputed rent of an owner occupied premises(d) Scholarship given to the backward class students

Use following table to answer the below mentioned questions and (144 – 145)

Hours of Total Marginal

Labour Output Output

0 -

1 350 350

2 - 230

3 670 -

144. What is the marginal output when 3rd hour of labour is employed?

(a) 90 (b) 670(c) 350 (d) 230

145. What is the total output when 2 hours of labour are employed?

(a) 500 (b) 580(c) 680 (d) 780

146. Which of the following is not the name of LAC curve?

(a) Planning curve (b) Enveloping curve(c) Round curve (d) None of the above



147. A firms average fixed cost is Rs.20 at 6 units of output. What will it be at 4 units of output:

(a) Rs. 60 (b) Rs. 30(c) Rs. 40 (d) Rs. 20

148. A firm has producing 7 units of output has an average total cost of Rs. 150 and has topay Rs. 350 to its fixed factors of production whether it produces or not. How much ofthe average total cost is made up of variable cost?

(a) 200 (b) 50(c) 300 (d) 100

149. A firm has variable cost of Rs.1,000 at 5 units of output. If fixed cost are Rs.400, what will bethe average total cost at 5 units of output?

(a) 380 (b) 280(c) 60 (d) 400

150. The vertical difference between TVC and TC is equal to:

(a) MC (b) AVC(c) TFC (d) None of the above


151. The ratio of the sum and the difference of two numbers is 7:1. Find the ratio of those twonumbers.


152. The difference between a two digit number and the number obtained by inter–changing thedigit is 54. What is the difference of the two digits of the number?


153. The numerator of a fraction is 4 less than its denominator. If the numerator is decreased by2 and the denominator is increased by 1, then the denominator is eight times the numerator.Then the fraction is

(a) 3/7 (b) 4/7(c) 9/7 (d) None of these

154. Father is six times as old as his son. Four years hence he will be four times as old as his son.Then the present ages are

(a) 42, 8 (b) 36, 6(c) 40, 10 (d) None of these


155. Find the value of 1 + 2 + 3 + …………….+ 105


156. If log3 = 0.48 and log 7 = 0.84, then the value of log 0.030.7

is

(a) – 2.26 (b) – 3.26(c) – 1.36 (d) None of these

157. Evaluate 4 0.5173


158. Evaluate 30.7214 20.37

69.8×


159. A sum of Rs. 4,000 is invested in an account that pays 6% interest compounded annually. Ifyields Rs. 5,353 after a number of years. Determine the number of years for which the sumwas inverted.


160. If log2 x + log8x + log32x =2315

then the value of x is


161. The number of ways in which n different books can be arranged in an almirah so that twoparticular books are always together is –

(a) n!×2! (b) (n–1)! × 2!(c) (n–2)! (d) None of these

162. There are 3 copies each of two books and two copies each of five books. In how many wayscan a book seller arrange the 16 books in a shelf so that the copies of the same book are neverseparated?




163. How many words can be formed with the letters of the world “PARALLEL” so that all U’sdo not come together?


164. Find the sum of four digit numbers made by the given digits 1, 3, 3, 0?

(a) 22554 (b) 22550(c) 22,000 (d) None of these

165. There are stalls for 10 animals in a ship. In how many ways can the shipload be made, ifthere cows, calves and horses to be transported, animals of each kind being not less than 10?


166. Evaluate +∫3 4x 3 5x dx

(a) ( )3/2316x 11 c

9+ + (b) ( )2/341

3 5x c9

− + +

(c) ( )3/ 2413 5x c

30+ + (d) None of these

167. Evaluate: ∫2x +1

dxx(x +1)

(a) log (x2 – x) + c (b) log (x2 + x) + c(c) log (x2 + 1) + c (d) None of these

168. Evaluate: dx

x + x∫

(a) 2 log (x + 1)+c (b) –2log ( x + 1)+c

(c) 2 log ( x + 1)+c (d) None of these

169. Evaluate ∫log x

dx3x

(a) ( )21log x c

3+ (b) ( )1

log x c3x

+

(c) ( )1log 3x x c

3x⎡ ⎤+ +⎣ ⎦ (d) None of these


170. Evaluate 2x 2e x dx×∫

(a)3 2 2x 2x

3xx x e ee c

3 2 4− + + (b)

2 2x 2x 2xx e xe ec

2 2 4− + +

(c)3 2x 2 xx e x e

c3 2


171. Evaluate: + −∫5 2

2 20

xdx

x (5 x)

(a) 0 (b) 1(c) –1 (d) None of these

172. Evaluate: →

−+

x

x 0

2 1lim

1 x – 1

(a) 2 log 2 (b) log 2(c) 0 (d) None of these

173. Evaluate: →x 0

| x – 1 |lim

x – 1

(a) –1 (b) 1(c) Does not exist (d) None of these

174. If f(x) = , ≠x– | x |x

x 0 and f(x) = 2 for x = 0 is f(x) continuous at x = 0?

(a) Yes (b) No(c) Cannot say (d) None of these

175. If y = log3 log3 x, finddydx

(a)1

x log 3.log x (b)1

x log 3.log x

−

(c)1

log 3.log x (d) None of these



176. A sum of money is put at compound interest for 2 years at 20% p.a. It would earn Rs. 482more, if the interest were payable half-yearly than it were payable yearly; then the sum is

(a) Rs. 20,000 (b) Rs. 25,000(c) Rs. 26,000 (d) None of these

177. What is the amount of an annuity if the size of the each payment is Rs. 3,000 payable at theend of each year for 3 years at an interest rate of 9% compounded annually?

(a) Rs. 9,000 (b) Rs. 9,800.50(c) Rs. 9,833.33 (d) None of these

178. Find the present value of an annuity of Rs. 1,000 payable at the end of each year for 10 years,if the money is worth 5% effective.

(a) Rs. 7,724 (b) Rs. 7000(c) Rs. 8000 (d) None of these

179. A company sets aside a sum of Rs. 45,000 annually for 9 years to pay off a debenture issue ofRs. 5,00,000. If the fund accumulates at 6% p.a., find the surplus after full redemption of thedebenture issue.


180. A company may obtain a machine either by leasing it for 5 years, (useful life) at an annualrent of Rs. 2,000 or by purchasing it for Rs, 8,100. If the company can borrow money at 10%p.a., which alternative is preferable?

(a) Leasing is preferable (b) Leasing is not preferable(c) Cannot say (d) None of these

181. The sum of deviations of the given values from their ………… is always 0.

(a) Arithmetic Mean (b) G.M.(c) H.M. (d) Median

182. The sum of squares of the deviations of the given values from their ………… is minimum.

(a) Arithmetic Mean (b) Median(c) Mode (d) None of these

183. Which is greatly affected by the extreme values?

(a) Arithmetic Mean (b) Median(c) Mode (d) None of these

184. Which is not amenable to further algebraic treatment?

(a) Arithmetic Mean (b) Median(c) Mode (d) Both (b) and (c)


185. In a frequency distribution, the mid value of a class is 15 and the class interval length is 4.The lower limit of the class is

(a) 10 (b) 12(c) 13 (d) 14

186. During a certain period, the cost of living index number goes up from 110 to 200 and thesalary of the worker is also raised from Rs. 3,250 to Rs. 5,000. Find the value of salary in realterms?


187. When the prices or quantities of all the goods are charging in the same ratio then theLaspeyre’s and Paasche’s Index Number will be

(a) Equal (b) Unequal(c) Either (a) or (b) (d) None of these

188. Between 1990 and 2000, the price of a commodity increased by 60% while the productiondecreased by 30%. By what percentage did the value index of production of commoditychange in 2000 with respect to its value 1990.

(a) 10% (b) 15%(c) 12% (d) None of these

189. The consumer price index over a certain period increased from 120 to 215 and the wages ofworker increased from Rs. 1,680 to Rs. 3000. What is the loss of the worker?


190. The consumer price index for a group of workers was 250 in 1994 with 1980 as the base.Compute the purchasing power of a rupee in 1994 Compared to 1980.


191. Three groups of children contain respectively 3 girls and 1 boys; 2 girls and 2 boys; 1 girland 3 boys. One child is selected at random from each group. Then the chance that the threeselected consist of 1 girl and 2 boys is:

(a)17

32(b)

15

32

(c)13

32(d) None of these



192. A, B, C are three mutually exclusive and exhaustive events associated with a randomexperiment. Find P(A), given that P(B) = 3/2 P(A) and P(C) = 1/2 P (B)

(a)3

13(b)

4

13

(c)5

13(d) None of these

193. A committee of four has to be formed from among 3 economists, 4 engineers, 2 statisticiansand 1 doctor. What the probability that the committee consists of the doctor and at least oneeconomist?


194. The probability that a company executive will travel by plane is 2/3 and that he will travelby train is 1/5. Find the probability of his traveling by plane or train.

(a)11

55(b)

13

15

(c)14

15(d) None of these

195. The probability that a contractor will get a plumbing contract is 2/3, and the probabilitythat he will not get an electric contract is 5/9. If the probability of getting at least one contractis 4/5. What is the probability that he will get both the contracts?

(a)14

45(b)

13

45

(c)11

45(d) None of these

196. The mean of normal distribution is 50 and 5% of the values are greater than 60; then theStandard Deviation of the distribution is: (Given the area under Standard Normal Curvebetween z = 0 & z = 1.64 is 0.45)


197. The mean monthly expenditure of a batch of students is Rs. 100 with standard deviation Rs.20. If the expenditure is normally distributed find out the maximum expenditure of those10% of the students whose expenditure is the lowest.



198. The mean monthly expenditure of a batch of students is Rs. 100 with standard deviation Rs.20. If the expenditure is normally distributed find the minimum expenditure of those 10%of the students whose expenditure is the highest.


199. Find the mean and Standard Deviation of a normal distribution, when 8% of the items are

over 64 and 31% are under 45.

0.496 1.405

0 0

Given : f(z)dz = 0.19 & f(z)dz = 0.42⎡ ⎤⎢ ⎥⎣ ⎦

∫ ∫

(a) 50,10 (b) 60,10(c) 60, 20 (d) None of these

200. Marks obtained by a number of students are assumed to be normally distributed with mean65 and variance 25. If 3 students are taken at random what is the probability that exactlytwo of them will have marks over 70?


❖❖❖

BOARD OF STUDIES








83 83Common Proficiency Test (CPT) Volume - II


1. Which error cannot be revealed on the preparation of trial balance?

(a) Wrong totaling of account

(b) Compensatory error

(c) Error of commission

(d) Wrong balancing of an account

2. A change in accounting policy is justified

(a) To comply with accounting standard

(b) To ensure more appropriate presentation of the financial statement of the enterprise

(c) To comply with law

(d) All of the above.

3. The determination of expenses for an accounting period is based on the principle of

(a) Periodicity (b) Matching

(c) Materiality (d) Objectivity

4. In the case of downward revaluation of an asset, which is for the first time revalued,

................account is debited.

(a) Fixed Asset (b) Revaluation Reserve

(c) Profit and Loss A/c (d) General Reserve



5. Parties to a bill of exchange are

(a) Drawee (b) Payee(c) Drawer (d) All of the above

6. Inventories should be generally valued at lower of cost or............

(a) Present value (b) Net Realisable Value(c) Replacement Value (d) Fair Market Value

7. The value of on asset after deducting depreciation from the historical cost is known as

(a) Fair Value (b) Market Value(c) Net Realisable Value (d) Book Value

8. Fluctuating capital account is credited with..........

(a) Profit of the year (b) Interest on capital(c) Salaries of the partner (d) All of the above

9. The amount of calls in arrear is deducted from...............to arrive at.........

(a) Paid up capital, called up capital (b) Called up capital, paid up capital(c) Issued capital, called up capital (d) Called up capital, Issued capital

10. Debit balance as per pass book means

(a) Bank overdraft as per cash book (b) Debit balance in pass book(c) Cash balance with bank (d) None of the above

11. If del-credere commission is allowed for bad debt consignee will debit the bad debt amountto :

(a) Debtors A/c (b) General Trading A/c(c) Commission Earned A/c (d) Consignee A/c

12. Accommodation bill is drawn

(a) To finance actual purchase or sale of goods(b) To facilitate trade transmission(c) To cater the fund requirements of both the parties(d) None of the above

13. Accounts receivable normally has...........balance

(a) Credit (b) Debit(c) Unfavourable (d) None of the above

14. The un-expired portion of capital expenditure is shown in the financial statement

(a) As a liability (b) As an asset(c) As an Income (d) As an expense


15. Rs. 5,000 spent on maintenance of computer is...........

(a) Deferred capital expenditure (b) Capital expenditure(c) Revenue expenditure (d) None of the above

16. The assumption underlying the fixed instalment method of depreciation is that of.........of theasset over its useful life

(a) Equal usage (b) Usage(c) Charge (d) None of the above

17. Abnormal loss on consignment is credited to........

(a) Consignment account (b) Consignee’s account(c) Profit & loss account (d) None of the above

18. .............will generally show a debit balance

(a) Bank loan (b) Bad debts recovered(c) Drawings (d) Salary payable

19. Memorandum joint venture account is a

(a) Nominal A/c (b) Real A/c(c) Personal A/c (d) None of the above

20. The portion of the acquisition cost of the asset yet to be allocated is known as........

(a) Salvage value (b) Realisable Value(c) Accumulated value (d) Written down value

21. XYZ Ltd. purchased goods for Rs. 25,00,000 and sold 80% of such goods during theaccounting year ended 31st March 2005. The Market Value of the remaining goods was Rs.4,00,000. The company valued the closing stock at cost. They violated the concept of

(a) Conservatism (b) Money Measurement(c) Periodicity (d) Cost

22. Rohan, Mohan and Sohan are partners in the firm sharing profits and losses in 5:3:2 ratio.The firm’s balance sheet as on 31.3.2006 shows the reserve balance of Rs. 25,000. Profit ofthe last year Rs. 1,00,000, joint life policy of Rs. 5,00,000, fixed asset of Rs. 50,00,000. On 1stOctober Rohan died and on the same date assets were revalued. The executor of the deceasedpartner will get........... along with the capital of Rohan

(a) Share in joint life policy(b) Share in reserve account the firm(c) Proportionate share of profit upto the date of death(d) All of the above



23. A building purchased on 1st January 2003 at Rs. 15,00,000 having useful life of 15 years wasdepreciated on straight line basis. On 1st January 2006 the same building was revaluedupward by Rs. 3 lakhs. The revised amount of depreciation for the year 2006 will

(a) Rs. 1,33,000 (b) Rs. 1,26,000(c) Rs. 1,25,000 (d) Rs. 1,30,000

24. Gopal sent out certain goods to Ramesh of Delhi. 1/10th of the goods were lost in transit.Invoice value of goods lost is Rs. 12,500. Invoice value of goods sent out on consignment will be

(a) Rs. 1,25,000 (b) Rs. 1,20,000(c) Rs. 1,40,000 (d) Rs. 1,00,000

25. Ram drew a bill on Shyam for Rs. 50,000 for 3 months proceeds of which are to be sharedequally. Ram got the bill discounted at 12% p.a. and remits proceeds to Shyam. The amountof such remittance will be

(a) Rs. 16,167 (b) Rs. 32,333(c) Rs. 24,250 (d) Rs. 25,000

26. If sales are Rs. 2,000 and the rate of gross profit on cost of goods sold is 25% than the cost ofgoods sold will be

(a) Rs. 1,600 (b) Rs. 1,700(c) Rs. 1,500 (d) Rs. 1,800

27. The profit of last three years are Rs. 42,000, Rs. 39,000 and Rs. 45,000. Find out the goodwillat two year’s purchase.

(a) Rs. 1,26,000 (b) Rs. 42,000(c) Rs. 36,000 (d) Rs. 84,000

28. If a purchase return of Rs. 1,000 has been wrongly posted to the debit of the sales returnaccount, but has been correctly entered in the suppliers account then the total of the

(a) The credit side of the trial balance will be 2000 more than the debit side(b) The debit side of the trial balance will be 2000 more than the credit side(c) Trial balance would show the credit side to be Rs. 1000 more than the debit(d) Trial balance would show the debit side to be Rs. 1000 more than the credit

29. 10000 equity shares of Rs. 10 each were issued to public at a premium of Rs. 2 per share.Applications were received for 12,000 share. Amount of securities premium account will be

(a) Rs. 40,000 (b) Rs. 20,000(c) Rs. 16,000 (d) Rs. 24,000

30. Rachna and Payal are partners sharing profits and losses equally. They admitted Ashna for1/3 share in the firm. The new profit sharing ratio will be

(a) 2:2:1 (b) 3:2:1(c) 1:2:1 (d) 1:1:1


31. Rohit purchased a machine on 1.1.2005 for Rs. 1,20,000 installation expenses were Rs. 10,000.Residual value after 5 years Rs. 5,000. On 01.02.2005 expenses for repair were incurred tothe extent of Rs. 2,000. Depreciation is provided under straight line method. Annualdepreciation is

(a) Rs. 20,000 (b) Rs. 22,000(c) Rs. 25,000 (d) Rs. 26,000

32. A firm has on average profit of Rs. 60,000; rate of return on capital employed is 12.5% p.a.;total capital employed in the firm was Rs. 4,00,000. Goodwill on the basis of two year’spurchase of super profit is


33. Ansh and Vansh entered into a joint venture where Ansh purchased goods costing Rs.2,40,000.Vansh sold goods costing Rs. 1,60,000 at Rs. 2,40,000. Balance goods were taken over byAnsh at same gross profit percentage as in case of sale. The sale value of goods taken overwill be

(a) Rs. 40,000 (b) Rs. 1,00,000(c) Rs. 1,20,000 (d) Rs. 80,000

34. 18% investment of Rs. 1,00,000 and interest received on investment Rs. 15,000 have beengiven in the trial balance for the period ended on 31.3.2006. The amount of interest outstandingin the final accounts will be

(a) Rs. 3,000 (b) Rs. 15,000(c) Rs. 4,000 (d) Rs. 8,000

35. A draws a bill on B for Rs. 30,000 for mutual accommodation. A discounted that bill for Rs.28,000 from bank and remitted Rs.14,000 on B. On due date A will send to B

(a) Rs. 15,500 (b) Rs. 15,700(c) Rs. 17,000 (d) Rs. 15,000

36. If sales revenue is Rs. 4,00,000, cost of goods sold is Rs. 3,10,000 and operating expenses areRs. 60,000, the gross profit is

(a) Rs. 90,000 (b) Rs. 60,000(c) Rs. 30,000 (d) Rs. 2,50,000

37. Average stock = Rs. 12,000. Closing stock is Rs. 3,000 more than opening stock. The value ofclosing stock will be

(a) 24,000 (b) 12,000(c) 10,500 (d) 13,500



38. Goods costing Rs. 2,00,000 sent out to consignee at cost + 25%. Invoice value of the goodswill be


39. The Board of Directors of a company decides to issue minimum number of equity shares ofRs. 10 each at 10% discount to redeem Rs. 5,00,000 preference shares. The maximum amountof divisible profits available for redemption is Rs. 3,00,000. The number of share to be issuedby the company will be

(a) 18,182 shares (b) 22,223 shares(c) 20,000 shares (d) 25,000 shares

40. Ajay bought goods of the value Rs. 20,000 and consigned them to Saroj to be sold by them ona joint venture, profits being divided equally. Ajay draws a bill on Saroj for an amountequivalent to 80% of cost of consignment. The amount of bill will be


41. Beta Ltd. was formed as a public limited company with on authorised capital of Rs. 20,00,000divided into shares of Rs. 10 each. Beta Ltd. issued fully paid up share of Rs. 10 each inconsideration of acquiring asset worth Rs. 3,80,000 from M/s Rahim Bros. The shares areissued at a premium of 25%. To record this transaction share capital need to be credited by

(a) Rs. 3,04,000 (b) Rs. 76,000(c) Rs. 3,80,000 (d) Rs. 3,00,000

42. Manish purchased a car for Rs. 5,00,000 making a down payment of Rs. 1,00,000 and signinga bill payable of Rs. 4,00,000. As result of this transaction

(a) Asset will increase by 4,00,000(b) Liabilities will increase by 4,00,000(c) Both (a) and (b)(d) Asset will increase by 5,00,000

43. The cash-book showed on overdraft of Rs. 1,500 but the pass book made up to the same dateshowed that cheque of Rs. 100, Rs. 50 and Rs. 125 respectively had not been presented forpayment and the cheque of Rs. 400 paid into account had not been cleared. The balance asper the cash book will be

(a) Rs. 1,625 (b) Rs. 1,375(c) Rs. 2,175 (d) Rs. 1,100

44. If repair cost is Rs. 25,000, white wash expenses are Rs. 5,000 cost of extension of building isRs. 2,50,000 and cost of improvement in electrical wiring is Rs. 19,000. The amount to becapitalized will be

(a) Rs. 2,69,000 (b) Rs. 2,99,000(c) Rs. 2,80,000 (d) Rs. 2,74,000


45. Ram draws a bill on Rahim for Rs. 30,000. Ram wants to endorse it to Shyam in settlementof Rs. 35,000 at 2% discount and balance in cash. How much cash Ram will pay to Rahim.

(a) Rs. 5,000 (b) Rs. 4,200(c) Rs. 4,300 (d) Rs. 4,600

46. Gopal Ltd. issued 20000, 8% debentures of Rs. 10 each at par which are redeemable after 5years at a premium of 20%. The amount of loss on redemption of debenture to be written offevery year will be

(a) Rs. 10,000 (b) Rs. 8,000(c) Rs. 2,000 (d) Rs. 30,000

47. Gopal sent out certain goods to Kamal of Mumbai. 1/10 of the goods were lost in transit.Invoice value of goods lost Rs. 12,500. Invoice value of goods sent out on consignment will be

(a) Rs. 1,20,000 (b) Rs. 1,40,000(c) Rs. 1,25,000 (d) Rs. 1,00,000

48. Mohan and Sohan enter into joint venture sharing profits and losses equally. Mohanpurchased 100 kg of rice @ 20 kg. Brokerage paid Rs. 200, carriage Rs. 300 Sohan sold 90 kgof rice @ Rs. 22 Kg. Balance rice was taken over by Sohan at cost. The value of rice takenover to be recorded in joint venture will be

(a) Rs. 200 (b) Rs. 250(c) Rs. 220 (d) Rs. 230

49. If unsold goods costing Rs. 20,000 is taken over by venturers at Rs. 15,000 the joint ventureA/c will be credited by

(a) Rs. 5,000 (b) Rs. 15,000(c) Rs. 20,000 (d) NIL

50. On 1.6.07 X draw a bill on Y for Rs. 25,000. At maturity bill was dishonoured and notingcharges incurred Rs. 100. Y requested X to accept Rs. 5,100 in cash and for the balance Xdraw a bill on Y for 2 months at 12% p.a. Interest amount will be

(a) Rs. 440 (b) Rs.400(c) Rs.420 (d) Rs.410

51. On 1.8.07 Ram draw a bill on Moti for 30 days after sight. The date of acceptance is 8.8.07the due date of the bill will be

(a) 10.9.07 (b) 8.9.07(c) 9.9.07 (d) 11.9.07

52. Fees paid in cash to Notary Public is charged by

(a) Drawer (b) Drawee(c) Holder of bill of exchange (d) None of the above



53. Ryan Ltd. issued 5,000, 12% debentures of Rs. 100 each at a premium of 10% which areredeemed after 10 years at a premium of 20%. The amount of loss on redemption of debentureto be written off every year will be

(a) Rs.8,000 (b) Rs.10,000(c) Rs.30,000 (d) Rs.40,000

54. As per the Companies Act, “Interest accrued and due on debentures” should be shown

(a) Under Debentures Account(b) As Current liabilities(c) As Provision(d) As a reduction of bank balance

55. Preference share amounting to Rs. 2,00,000 are redeemed at a premium of 5% by issue ofshare amounting to Rs. 1,00,000 at a premium of 10% the amount to be transferred tocapital redemption reserve account will be

(a) Rs.1,05,000 (b) Rs.1,00,000(c) Rs.2,00,000 (d) Rs.1,11,000

56. Out of the following at which point the treatment for “Sales” and “Consignment” is similar

(a) Money received (b) Stock outflow(c) Risk (d) Ownership transfer

57. A of Mumbai send goods to B of Delhi, the goods are to be sold at 125% of cost which isinvoice price or above. B was entitled the commission of 10% on sales plus 25% on anysurplus realised above invoice price. 10% of goods sent out on consignment (invoice valueof which is Rs. 12,500) were destroyed. 75% of the total consignment is sold by B at Rs.1,00,000. The amount of commission payable will be

(a) Rs.10,000 (b) Rs.11,562.50(c) Rs.9,700 (d) Rs.9,000

58. A and B enter into a joint venture sharing profits and losses in the ratio 2:3. Goods purchasedby A for Rs. 45,000. Expense increased by A Rs. 13,500 and by B Rs. 5,200. B sold the goodsfor Rs. 85,000. Remaining stock taken over by B as Rs. 7,200. The profit of the venture willbe

(a) Rs.9,800 (b) Rs.35,700(c) Rs.21,300 (d) Rs.28,500

59. On 1.4.2006 Mohan invested Rs. 1,00,000 in a business. Interest of capital is to be allowed @12% p.a. Accounting year is financial year. Amount of interest to be charged to Profit andLoss account for the year 2006-2007 is

(a) Rs.12,000 (b) Rs.9,000(c) Rs.10,000 (d) Rs.11,000


60. 1000 kgs. of Apple are consigned to a whole saler the cost being Rs. 8 per kg. plus Rs. 925 offreight it is concluded that a loss of 15% is unavoidable the cost per kg. of apple will be

(a) Rs.9.41 (b) Rs.10.50(c) Rs.10.00 (d) Rs.9.50


61. Which of the following is not the legal requirements of a valid offer

(a) It must be communicated to the offeree(b) It must be made with a view to obtain offeree’s assent(c) It must express offeror’s final willingness(d) It must be made to specific person and not to public at large

62. A promisee is a person

(a) Who makes a promise(b) A person who monitors the statement intentions of two parties(c) To whom the promise is made(d) Who fails to perform the promise

63. Silence cannot amount to offer by conduct. It is


64. Coercion involves moral or mental pressure.


65. ‘A’ Offers to sell his car to ‘B’. Only A can accept or reject it. This is a case of

(a) General offer (b) Express offer(c) Specific offer (d) Standing offer

66. A voidable contract is one which

(a) Can be enforced at the option of aggrieved party(b) Cannot be enforced in a court of law(c) Can be enforced at the option of both the parties(d) Courts prohibit

67. According to Section 25 of the Indian Contract Act, 1872 an agreement must be

(a) In writing(b) Registered(c) Out of natural love and affection between two relations(d) All of the above



68. Which one of the following is an essential element of a valid contract?

(a) Free consent (b) Consideration(c) Competent parties (d) All of the above

69. Where no price is fixed by express agreement or by implication, the buyer shall pay theseller

(a) Net realisable value (b) Reasonable price(c) Resale price (d) Ad hoc price

70. Which of the following statements are correct.

(a) In case of sale the subject matter of contract exists at the time of sale(b) The term does not include shares(c) In a contract of sale, the price may be paid partly in cash and partly in goods valued in

terms of money(d) A contract of sale must be in writing

71. According to Sale of Goods Act, a warranty is

(a) A stipulation essential to the main purpose of the contract(b) A stipulation collateral to the main purpose of the contract(c) Either (a) or (b)(d) Both (a) and (b)

72. A stipulation in a contract of sale with reference to the goods which are the subject matterthereof may be

(a) Condition (b) Warranty(c) Condition precedent (d) Either (a) or (b)

73. Breach of a condition gives a right to

(a) Repudiate a contract(b) Claim damages only(c) Repudiate the contract and claim damages(d) None of the above

74. Any stipulation other than time of payment is of the essence of the contract depends upon

(a) Application of Section 11(b) Operation of law(c) Terms of the contract(d) All of the above

75. Lien in Sale of Goods Act, is a right to

(a) Regain possession of goods(b) Retain possession of goods(c) Give away possession of goods(d) All of the above


76. The right of lien is available to the unpaid seller, only when

(a) Seller is not in possession of the goods(b) Seller is in possession of goods(c) Seller delivered the goods to the carrier(d) Seller has delivered the goods to the buyer

77. As per Section 2(b) of The Partnership Act, the term business includes

(a) Trade (b) Occupation(c) Profession (d) All of the above

78. A minor when admitted into partnership

(a) Can opt to continue as a partner or not, on attaining majority(b) Becomes personally liable(c) Cannot inspect any books of accounts of the firm(d) Can interfere in the day to day affairs of the firm

79. For admitting a minor into the benefits of the partnership, which of the following is required?

(a) Consent of guardian(b) Consent of Registrar of firms(c) Consent of all the partners of the firms(d) Consent of majority partners of the firm

80. A partnership firm is compulsorily dissolved where___________.

(a) All partners have become insolvent(b) Firm’s business has become unlawful(c) The fixed term has expired(d) In cases (a) and (b) only

81. Unregistered firm cannot file a suit against a _________ to enforce any right arising from acontract.

(a) Incoming partner(b) Outgoing partner(c) Third party(d) Minor admitted to benefits of partnership.

82. An implied condition as to fitness of goods for a particular purpose provided under Section16, ________ where the buyer relies on his own judgement.

(a) Is applicable (b) Is not applicable(c) Is presumed (d) Exists

83. Section __________ of the Sale of Goods Act provides for implied condition as to quality orfitness.

(a) 14 (b) 15(c) 16 (d) 17



84. In a contract of sale of goods, implied condition as to description of goods applies wheregoods are sold by _________.

(a) Sample (b) Description(c) Sample and description (d) Junk dealer

85. When the goods have not been sold on credit and the buyer fails to pay the ________, theunpaid seller can exercise his right of lien.

(a) Substantial portion of the price(b) Whole of the price(c) Part of the price(d) Minimum portion of the price

86. Dissolution agreement as per Section 40, can be ________.

(a) Implied from conduct of the parties(b) In a express form i.e. written document(c) (a) or (b)(d) (a) and (b)

87. A travel agency operates buses from Jaipur to Agra. The bus standing at its bus terminals iswith a view to taking the passengers. There is __________to take passengers.

(a) Internal offer (b) External offer(c) Implied offer (d) Express offer

88. The parties to a contract should be __________ to contract.

(a) Able (b) Competent(c) Reliable (d) Incapacitated

89. In a wagering agreement, the future event is the _________ in determining the agreement.

(a) Collateral aspect (b) Primary factor(c) Secondary factor (d) (a) and (b)

90. In case of firms carrying on business other than banking, maximum numbers of partnersare ________.

(a) 20 (b) 21(c) 25 (d) 10

91. _________ is an error ...... belief about something.

(a) Fraud (b) Representation(c) Mistake (d) Misrepresentation

92. There can be a stranger to a ________.

(a) Contract (b) Consideration(c) Agreement (d) Promise


93. Every partner has the right to retire by___________.

(a) Majority of partners (b) Consent of all the partners(c) Will (d) Giving notice

94. When a seller of goodwill of a business agrees not to carry on similar business, the limits andconditions imposed have to be _________ having regard to the nature of the business.

(a) Reasonable (b) Understandable(c) Considerable (d) Unreasonable

95. _________ awarded with a view to punish the defendant, and not solely with the idea ofawarding compensation.

(a) Nominal Damages (b) Special Damages(c) Vindictive Damages (d) Ordinary Damages

96. Section ________ of the Indian contract Act deals with Misrepresentation.

(a) 15 (b) 6(c) 17 (d) 18

97. In a contract of auction sale, the property in the goods passes with _______.

(a) Payment of price (b) Fall of the hammer(c) Consent of the owner goods (d) Happening of all the above

98. Partnership is merely an ________ relation between the partners.

(a) Legal (b) Implied(c) Express (d) Birth

99. ‘A’ contracts to sing for ‘B’ at concert for Rs. 5000 which is paid in advance. ‘A’ is too ill tosing. Decide.

(a) A will not refund the advance of Rs. 5000 to B.(b) A must refund the advance of Rs. 5000 to ‘B’(c) A should make a new contract for sing(d) B will compel A to sing

100. ‘A’ and ‘B’ are partners in a stationary business. ‘A’ buys on credit certain quantity ofpencils for a whole seller in the firm’s name. He uses these pencils for the family. Decide.

(a) ‘A’ will be personally liable(b) It will bind the firm(c) A as well as firm both will be liable(d) All of these




101. The definition “Economics is the science which studies human behavior as a relationshipbetween ends and scarce means which have alternative uses” was given by:

(a) J. B. Say (b) Alfred Marshal(c) Robbins (d) Paul. A. Samuelson

102. Economics is _________.

(a) Not a normative Science.(b) Not a positive Science.(c) Partly Science and partly Art(d) Neither a normative nor a positive Science.

103. Which of the following statements is incorrect in case of capitalist economy?

(a) There is equality of income among people in the economy(b) Profit-motive gets precedence over social motive(c) Freedom of enterprise about what to produce(d) Right to own property

104. Which of the following is likely to cause an inward shift in a country’s PPC?

(a) Scientist discovering new techniques of production(b) Workers getting job in making fly-over(c) War destroying resources of the country(d) The country finds new techniques of agricultural production

105. Calculate Income-elasticity for the household when the income of a household rises by 5%and the demand for bajra falls by 2%.

(a) + 2.5 (b) – 2.5(c) - .4 (d) + .4

106. The consumer surplus concept is derived from:

(a) Law of demand(b) Indifference curve analysis(c) Law of diminishing marginal utility(d) All of above

107. The consumer is in equilibrium when:

(a) When marginal utility is constant(b) When marginal utility is greater than price of the good(c) When marginal utility is less than price of the good(d) When marginal utility is equal to price of the good


108. Which is not the property of Indifference curve analysis?

(a) Indifference curves slope downward to the left(b) Indifference curves are always convex to the origin(c) Indifference curves can never intersect each other(d) A higher indifference curve represents a higher level satisfaction than the lower indifference

curve

109. Capital is a:

(a) Stock concept (b) Flow Concept(c) Both (a) and (b) (d) None of the above

110. Which is not the function of an entrepreneur?

(a) Initiating a business enterprise and resource co-ordination(b) Risk bearing or uncertainty bearing(c) Innovation(d) Mobilisation of savings

111. Types of balance of trade are

(a) Favorable balance of trade (b) Unfavorable balance of trade(c) Balanced balance of trade (d) All of the above

112. A full fledged Department of Family Planning was created in India in

(a) 1950 (b) 1951(c) 1966 (d) 1955

113. Least Densely populated state is:

(a) M. P. (b) Assam(c) Nagaland (d) Tripura

114. Highest density of population is in:

(a) Punjab (b) Maharashtra(c) U. P. (d) Delhi

115. Wealth Tax was abolished in:

(a) 1985 (b) 1998(c) 2005 (d) False it is still continuing

116. In order to improve production of power, Electricity Act was passed in

(a) 2003 (b) 2005(c) 2002 (d) 2004

117. Petroleum, Oil and Lubricants constitute —— of our import bill

(a) 29% (b) 27%(c) 33% (d) 18%



118. About ———— percent of sick units are other than small units

(a) 98% (b) 2%(c) 5% (d) 30%

119. The industrial sector depends on the agricultural sector because:

(a) The agricultural sector provides food and other products for the consumption purpose ofindustrial sector

(b) The agricultural sector provider market for the industrial products(c) The agricultural sector provides raw – materials to industry(d) All of the above

120. The service sector in India now accounts for:

(a) 50-60% of GDP (b) 60-70% of GDP(c) 40-50% of GDP (d) 30-40% of GDP

121. On which of the following, income tax is not imposed in India?

(a) Income from salary. (b) Income from house property.(c) Interest on fixed deposits. (d) None of the above

122. PPF stands for:

(a) Private Provident Fund (b) Personal Provident Fund(c) Public Provident Fund (d) Public Presidency Fund

123. Income Tax was introduced first time in India in 1860 and then discontinued in 1873. It wasre-introduced in the year:

(a) 1885 (b) 1886(c) 1887 (d) 1890

124. Which of the following is not the example of direct tax?

(a) VAT (b) Wealth Tax(c) Corporate Tax (d) Income Tax

125. Excise duty is imposed on

(a) Goods imported in India (b) Goods sold in India(c) Goods manufactured in India (d) Goods exported from India


(a) Expenditure on financial assets which are produced and owned within the country isincluded in national expenditure

(b) Expenditure on financial assets of foreign countries is included in national expenditure(c) Goods produced in preceding years are also included in national income.(d) None of the above


127. Which of the following is included in national income ?

(a) Scholarship (b) Old age pensions(c) Unemployment Allowance (d) None of the above

Use table to answer question 128-129

House of Total MarginalLabour Output Product

0

1 200 200

2 - 180

3 480 __

128. What is the total output when 2 hours of labour are employed?

(a) 180 (b) 200(c) 480 (d) 380

129. What is the marginal product of the third hour labour?

(a) 120 (b) 100(c) 180 (d) 480

130. The cost that firm incurs in hiring or purchasing any factor of production is referred as:

(a) Explicit cost (b) Implicit cost(c) Variable cost (d) Fixed cost

131. Per capita national income means:

(a) NNP/ Population (b) Total capital / Population(c) Population / NNP (d) None of the above

132. According to the World Development Report – 2006, the GINI index for India in 1999-00(survey year) was:

(a) . 33 (b) . 29(c) . 53 (d) . 18

133. TRAI is regulatory, authority for —— in India

(a) Tourism (b) Telecom(c) Transport (d) Technical Education

134. Optimum population is that level of population at which

(a) Output per capita is the highest(b) Output per capita is the lowest(c) Output per capita is the same(d) None of the above



135. Tenth plan aims at reducing the maternal mortality rate to — per thousand birth by 2007

(a) 5 (b) 2(c) 1 (d) 3

136. The main objective of fiscal policy in developing countries is to:

(a) Promote economic growth(b) Mobilise resources for economic growth(c) Ensure economic growth and equitable distribution(d) All the above

137. Suppose income of the consumers increases by 50 % and the demand for commodity xincreases by 20 % what will be the income elasticity of demand for commodity x ?

(a) . 04 (b) . 4(c) 4 (d) – 4

138. ———— depicts complete picture of consumer tastes and preferences.

(a) Budget line (b) Average cost curve(c) Indifference map (d) Marginal revenue curve

139. At present, the area covered by forest as a percentage of total land area in India lies withina range of :

(a) 11 % to 15 % (b) 16 % to 20 %(c) 21 % to 25 % (d) 26 % to 30 %

140. Population explosion occurs in ——— stage of the theory of demographic transition

(a) First (b) Second(c) Third (d) Fourth

141. A higher indifference curve shows:

(a) A higher level of satisfaction (b) A higher level of production(c) A higher level of income (d) None of the above

142. In fiscal deficit we add borrowing and other liabilities to the ———

(a) Primary Deficit (b) Capital Deficit(c) Budget Deficit (d) Money Deficit

143. In the case of a Giffen good, the demand curve will be

(a) Downward sloping to the right (b) Upward sloping to the right(c) Vertical (d) None of the above

144. In case of an inferior good the income elasticity of demand is:

(a) Zero (b) Positive(c) Negative (d) None of the above


145. When quantity demanded changes by larger percentage than does price, elasticity is termedas:

(a) Inelastic (b) Elastic(c) Perfectly Elastic (d) Perfectly Inelastic

146. The share of concessional debt in total external debt of India has:

(a) Remained the same (b) Doubled(c) Reduced (d) Increased

147. The incidence of taxes refers to:

(a) The level and rate of taxation(b) Who ultimately bears the money burden of the tax(c) The growth of taxation(d) The way in which a tax is collected

148. Marginal cost is defined as:

(a) The change in total cost due to a one unit change in output(b) Total cost divided by output(c) The change in output due to a one unit change in an input(d) Total product divided by the quantity of input

149. Which is the other name that is given to the Long run average cost curve?

(a) Enveloping curve (b) Profit curve(c) Demand curve (d) Supply Curve

150. Diminishing marginal returns imply:

(a) Decreasing average variable cost (b) Decreasing marginal cost(c) Increasing Marginal cost (d) Decreasing average fixed cost


151. A person opened a savings bank account 4 months ago, which has now a balance ofRs. 21,315. If the bank pays 4.5% simple interest, how much money was deposited byhim, initially?


152. Mohan deposits Rs. 500 into an account paying 8% simple interest. He makes two moredeposits of Rs. 1,000 each; first after 3 months and second after 6 months. How much will bein his account at the end of the year, if he makes no other deposits and withdrawals duringthe time?




153. How long will it take Rs. 1,200 to amount Rs. 2,000 at 5% converted quarterly at CompoundInterest?

(a) 10 years 3 months (b) 10 years 5 months(c) 10 years (d) None of these

154. A man borrowed Rs. 20,000 from a money lender but he could not repay the amount for aperiod of 4 years. According the money lender’s demand showed Rs. 26,500 due from him.At what rate percent annum compound interest did the money lender lend his money?

(a) 7% (b) 8%(c) 7.5% (d) None of these

155. The compound interest earned by a money lender on Rs. 7,000 for 3 years if the rate ofinterest for 3 years are 7%, 8% and 8.5% respectively is


156. What annual payment will discharge a debt of Rs. 770 due in years, the rate of interest being5% per annum?


157. The rate of interest for the first 2 years is 3% per annum, for the next 3 years is 8% perannum and for the period beyond 5 years, 10% per annum. If a man gets Rs. 1520 as asimple interest for 6 years; how much money did he deposit?


158. Rs. 7500 is borrowed at compound interest at the rate of 4% per annum. What will be theamount to be paid after 6 months, if interest is compounded quarterly?

(a) Rs. 7650.75 (b) Rs. 7600.50(c) Rs. 7000 (d) None of these

159. The compound interest on any sum at the rate of 5% for two years is Rs. 512.50. Find thesum.

(a) Rs. 4000 (b) Rs. 5,000(c) Rs. 3,000 (d) None of these

160. In what rate per cent per annum will Rs. 1,000 amount to Rs. 1331 in 3 years? The interestis compounded yearly is:



161. The range of 10 observations is 20. If each item is increased by 15, then the range of newseries is


162. The range of 10 observations is 20. If each item is divided by –2, then the range of new seriesis

(a) –10 (b) 10(c) 20 (d) None of these

163. The relation between two variables is 2x – 3x + 12 = 0. If mean deviation of y is 6 then meandeviation of x is


164. In grouped frequency distribution, if the Class interval Gap is unequal; then which dispersionis more appropriate?

(a) Q.D. (b) Range(c) Mean deviation (d) Standard Deviation.

165. If the Standard Deviation of 10 observations is 4 and if each item is divided by – 2 thenStandard Deviation of new series is


166. Find the average of first 25 multiples of 5.


167. If a, b, c, d, e are five consecutive odd integers, then their average is

(a) a + 5 (b)abcde

5(c) 5(a + b + c + d + e) (d) a + 4

168. A cricketer scored 180 runs in the first test and 258 runs in the second. How many runsshould be score in the third test so that his average score in three tests would be 230 runs.




169. In a coconut grove, (x+2) trees yield 60 nuts per year, x trees yield 120 nuts per year and(x–2) trees yield 180 nuts per year. If the average yield per year per tree be 100, then thevalue of x is –

(a) 4 (b) 6(c) 8 (d) 2

170. The average age of 24 students and the class teacher is 16 years. If the class teachers age isexcluded, the average reduces by 1 year. What is the age of the class teacher?

(a) 50 years (b) 40 years(c) 60 years (d) None of these

171. If r = 0, then

(a) There is a perfect correlation between x & y.(b) x and y are not correlated.(c) There is a positive correlation between x & y.(d) Do not exist.

172. If Covariance (x, y) < 0; then the relation between two variable is

(a) Positive (b) Negative(c) (a) or (b) (d) None of these

173. Consider the two regression lines 3x+2y = 26 & 6x + y = 31. Find the mean values of x and y.

(a) x = 4 & y = 7 (b) x = 7 & y = 4

(c) x = 5 & y = 6 (d) None of these

174. Consider the two regression lines 3x+2y = 26 & 6x + y = 31. Find the correlation coefficientbetween x & y.

(a) 0.5 (b) –0.5(c) 0.6 (d) None of these

175. Two regression lines are

(a) Reversible (b) not reversible(c) cannot say (d) None of these

176. A problem of Mathematics is given to three students X, Y and Z whose chances of solving it

are 13

, 14

and 15

respectively. Find the chance that the problem will be solved?

(a)4

5(b)

2

5

(c)3

5(d) None of these


177. If P(A) = 12

; P(B) =13

and P( A B∩ ) = 14

then the value of P(A / B) is

(a)3

4(b)

1

4

(c)2

5(d) None of these

178. If P(A) = 12

; P(B) = 13

and P( A B∩ ) =14

then the value of P( A B∩ ) is

(a)1

3(b)

11

12(c) 1 / 12 (d) None of these

179. If P(A) = 12

; P(B) = 13

and P( A B∩ ) = 14

then the value of P ( A B∩ ) is

(a)5

12(b)

7

12

(c)1

2(d) None of these

180. If P(A) = 12

; P(B) = 13

and P( A B∩ ) = 14

then the value of P ( A B∩ ) is

(a)1

4(b)

3

4

(c)2

5(d) None of these

181. From the following probability distribution table, find E(x).

x: 1 2 3

f(x):1

2

1

3

1

6

(a) 1 (b) 1.50(c) 1.67 (d) None of these



182. From the following probability distribution table, Find V(X)

x: 1 2 3

f(x):1

2

1

3

1

6


183. In a box carrying one dozen of oranges, one third has become bad. If 3 oranges are taken outfrom the box at random, what is the probability that at least one orange out of the threeoranges picked up is good?

(a)54

55(b)

1

55

(c)45

50(d) None of these

184. A and B are two candidates seeking admission in I.I.T. The probability that A is selected is0.5 and the probability both A and B are selected is at most 0.3. Then the probability of Bgetting selected is

(a) < 0.8 (b) < 0.9(c) < 0.7 (d) None of these

185. One of the two events must happen. Given that the chance of one is two – third that of theother. Then the odds in favour of the other


186. If x be a poison variates with parameter 1; then find P(3<x<5) (Given: e–1 = 0.36783)


187. Find the probability that at least 5 defective bolts will be found in a box of 200 bolts. If it isknown that 2% of such bolts are expected to be defective (Given:e–4 = 0.0183)


188. A man is dealt 4 spade cards from an ordinary pack of 52 cards. If he is given three morecards, find the probability p that at least one of the additional cards is also a spade.



189. The mean and variance of the poison distribution are equal.


190. If a variable x follows a poison law such that P(x = 1) = P(x = 2); then the variance of thedistribution is

(a) –2 (b) 2


191. A random sample of the heights of 500 oranges was taken from a large consignement. 65were found to be defective. Find Standard Error of the proportion of defectives.


192. A random sample of the heights of 100 students from a large population of students ina College having Standard Deviation of 0.75 ft. has an average height of 5.6 ft., Find95% confidence limits for the average height of all the students of the College. (For95%, Z = 1.96)

(a) 5.453, 5.747 (b) 16.453, 7.747(c) 6.485, 7.647 (d) None of these

193. A sample of size 64 was drawn from a population consisting of 128 units. The samplemean of the measurements on a certain characteristic was found to be 28. If thepopulation Standard Deviation is 4 then find the 96% confidence limit for the populationmean? (For 96%, Z = 2.05)

(a) 30.72, 27.32 (b) 27.272, 28.728(c) 30.272, 32.728 (d) None of these

194. In a large consignment of oranges a random sample of 500 oranges revealed that 65 orangeswere bad. Find the 99.73% Confidence limit of bad ones? (For 99.73%, Z = 3)

(a) 8.5%, 17.5% (b) 0.85%, 0.175%(c) 8%, 12% (d) None of these

195. Find the sample size such that the probability of the sample means differing from the

population mean by not more than 1

10th of the Standard Deviation is 0.95.


196. The variance of 10 observations is 4, then their Standard Deviation is +2 or –2. This is




197. Find the variance of binomial distribution with n = 10, p = 0.3

(a) 2.1 (b) 3(c) 7 (d) None of these

198. When the cost of living increases, the standard of living improves. This is


199. The 95% confidence limit for the sample mean ( ) .x is 1.96n

σ⎛ ⎞μ± ⎜ ⎟⎝ ⎠

This is


200. The mean and variance of Binomial distribution is 12. This is


❖❖❖

BOARD OF STUDIES









1. Profit and Loss account is prepared for a period of one year by following

(a) Periodicity period concept (b) Business entity concept(c) Accrual concept (d) None of the above.

2. Basic concepts related to Balance Sheet are

(a) Conservatism concept (b) Business entity concept(c) Going concern concept (d) Both (b) or (c)

3. Purchases for cash

(a) Increase liability (b) Decrease assets(c) No change in the total assets (d) Increase assets

4. Difference in bank balance as per bank pass book and cash pass book may arise onaccount of

(a) Cheque issued but not dishonoured(b) Direct payment by customer in bank(c) Cheque issued but not presented(d) All of the three



5. Trade discount allowed at the time of sale of goods is

(a) Recorded in Journal (b) Not recorded on book of accounts(c) Recorded in Cash book (d) Recorded in Sales book

6. Which of the following is not an asset

(a) P & L A/c (Cr. balance) (b) Inventory(c) Goodwill (d) Cash

7. Purchases of goods on credit

(a) Increase liability (b) Decrease assets(c) Increase assets (d) Both (a) and (c)

8. A bill of exchange is drawn on 1 January 2007 payable after 3 month. The due date of bill is

(a) 4 April 2007 (b) 31 March 2007(c) 1 April 2007 (d) None of the above

9. The noting charges levied on dishonour of an endorsed bill by the notary public are to befinally borne by

(a) Holder of the bill (b) Drawer of the bill(c) Drawee (d) Either (a) or (b)

10. Under inflationary conditions, FIFO method will lead to

(a) Lower profit (b) Higher profit(c) Higher sales (d) No change in sales

11. Which of the following assets are to be valued at the lower of cost and net realizable values

(a) Sundry Debtors (b) Investment(c) Goodwill (d) Stock (Inventories)

12. Bad debts recovered account will be transferred to

(a) Provision for doubtful debt A/c (b) P & L A/c(c) Bad debt A/c (d) Debtors A/c

13. Goods distributed as free samples is debited to

(a) Advertisement A/c (b) Charity A/c(c) Purchases A/c (d) Goods A/c

14. State which of the following is not a foreign bill

(a) A bill drawn outside India and made payable outside(b) A bill drawn outside India and made payable in India(c) A bill drawn in India and made payable in India(d) A bill drawn in India on a person resident outside India and made payable outside India.


15. Which of the following enhances the earning capacity of an assets?

(a) Reduction in operating costs(b) Increase in working capacity of an assets(c) Replacing damage parts of an assets(d) Both (b) and (c)

16. Depreciation is a process of

(a) Allocation of profit (b) Valuation of expenses(c) Segregation of profit (d) Appropriation of profit

17. Which of the following are fixed assets

(a) Closing Inventory (b) Fixed deposits in Bank (for 3 years)(c) Prepaid Expenses (d) Patents

18. A Club paid subscription fees of Rs. 1,800 out of which Rs. 400 is prepaid. In such case

(a) P & L A/c is debited with Rs. 1,400 (b) Rs. 400 is shown as current assets(c) Both (a) and (b) (d) None of the above.

19. If goods worth Rs. 2,000 returned to a supplier is wrongly entered in sales return books asRs. 1,500 then

(a) Gross profit will decrease by Rs. 4,000(b) Gross profit will increase by Rs. 3,500(c) Gross profit will decrease by Rs. 3,500(d) None of the above

20. Gross profit is equal to

(a) Opening stock + purchases – closing stock(b) Net profit – Expenses(c) Sales – Closing stock + purchases(d) Sales – Cost of goods sold

21. Sohan as a trader purchased goods for Rs. 5,00,000 and sold 70% of such goods during theaccounting year ended 31st December 2006. The Market value of the remaining goods wasRs. 1,00,000. He valued the closing stock at Rs. 1,00,000 and not Rs. 1,50,000 due to

(a) Conservatism concept (b) Cost concept(c) Money measurement (d) None of the above

22. Narain Brothers which was registered in the years 2006, has been following FIFO methodfor valuation of share. It changed its method from FIFO to LIFO method in the year 2007.The auditor raised objection to this change in the method of valuation of investments.

(a) Method can not be changed under any circumstances(b) Change in the method should be done only if it is required by some statute and change

would result in appropriate presentation of financial statement(c) Change in the method should be done only with consent of the auditor(d) None of the above.



23. The opening stock of the current year is over stated by Rs. 10,000. and closing stock is overstated by 17,000. These errors will lead the net income for the current year to be

(a) Rs. 7,000 understated (b) Rs. 17,000 overstated(c) Rs. 7,000 overstated (d) Rs. 17,000 understated

24. When the overdraft as per cash book is the starting point and a cheque of Rs. 1500 depositedinto bank has not been recorded in cash book, then in the bank reconciliation statement itwill be

(a) Added by Rs.1,500 (b) Deducted by Rs.1,500(c) Deducted by Rs.3,000 (d) Added by Rs.3,000

25. A draws a bill on B for Rs. 5,000. A endorsed it to C. B will pay the amount of the bill onmaturity to

(a) ‘C’ (b) Bank(c) ‘A’ (d) None of the above

26. On 1.04.07 Ram draws a bill on Rahim for 2 months for Rs. 1,000, 4th June was a suddenholiday due date of the bill will be

(a) 1st June, 2007 (b) 4th June, 2007(c) 5th June, 2007 (d) None of the above.

27. On 10.05.06 Ramesh draw a bill on Suresh for 4 months for Rs. 4,000. 13 September is apublic holiday, due date of the bill will be

(a) 13 September (b) 10 September(c) 14 September (d) 12 September

28. Rs.40,000 spent by a factory in overhauling of its existing plant & machinaries. It hasenhanced its working life by five years. The aforesaid expenditure is

(a) Capital expenditure(b) Revenue expenditure(c) Deferred revenue expenditure(d) None of the above

29. If repairs cost is Rs. 30,000 white wash expenses are Rs. 5,000, cost & extension of buildingis Rs. 300000 and cost of improvement in electrical wiring system is Rs. 30,000 the amountof revenue expenses will be

(a) Rs. 35,000 (b) Rs. 65,000(c) Rs. 3,65,000 (d) Rs. 3,35,000

30. Rajesh returned goods amounting Rs. 5,200 to us but was recorded Rs. 2,500 in his account.In the rectifying entry. Rajesh A/c will be debited with

(a) Rs. 2,500 (b) Rs. 2,700(c) Rs. 7,700 (d) Rs. 5,200


31. A Bill Receivable of Rs. 4,000 was dishonoured and credited as Rs. 400. The error will berectified by

(a) Debiting Bill by Rs. 3,600(b) Debiting Bill Rs. 4,400(c) Crediting Bill Rs. 3,600(d) Crediting Bill Rs. 4,400

32. Opening Stock = Closing Stock + ? – Purchases

(a) Cost of goods sold (b) Gross profit(c) Sales (d) Net Profit

33. The following information pertaining to a firm as on 31 December 2006

Opening Stock Rs. 20,000Purchases Rs. 1,50,000Sales Rs. 1,40,000Gross profit on sales has been 25%. The cost of goods sold during the year will be

(a) Rs. 12,000 (b) Rs. 1,75,000(c) Rs. 1,40,000 (d) Rs. 1,05,000

34. Original cost of an asset was Rs. 3,00,000. Salvage value was 40,000. Depreciation for 3rd

year @15% p.a. under W.D.V method will be

(a) Rs. 38,250 (b) Rs. 45,000(c) Rs. 1,35,000 (d) Rs. 32,512.50

35. What would be the amount of sales when opening stock is Rs. 20,000. Purchase Rs. 50,000wages Rs. 10,000. Closing stock Rs. 20,000 and gross profit is 1/7th of sales.


36. X send out goods costing Rs. 2,00,000 to Y. Consignor expenses Rs. 5,000. Consignee expensesin relation to sales Rs. 3,000. 4/5th of the goods were sold at 20% above cost. The profit onconsignment will be

(a) Rs. 20,000 (b) Rs. 30,000(c) Rs. 25,000 (d) Rs. 40,000

37. R & S entered into a joint venture. They purchased a piece of land for Rs. 60,000 and sold itfor Rs 80,000 in 2006. Originally R had contributed Rs. 40,000 and S Rs 20,000. What will bethe profit on venture?

(a) Rs. 25,000 (b) Rs. 20,000(c) Rs. 60,000 (d) Rs. 80,000



38. Following trading results are available in respect of the business carried on by a firm

2003 – Loss Rs. 20,000 2005 – Profit Rs. 30,000

2004 – Loss Rs. 5,000 2006 – Profit Rs. 15,000

The value of goodwill on the basis of 3 years purchases of average profit of the business will be

(a) Rs. 20,000 (b) Rs. 14,000(c) Rs. 15,000 (d) Rs. 70,000

39. M and N share profit in the ratio of 2:1. O has been admitted with 1/4th share in profit. Thenew profit sharing ratio of partner will be

(a) 1:2:1 (b) 1:1:2(c) 2:1:1 (d) None of the above

40. X, Y and Z are partner sharing profit and losses in the ratio of 5:3:2. Z retires and goodwillof the firm is to be valued at Rs. 50,000 find the amount payable to retiring partner onaccount of goodwill.


41. Jain & Co. forfeited 50 shares of Rs. 10 each. Rs.8 called up on which application money ofRs. 5 per share was paid. The entry for forfeiture is.

(a) Share Capital A/c Dr. 400To Share premium A/c 150To share allotment A/c 250

(b) Share Capital A/c Dr. 400To Share forfeiture 250To Share allotment A/c 150

(c) Share Capital A/c Dr. 500To Share forfeiture A/c 250To Share allotment A/c 250

(d) None of the above.

42. Preference shares of Rs. 3,00,000 are redeemed at par for which fresh equity shares of Rs.1,20,000 are issued at 20% premium. What amount should be transferred to capitalredemption reserve account?

(a) Rs. 60,000 (b) Rs. 24,000(c) Rs. 36,000 (d) Rs. 1,80,000

43. Goodwill of a firm of Sanju and Manju is valued at Rs. 45,000. It is appearing in the booksat Rs. 15,000. Anju is admitted for 1/4th share. The amount of goodwill, which she is supposedto bring will be



44. X Ltd. issued 5000 10% debentures of Rs. 125 each at a discount of 5% payable at a premiumof 5% at the end of 5 years. The loss on issue of debentures will be

(a) Rs. 62,500 (b) Rs. 12,500(c) Rs. 37,500 (d) Rs. 25,000

45. In case a trial balance does not agree the difference is put to

(a) Trading A/c (b) Profit & Loss A/c(c) Capital A/c (d) Suspense A/c

46. The capital of O and P are Rs. 60,000 and Rs. 20,000 respectively with the profit sharingratio 3:1. They decide to change the ratio to 5:3. On the date of change goodwill is valued atRs. 75,000. Goodwill account will not appear in the books. Journal entry to give the aboveeffect will be

(a) Goodwill A/c Dr. 75,000To O’s Capital A/c 56,250To P’s Capital A/c 18,750

(b) Goodwill A/c Dr. 75,000To O’s Capital A/c 46,875To P’s Capital A/c 28,125

(c) O’s Capital A/c Dr. 9,375To P’s Capital A/c 9,375


47. In the absence of any agreement, it is presumed that the new partner acquires. his share inprofit from the old partner in the

(a) Old ratio (b) Gaining ratio(c) New ratio (d) Sacrificing ratio

48. Purchased goods from Maya for Rs. 2,400 but was recorded as Rs. 4200 to the debit ofMaya. In the rectifying entry Maya’s A/c will be credited with

(a) Rs. 4800 (b) Rs. 6600(c) Rs. 8400 (d) None of the above

49. Bank reconciliation statement is prepared with the either balances of

(a) Pass book (b) Cash book(c) Both (a) or (b) (d) None of the above

50. If a bill is drawn on 28th January 2007 for 1 month, it will mature on

(a) 28 February 2007 (b) 3rd March 2007(c) 2nd March 2007 (d) None of the above



51. A Machinery was purchased for Rs. 50,000 on which depreciation was provided @ 15% bySLM method. The Written Down Value of the assets at the end of two years is

(a) Rs. 35,000 (b) Rs. 36,125(c) Rs. 42,500 (d) Rs. 50,000

52. Goods purchased for Rs. 80,000; sales Rs. 60,000; Margin 20% on cost closing stock will be

(a) Rs. 40,000 (b) Rs. 10,000(c) Rs. 2000 (d) Rs. 30,000

53. The first Accounting Standard (AS-1) issued by the Institute of Chartered Accountants ofIndia is on

(a) Disclosure of Accounting Policies(b) Valuation of Inventories(c) Revenue Recognition(d) Change in Financial Position of an Entity

54. A machinery purchased for Rs. 30,000 had its book value Rs. 18,000 was sold for Rs. 40,000the capital profit will be

(a) Rs. 12,000 (b) Rs. 10,000(c) Rs. 48,000 (d) Rs. 58,000

55. In case opening stock was Rs. 15,000, purchases Rs. 25,000, factory lighting Rs. 5,000 andclosing stock Rs. 10,000. Then, the cost of goods sold had been

(a) Rs. 30,000 (b) Rs. 45,000(c) Rs. 35,000 (d) Rs. 25,000

56. A Machinery purchased for Rs. 40,000 and paid Rs. 5,000 on its installation. The useful lifeof plant is 5 years and its estimated scrap value is Rs. 5,000. Annual depreciation under thefixed instalment method would be

(a) Rs. 6000 (b) Rs. 11000(c) Rs. 8000 (d) Rs. 9000

57. Preference shares amounting Rs. 50,000 are redeemed at a premium of 5% by issue of equityshares amounting to Rs. 25,000 at a premium of 10%. The amount to be transferred tocapital redemption reserve

(a) Rs. 75,000 (b) Rs. 25,000(c) Rs. 10,000 (d) Rs. 50,000

58. Account receivable is

(a) A Liability (b) An Asset(c) An Expense (d) A Revenue


59. If total assets of the firm is Rs. 2,00,000; outside liabilities is Rs. 1,60,000, then capitalcontributed by the owner will be

(a) Rs. 60,000 (b) Rs 40,000(c) Rs. 3,60,000 (d) None of the above

60. Sales to Ranjan Rs. 600 was not recorded in the book. This will affect

(a) Ranjan A/c (b) Sales A/c(c) Neither (a) nor (b) (d) Both (a) and (b)


61. Section 27 of the Indian Contract Act states an agreement in restraint of trade is valid ifrelates to

(a) Sale of goodwill(b) Mutual agreement(c) Business contingency(d) All of above

62. An agreement to do an impossible act itself is


63. Which of the following agreements are valid?

(a) Wagering agreements(b) Agreement contingent upon impossible events(c) Uncertain agreements(d) None of the above

64. Which of these are opposed to public policy?

(a) Restraint of marriage(b) Restraint of personal liberty(c) Interference with course of Institute(d) All of the above

65. An illegal agreement is void. However, a collateral transaction to an illegal agreement e.g.money borrowed to carry on an illegal business, is

(a) Void (b) Valid(c) Voidable (d) Uncertain

66. A contract is discharged if it is not performed within the limitation period prescribed bylaw. The limitation period for recovery of money is

(a) 2 years (b) 3 years(c) 4 years (d) 5 years



67. A contingent contract to do or not to do anything, if an impossible event happens, is


68. In case of joint promise, a promisee can compel

(a) All the joint promisors to perform(b) Any one of them to perform(c) Some of them to perform(d) Any of the above

69. Assignment of contract may be by

(a) Operations of law (b) The act of parties(c) (a) or (b) (d) None of the above

70. Contract to marry a person shall be performed by

(a) A third person (b) Promisor himself(c) Representative of the promisor (d) None of the above

71. The right of joint promisees to demand performance is

(a) Joint (b) Several(c) Joint or several (d) Joint and several

72. A bill of exchange which was accepted by X reaches ‘X’s hands after being negotiated andendorsed through 3 other parties. The contract is

(a) Valid (b) Void(c) Discharged (d) Voidable

73. In case of future goods

(a) Only agreement to sell is possible(b) Both sale and agreement to sell is possible(c) They are owned by the seller at the time of sale(d) None of the above

74. The term partnership has been defined under Section

(a) 2 (b) 4(c) 6 (d) 8

75. The leading case laying down the test for determining the existence of a partnership

(a) Powell Vs Lee (b) Hadley Vs B a x end ale(c) Abdul Aziz Vs Masum Ali (d) Chinnaya Vs Ramayya


76. A firm is the name of

(a) The partners(b) The minors in the firm(c) The business under which the firm carries on business(d) The collective name under which partners carry on business.

77. The ratio in which partners share profits and losses are

(a) Based on agreement(b) Based on the contract Act(c) Equal(d) Based on the decision of the registrar of firms.

78. The Partnership Act extends to the whole of India except the state of

(a) Uttar Pradesh (b) Maharashtra(c) Jammu and Kashmir (d) Goa

79. A contract can be discharged?

(a) By operation of law (b) By lapse of time(c) By performance (d) By all of the above

80. On substitution of a new contract, the old contract is discharged is known as ______.

(a) Rescission (b) Novation(c) Alteration of contract (d) Waiver

81. ________ means termination of contract.

(a) Rescission (b) Injunction(c) Specific performance (d) Quantum meruit

82. Where there is breach of contract, special damages are awarded only when _________.

(a) There are special circumstances(b) There is special loss(c) There is notice of the likely special loss(d) In all cases

83. The _________ is empowered to grant exemption from the application of chapter VII of thePartnership Act, 1932 (dealing with registration of firms).

(a) State Government (b) Central Government(c) Local bodies (d) None of the above

84. The goods which have not been identified and agreed upon at the time of contract of sale are_________ goods.

(a) Contingent (b) Future(c) Unascertained (d) Unappropriated



85. Section __________ of the Sale of Goods Act, provides for passing of property in goods whenthere is an unconditional contract in a deliverable state.

(a) 18 (b) 19(c) 20 (d) 21

86. A Quasi – Contract is not a _________ contract.

(a) Real (b) Valid(c) Real and valid (d) Voidable

87. A contract implied by law is known as __________.

(a) Contingent Contract (b) Alternation(c) Quasi Contract (d) Implied contract

88. Implied contract even if not is writing or express words, is perfectly __________ if otherconditions are satisfied.


89. The implied condition as to quality or fitness __________ where the buyer contracts for aspecified article under its patent or other trade name not relying on the spill and judgmentof the seller.

(a) Is presumed (b) Is applicable(c) Is not applicable (d) Does not exist

90. Section __________ of the partnership Act, 1932 deals with partnership at will.

(a) 6 (b) 7(c) 8 (d) 9

91. Co-ownership may arise either by ___________.

(a) Contract or understanding (b) Status or contract(c) Mutual agency (d) Either (a) or (b)

92. Sharing of profits is __________ evidence of existence of partnership.

(a) Collaborative (b) Confirmative(c) Conclusive (d) Not a Conclusive

93. Goods means every kind of immovable property excluding _________.

(a) Stock and shares (b) Growing crops, grass(c) Both (a) and (b) (d) Actionable claims and currency money


94. Where the contingency of event merely indicates the mode or manner of performance, thecontract is not _________.

(a) Valid (b) Void(c) contingent (d) Lawful

95. The event upon which performance of a contingent contract depends must not depend onthe __________ of the promisor.

(a) Will (b) Deeds(c) Rules (d) Principles

96. Section __________ of the Indian Contract Act, states that in order to convert a proposalinto a promise, it is necessary that acceptance must be absolute and unqualified.

(a) 7 (b) 9(c) 10 (d) 11

97. Under Sec. 10 of the partnership Act, every partner shall indemnity the firm for loss causedto it by his __________.

(a) Fraud (b) Error(c) Mistake (d) Misrepresentation

98. Section ____________ of the partnership Act, 1932 deals with “introduction of a partner”.

(a) 21 (b) 31(c) 41 (d) 51

99. A invites ‘B’ to stay with him during winter vacation ‘B’ accepts the invitation and informs‘A’ accordingly when ‘B’ reaches ‘A’ s house he finds it locked and he has to stay in a hotel.Can ‘B’ claim damages from A.

(a) B can claim damages (b) B cannot claim any damages(c) B can file a suit against A (d) None of these

100. ‘A’ and ‘B’, co-owners of a house, let it to a paying guest. They divide the net rents betweenthem. Are they partners?

(a) A and B are partners (b) A and B are not partners(c) A and B are half partners (d) None of these


101. Who said “Economics is a science of dynamic growth and development”?

(a) J. B. Say (b) Paul A. Samuelson(c) Alfred Marshal (d) Robbins

102 Who Said “Economics should be neutral between ends”?

(a) J. B. Say (b) Alfred Marshall(c) Robbins (d) A. C. Pigou



103 If marginal opportunity cost is falling, the PPF would be:

(a) Straight line (b) Concave(c) Backward bending (d) Convex

104 Which of the following would result in a rightward shift of PPF?

(a) An increase in investment in speculative activities by diverting funds from other productiveactivities.

(b) A reduction in unemployment rate(c) The discovery of new gold reserves in the country(d) Increase in number of people taking leisure activities by taking early retirement from their

jobs

105 Calculate Income-elasticity for a household when the income of this household rises by 5%and the demand for buttons does not change at all.

(a) Infinity (b) 1(c) 5 (d) Zero

106 If the goods are perfect substitutes for each other then cross elasticity is

(a) Infinite (b) One(c) Zero (d) None of the above

107 Consumer Surplus is:

(a) What a consumer is ready to pay + what he actually pays(b) What a consumer is ready to pay – what he actually pays(c) What he actually pays - what a consumer is ready to pay(d) None of the above

108 Indifference curve is convex to the origin due to:

(a) Falling MRS (b) Rising MRS(c) Constant MRS (d) None of the above

109 Which of the following is not included in the stages of capital formation?

(a) Savings (b) Mobilisation of Income(c) Mobilisation of Saving (d) Investment

110 Which of the following in correct?

(a) Disinvestment and Privatisation are separate(b) Privatisation is a narrower concept as compared to disinvestment(c) Privatisation and Disinvestment mean the same(d) Disinvestment is a narrower concept than privatisation


111 In 1973-74, the maximum marginal rate of individual income tax was as high as:

(a) 77.9% (b) 97.7%(c) 50% (d) 90%

112 SEZ stands far

(a) Software Economic Zones (b) Special Economic Zones(c) Special Efficiency Zone (d) Software Efficiency Zone

113 FRBMA, 2003 emphasises on the following except:

(a) Revenue-Led Fiscal Consolidation(b) Rationalisation of Tax Regime(c) Improve competitiveness of domestic goods and services in a globalised economic

environment(d) Capital – led fiscal consolation

114 Tax Reform Committee was set up in:

(a) 1992 (b) 1991(c) 1994 (d) 2000

115 Vishesh Krishi Upaj Yojana has been started to:

(a) Promote agricultural production(b) Promote agricultural imports(c) Promote agricultural exports(d) None of the above

116 A minimum capital required by the companies seeking entry into defense production:

(a) Rs 100 crore (b) Rs 10 crore(c) Rs 200 crore (d) Rs 50 crore

117 Economic Reforms in India were started in the year:

(a) 1990 (b) 1991(c) 1992 (d) 1993

118 Which of the following statement is correct?

(a) In 1991 foreign exchange reserves were just sufficient to finance imports of 3 days.(b) In 1991 foreign exchange reserves were just sufficient to finance imports of 3 weeks.(c) In 1991 foreign exchange reserves were just sufficient to finance imports of 3 months(d) In 1991 foreign exchange reserves were just sufficient to finance oil import bill of 3 weeks.

119 DFEC stands far:

(a) Duty Freedom Export Credit (b) Duty Free Export Credit(c) Direct Foreign Exchange Control (d) Duty Free Exchange Credit



120 FIEO Stands for

(a) Federation of Indian Export organisation(b) Federation of Export organisation(c) Foreign Import Export organisation(d) Financial Import Export organisation

121 Rupee was devalued in:

(a) July 1990 (b) July 1992(c) July 1991 (d) July 1994

122 At present there are only _____________ industries for which licensing in compulsory

(a) 6 (b) 10(c) 18 (d) 9

123 At present _____________ industries are reserved for the public sector

(a) 3 (b) 5(c) 7 (d) 8

124 If any country needs funds for long term development of the nation, then the country shouldapproach___________.

(a) World Bank (b) UNO(c) IMF (d) WTO

125 Dematerialisation of TDS certificates will be made effective from:

(a) 1-1-2008 (b) 1-6-2007(c) 1-4-2008 (d) 1-4-2009

126 100% FDI is allowed in

(a) Insurance (b) Banking(c) Hotels and Tourism (d) Defence

127 Which of the following is not the suggestion for improving education system?

(a) Education should be made job oriented(b) Vocational education should be discouraged(c) The standard of education should be raised(d) Expansion of education should be carefully planned since it is costly

128 NIXI stands for:

(a) National Internet Exchange of India(b) New Information Exchange of India(c) National Information Exchange of India(d) Nutrition Information Exchange of India


129 NHPC stand for:

(a) Nuclear Hydroelectric Power Corporation(b) National Hydro Power Corporation(c) National Hydro Public Corporation(d) National Hydroelectric Power Corporation

130 Non-Commercial traditional sources of energy are

(a) Fire wood (b) Dung Cakes(c) Agricultural wastes (d) All of the above

131 Three steel plants in Bhilai, Raurkela and Durgapur were set up in the:

(a) First Plan (b) Second Plan(c) Third Plan (d) Fourth Plan

132 Which of the following statements in correct?

(a) Large number of industries face under utilization of production capacity(b) The incremental capital output ratio has been falling over the planning period(c) Industrial Development is balanced in all regions(d) None of the above

133 Nearly _______ % of labour force is engaged in service sector

(a) 20-25% (b) 25-30%(c) 30-35% (d) 35-40%

134 India has the ________ largest scientific and technical manpower in the world

(a) Third (b) Second(c) Fifth (d) Ninth

135 Small units exist in India because:

(a) They are labour intensive and India is a labour surplus economy(b) They are capital intensive and India is a capital surplus economy(c) They offer method of inequitable distribution of income and wealth(d) None of the above

136 CENVAT was introduced in the year:

(a) 2001-02 (b) 2000-01(c) 2002-03 (d) 2004-05

137 The basic rate of Excise duty is:

(a) 6% (b) 16%(c) 24% (d) None of the above



138 Advalorem duty means duty imposed on the basis of:

(a) Percentage of price of the commodity(b) Per unit on the commodity(c) Both (a) and (b)(d) None of the above

139 We mainly study the following in Micro Economics :

(a) Location of a Industry (b) Study of firms(c) Factor pricing (d) All of the above

140 When we study why saving rates are high or low, we are studying:

(a) Macro Economics (b) Micro Economics(c) Both (a) and (b) (d) None of the above

141 When ______________, we know that firms are earning just normal profits

(a) AR = MR (b) MC = AC(c) MC = MR (d) AC = AR

142 MC curve cuts ______________ curves at their minimum points.

(a) AVC and AC (b) AFC and AVC(c) AC and AFC (d) All the above

143 In perfect competition in the long run there will be___________.

(a) Normal Profits (b) Super Normal Profit(c) Less production (d) Cost will be falling

144 Which of the following statements is correct?

(a) Monopolist can earn only profits(b) Firms in a perfectly competitive market are price maker(c) Industry in a perfectly competitive market is a price taker(d) AR curve and demand curve are same

145 Soap industry is an example of:

(a) Oligopoly (b) Perfect competition(c) Monopolistic competition (d) Monopoly

146 A purely competitive firm’s supply schedule in the short run is determined by:

(a) Its average revenue (b) Its marginal revenue(c) Its marginal cost curve (d) Marginal utility for money curve


147 When price is less than average variable cost at the profit maximizing level of output, a firmshould:

(a) Shut down, since it cannot recover its variable cost(b) Produce where MC = MR, if operating in short run(c) Produce where MC = MR, if operating in long run(d) None of the above

148 A firm encounters its shut down point when:

(a) Average total cost equals price at the profit maximising level of output(b) Average variable cost equals price at the profit maximising level of output(c) Average fixed cost equals price at the profit maximising level of output(d) Marginal cost equals price at the profit maximising level of output

149 In which form of the market structure is the degree of control over the price of its productby a firm is very large?

(a) Imperfect competition (b) Monopoly(c) Oligopoly (d) Perfect competition

150 For the Price taking firm:

(a) Marginal Revenue is less than price(b) Marginal revenue is greater than price(c) The relationship between marginal revenue and price is not clear(d) Marginal revenue is equal to average revenue


151. A fraction is such that if the numerator is multiplied by 3 and the denominator is reduced by3, we get 18/11, but if the numerator is increased by 8 and the denominator is doubled, weget 2/5. Then the fraction is


152. When a number is added to another number the total becomes 150 percent of the secondnumber. What is the ratio between the first and the second number.


153. The sum of three consecutive even numbers is 15 less than three–fourth of 60. What ismiddle number?




154. Five years ago, I was thrice as old as my son and ten years later I shall be twice as old as myson. How old are we now ?


155. The compound ratio of 4: 3, 9:13, 26 : 5 and 2 : 15 is

(a)4

25(b)

16

25

(c)18

27(d) None of these

156. If 56 Pr+6 : 54 Pr+3 = 30800 : 1 then the value of r is


157. When John arrives in New York, he has eight shops to see, but he has times only to visit sixof them. In how many different ways can he arrange his schedule in New York?


158. There are 6 students of whom 2 are Indians, 2 Americans, and the remaining 2 are Russians.They have to stand in a row for a photograph so that the two Indians are together, the twoAmericans are together and so also the two Russians,. Find the number of ways in whichthey can do so.


159. Find the number of different poker hands in a pack of 52 playing cards.

(a) 2598960 (b) 1506210(d) 5298216 (d) None of these

160. Sum of the digits of a two digits number is 9. The number obtained by reversing the order ofdigits of the given number exceeds the given number by 27. Then the given number is


161. Evaluate x x

x x→

−−x 0

9 3lim

4 2

(a)log3

log2 (b) log 3

2⎛ ⎞⎜ ⎟⎝ ⎠

(c) log 6 (d) None of these


162. Evaluate

x 2

e

−+

(5 1)log (1 x)

(a) log 5 (b) (log 5)2

(c) 2log 5 (d) None of these

163. If f(x) = x + 1; for x < 1 and f(x) = 3 – x2; for x > 1 find x 1lim f(x)→

(a) 2 (b) –2(c) Does not exist (d) None of these

164. If f(x) = x–1; if 1 < x < 2 , f(x) = 2x–3; if 2 < x < 3, then given function is

(a) Continuous at x = 2 (b) Discontinuous at x = 2(c) Cannot say (d) None of these

165. The points of discontinuity of the function 2

2

3x 2x 7x 3x + 2

+ +−

is

(a) 1, 2 (b) –1,2(c) 1, –2 (d) None of these

166. Evaluate ∫1

dxx log x

(a)

2xlog log c

2

⎛ ⎞+⎜ ⎟

⎝ ⎠(b) log (log x ) + c

(c) log (log x2 ) + c (d) None of these

167. Evaluate ∫ 10log x dx

(a) log10

(x log x – x) + c (b) log10

e(x log x – x) + c(c) log

10 e(x log x – 10) + c (d) None of these

168. Evaluate −

−

+−∫

x x

x x

4e 6edx

9e 4e

(a) ( )2x 2x3 35log e log 9e 4 c

4 36− + − +

(b) ( )x x x9 36log e log 4e 6e c

8 35−− + + +



(c) ( )x x x3 35log e log 9e 4e c

2 36−− + − +

(d) None of these

169. Evaluate 5 x

dxx 2−−∫

(a) ( )( )2 1 35 x x 2 Cos c

x 2− ⎛ ⎞

− − − +⎜ ⎟⎜ ⎟−⎝ ⎠

(b) ( )( )2 2 1 x 35 x x 2 tan c

3− ⎛ ⎞−− − − +⎜ ⎟⎜ ⎟⎝ ⎠

(c) ( )( ) 1 x 25 x x 2 3 Cos c

3− ⎛ ⎞−− − − +⎜ ⎟⎜ ⎟⎝ ⎠

(d) None of these

170. Evaluate − +∫2(x - 3) x 6x 100 dx

(a) ( )3/221x 6x 100 c

3− + + (b) ( )2/33 21

x 6x 100 c6

− + +

(c) ( )2/33 21x 6x 100 c

3− + + (d) None of these

171. In how many different ways can I invite one or more of my 6 friends?


172. In an examination a candidate has to pass in each of the 4 papers. In how many differentways can be failed?


173. In an election the number of candidates is one more than the number of members to beelected. If a voter can vote in 254 different ways; find the number of candidates.



174. From 17 consonants and 5 vowels, how many words of 3 consonants and 2 vowels can bemade if all the letters are different?


175. A boat is to be manned by 8 men of which 3 can row only one side and 2 only on the other. Inhow many ways can the crew be arranged?


176. Earnings from a new machine after taxes (cost savings or profits) are expected to be Rs.34,000 per year. The machine costs Rs. 1,50,000 and after 5 years, it has no resale value. Aloan can be made for this amount payable in five equal annual instalments at 5% p.a. on theunpaid balance of the loan. Should management buy the machine?

(a) It should not be purchased(b) It should be purchased(c) Cannot determined(d) None of these

177. If simple interest on Rs. 2,000 increases by Rs. 40, when the time increases by 4 years. Findthe rate percent per annum.

(a) 1% (b) 0.5%(c) 2% (d) None of these

178. A man deposits Rs. 2,000 in a bank at 4% per annum and Rs. 3,000 in UTI at 14% perannum. Find the rate of interest for the whole sum.


179. If the simple interest on Rs. 1,200 be more the interest on Rs. 1,000 by Rs. 30 in 3 years. Findthe rate percent per annum.


180. If Simple Interest on Rs. 2,000 increases by Rs. 40, when the rate percent increases by 2%per annum. Find the time (in years)?

(a) 1 (b) 2(c) 1½ (d) None of these

181. The average of 2 numbers is 20 and their Standard Deviation is 5. Find the two numbers.




182. In series of 5 observations, the values of mean and variance are 4.4. and 8.24 respectively. Ifthree observations are 1, 2 and 6 then the value of other two observations are


183. For individual series, the rank of the median is

(a)thN 1

4

+term (b)

thN 1

2

+term

(c)( )th

3 N 1

2

+term (d) None of these

184. Find the rank of the Median in the given series 3, 2, 4, 6, 5, 7

(a) 3.5 (b) 4(c) 4.5 (d) None of these

185. The relation between two variables is 2x + 3y – 10 = 0. If mean of y is 50, then mean of x is


186. The two regression lines are 5x = 22 + y & 64x = 24 + 45y. Find the Standard Deviation of yfrom the given information.

(a) 4 (b) 5(c) Cannot determined (d) None of these

187. Which one of the following is a true statement?

(a) 1/2 (bxy

+ byx

) = r (b) 1/2 (bxy

+ byx

) < r(c) 1/2 (b

yx + b

yx) > r (d) None of these

188. The correlation between two variables x and y is found to be 0.4. What is the correlationbetween 2x and (–y) ?

(a) 0.4 (b) –0.4(c) 0.6 (d) None of these

189. Find the coefficient of correlation between the following set of observation:

X: 69 85

Y: 70 87

(a) 1 (b) -1(c) 0 (d) None of these


190. Find the correlation coefficient between the following set of observation.

X: 102 109

Y: 50 48


191. The normal curve is …………. Shaped.

(a) Bell (b) U–Shaped(c) J–shaped (d) None of these

192. The total area of the normal curve or for that any probability curve is taken to be


193. The two tails of the normal curve extend infinitely on both sides of the curve…………. Thehorizontal axis.

(a) touch (b) never touch(c) either (a) or (b) (d) None of these

194. For a normal distribution with mean 2 and variance 9, find the value of x such that theprobability of the interval (2, x) is 0.4115.


195. For a normal distribution, the first moment about origin is 35 and the second moment about35 is 10. Find the first four central moments.

(a) 5, 10, 0, 100 (b) 10, 6, 0, 200(c) 0, 10, 0, 300 (d) None of these

196. The most commonly used confidence limit is

(a) 90% (b) 99%(c) 95% (d) 99.73%

197. Sample mean is a

(a) Parameter (b) Statistic(c) Both (d) None of these

198. Deliberate sampling is a

(a) Random sampling (b) Non – random sampling(c) Both (a) and (b) (d) None of these



199. Stratified random sampling is used for ……….. Population.

(a) Homogeneous (b) Non–homogeneous(c) Either (a) or (b) (d) None of these

200. Random sampling is also called lottery sampling.

(a) False (b) True(c) Both (d) None of these

❖❖❖

BOARD OF STUDIES







135


1. What is the important object of accounting?

(a) To maintain records(b) Depiction of financial position(c) Make information available to various groups and users.(d) All of the three

2. A collateral security of 8,000 10% Debentures of Rs.10 each has been issued at a premiumof 25% to A in lieu of a loan of Rs.1,00,000 taken on 1st January, 2006. At the end of the year,interest was paid on:

(a) The nominal value of debentures(b) The amount of loan outstanding(c) Difference of loan amount and nominal value of debentures(d) None of the above

3. Income is measured on the basis of

(a) Matching concept (b) Consistency concept(c) Cost concept (d) None of the above

4. Which of the following is long-term liability?

(a) Outstanding Expenses (b) Share Capital(c) Debenture (d) All of the above




5. Drawing is a type of

(a) Expenses (b) Withdrawal of Capital(c) Income (d) None of the above

6. The most common method of supplementing the capital available to a company is

(a) To issue debentures (b) To issue preference shares(c) To issue equity shares (d) None of the above

7. Which of the following is not an Intangible Asset?

(a) Investment (b) Goodwill(c) Copyright (d) Patents rights

8. The Enterprise is liable to the owner for capital investment made by the owner as per

(a) Entity concept (b) Money measurement concept(c) Accrual concept (d) Going concern concept

9. Which of the following is not a valuation Principle?

(a) Market Value (b) Future Value(c) Historical Value (d) All of the above

10. Purchase of office equipment on credit will lead to

(a) Decrease in Capital (b) Decrease in Liability(c) Increase in Assets (d) All of the above

11. Decrease in the amount of Creditors result in

(a) Decrease in Cash (b) Increase in Liability(c) Increase in Cash (d) None of the three

12. Trial Balance is a

(a) Final Account (b) Statement of day books(c) Subsidiary book (d) None of the above

13. When overdraft as per Cash Book is the starting point then wrong debit in pass book will be

(a) Deducted from the Bank Reconciliation Statement(b) No effect in the Bank Reconciliation Statement(c) Added in the Bank Reconciliation Statement(d) None of the three

14. Profit is a part of

(a) Income (b) Owner’s Capital(c) Assets (d) All of the above


15. Journal is books of

(a) All cash transactions only (b) All credit transactions only(c) Secondary entry (d) Original entry

16. Balance of Petty Cash Book is posted to ledger

(a) In the Bank a/c (b) In the Cash a/c(c) Nowhere (d) Both (a) and (b)

17. Petty Cash is used for payment of

(a) Salaries & wages of the staff(b) For purchase of assets(c) Small expenses relating to postages and conveyance etc.(d) All of the above

18. When a cheque is returned dishonoured, it is recorded on

(a) Bank column on the Debit side (b) Bank column on the Credit side(c) Cash column on the Credit side (d) None of the above

19. Promissory note is prepared by

(a) Drawer (b) Endorsee(c) Drawee (d) All of the above

20. Which of the following instrument is not a negotiable instrument

(a) Crossed cheque (b) Bill of exchange(c) Promissory note (d) Bearer cheque

21. Inventories are valued at lower of cost or net reliable value by applying the principle of

(a) Conservatism (b) Consistency(c) Materiality (d) Disclosure

22. Arti places an order to Anju for supply of certain goods yet to be manufactured. On receiptof order, Anju purchases raw materials, employs workers, produced the goods and deliveredthem to Arti. In this case sale will be presumed to have been made at the time of

(a) Production of goods (b) Delivery of goods(c) Purchase of material (d) None of the above

23. Ratan deposited a cheque on 25 January, 2006 for a sum of Rs. 20,000. The cheque wascollected on 2 February, 2006. If the bank balance as per passbook as on 31 January, 2006 isRs. 60,000; balance as per cash book will be

(a) Rs. 60,000 (b) Rs. 40,000(c) Rs. 70,000 (d) Rs. 80,000



24. The company charge interest on call in arrear at

(a) 5% (b) 10%(c) 15% (d) 20%

25. The maximum amount of capital that a company can raise is called

(a) Authorised capital (b) Subscribed capital(c) Issued capital (d) Called-up capital

26. Manish & Co. Ltd. forfeited 100 shares of Rs. 10 each, Rs. 8 called up, Rs. 4 paid onapplication; the amount to be forfeited is

(a) Rs. 800 (b) Rs. 400(c) Rs. 600 (d) Rs. 200

27. In the absence of any agreement, the partners are entitled to interest on the loan advancedto the firm at the rate of

(a) 5% (b) 7%(c) 6% (d) 8%

28. Calculate gross profit if rate of gross profit is 25% on sales and cost of goods are Rs.1,80,000

(a) Rs. 60,000 (b) Rs. 36,000(c) Rs. 45,000 (d) Rs. 30,000

29. Cost of motor Rs. 2,00,000, scrap value Rs. 20,000. Useful life 4 years. What will be amountof depreciation according to sum of years digit method in the first year?

(a) Rs. 72,000 (b) Rs. 1,08,000(c) Rs. 80,000 (d) Rs. 1,20,000

30. An asset has a useful life of 4 years. If it is depreciated by diminishing balance method. Itsbook value at the end of 4 years is 24% of its original cost. Hence the rate of depreciationapplied is

(a) 20% (b) 30%(c) 25% (d) 35%

31. Valuation of inventory is dealt within

(a) AS-2 (b) AS-3(c) AS-4 (d) AS-5

32. Consider the following items(1) Prepaid Salary (2) Accrued Interest

(3) Loan (4) Bank overdraftCurrent Liability would include

(a) 1,2,3,4 (b) 2,3,4(c) 4,3,1 (d) 3,4,


33. B’s trial balance contains the following information-

Make provision at the end of the year Rs. 10,000Provision for bad debts at thebeginning of the year Rs. 4,000Bad Debts Rs. 6,000The amount to be debited to Profit & Loss A/c

(a) Rs. 20,000 (b) Rs. 8,000(c) Rs. 12,000 (d) NIL

34. A trial balance at 31st March contains the following information: 15% Loan Rs. 30,000;Interest paid Rs. 3,000 ; Interest debited to the P & L A/c is

(a) Rs. 1,500 (b) Rs. 4,500(c) Rs. 6,000 (d) Nil

35. Total operating expenses 30,000; total direct expenses Rs.10,000; Miscellaneous incomeRs.5,000 the gross profit will be

(a) Rs. 25,000 (b) Rs. 20,000(c) Rs. 15,000 (d) Rs. 10,000

36. X and Y entered into a joint venture sharing profits and Losses equally. X provides goodsfrom his stock Rs. 20,000. He pays expenses amounting to Z 20,000. Y incurs further expenseson carriage Rs. 3,000. He received cash for sales Rs. 35,000. He also takes over goods to thevalue of Rs. 5,000. What will be the amount to be remitted by Y to X?

(a) Rs. 29,500 (b) Rs. 35,000(c) Rs. 7,500 (d) Rs. 22,000

37. Ram and Shyam entered into a Joint venture for equal profits. Ram purchases goods costingRs. 70,000. Shyam sold goods costing Rs. 60,000 at Rs. 80,000. Balance goods were takenover by Ram at same gross profit percentage as in case of sale. The value of goods taken overwill be

(a) Rs. 10,000 (b) Rs. 13,333(c) Rs. 3,333 (d) Rs. 23,333

38. Guarantee given to a partner Mohan by the other partner Suresh and Mahesh means

(a) In case of Loss or insufficient profit ‘Mohan’ will withdraw the minimum guaranteedamount

(b) In case of Loss ‘Mohan’ will not contribute towards that loss(c) Even in case of sufficient profit ‘Mohan’ will receive only the minimum guaranteed amount(d) None of the above



39. Naresh is drawing Rs. 2,000 per month at the end of the month. If the rate of interest is 10%p.a. the total interest chargeable from him in the accounting year will be


40. In the absence of any agreement, partners are entitled to

(a) Share Profit in capital ratio(b) Interest on capital(c) Salary on capital(d) Interest on loans and advances gain to the firm

41. Interest on capital will be paid to the partners if provided for in the agreement but only from

(a) Goodwill (b) Current profit(c) Reserves & Surplus (d) Accumulated profit

42. Sita and Gita are partners sharing ratio of 3:2 (Sita’s capital Rs. 6,000 and Gita’s capital Rs.3,000). They admitted Rita for 1/5th share of profit . How much Rita should bring towardher capital?

(a) Rs 2,250 (b) Rs. 3,000(c) Rs. 1,800 (d) Rs. 6,000

43. As per table A of the companies Act, 1956, a company pays interest on call in advance at therate of

(a) 4% (b) 5%(c) 6% (d) 7%

44. As per table A of the companies Act 1956, a Company can charge interest on call in arrearsat the rate of

(a) 5% (b) 6%(c) 7% (d) 8%

45. A share of Rs. 200 each issued at discount of 10% is forfeited for non-payment of final call @Rs. 50 per share. The maximum loss it can bear in the re-issue of shares will be

(a) Rs. 200 (b) Rs. 50(c) Rs. 20 (d) Rs. 70

46. If on a share of Rs. 50, only Rs. 40 has been called and the company has received Rs. 30 tilldate. The capital account should be credited with

(a) Rs. 50 (b) Rs. 30(c) Rs. 40 (d) Rs. 20


47. There are 60,000 preference share of Rs. 10 each fully called up. But there are call in arrearsof Rs. 4,000 @ Rs. 2 per share. Company can redeem at present

(a) 60,000 shares (b) 56,000 shares(c) 58,000 shares (d) None of the above

48. A company cannot issue redeemable preference shares for a period exceeding


49. Preference shares amounting to Rs. 75,000 are redeemed at a premium of 5% by issue ofequity shares amounting to Rs. 40,000 at a premium of 10%. The amount to be transferredto capital redemption reserve account will be

(a) Rs. 35,000 (b) Rs. 36,750(c) Rs. 38,500 (d) Rs. 1,15,000

50. Lal & Co. Ltd. has issued 15% debentures on 1st January, 2004 for Rs. 2,00,000. Interest ifpayable on 31st March and 30th September every year. Amount of outstanding interest on31st December, 2005 will be

(a) Rs. 7,500 (b) Rs. 30,000(c) Rs. 15,000 (d) Rs. 22,500

51. Loss on issue of Debentures is generally written off in

(a) 10 years (b) 8 years(c) Over the period of redemption (d) 15 years

52. Depreciation is provided on

(a) Fixed Assets (b) Current Assets(c) Liquid Assets (d) Fictitious Assets

53. A fixed assets costing Rs. 60,000 has an estimated life of 8 years. At the end of its useful lifeit can be sold for Rs. 12,000. Using the fixed instalment method, the annual depreciationagainst profit will be

(a) Rs. 9,000 (b) Rs. 6,000(c) Rs. 12,000 (d) Rs. 10,000

54. At what price goods pending approval or return as on the last day of accounting year arevalued

(a) Cost price (b) Selling price(c) Average price (d) Latest price

55. Rent paid to Landlord amounting to Rs. 1,000 was credited to rent account with Rs. 10,000.In the rectifying entry rent a/c will be debited with

(a) Rs. 11,000 (b) Rs. 1,000(c) Rs. 9,000 (d) Rs. 10,000



56. Sales to A of Rs. 600 not recorded in the books would affect

(a) Sales A/c (b) A’s A/c(c) Cash A/c (d) Sales A/c and A’s A/c

57. X draw an accommodation bill on Y for Rs. 7,000. The proceeds are to be shared by X and Yin the ratio of 3:2. The bill was discounted for Rs. 6,700. Discount borne by X will be

(a) Rs. 120 (b) Rs. Nil(c) Rs. 300 (d) Rs. 180

58. When overdraft as per cash book is the starting point, Bank charges of Rs. 300 recordedtwice in the passbook will be

(a) Added by Rs. 300 (b) Deducted by Rs. 300(c) Deducted by Rs. 600 (d) Added by Rs. 600

59. Ram send 50 fans to Shyam costing Rs. 500 per fan to be sold at 20% above cost price. Salesvalue will be

(a) Rs. 25,000 (b) Rs. 20,000(c) Rs. 30,000 (d) Rs. 31,250

60. If capital at the end of the year is Rs. 40,000; capital introduced during the year Rs. 30,000;Drawings for the year is Rs. 20,000 and Loss of the year is Rs. 60,000 then capital at thebeginning of the year was

(a) Rs. 90,000 (b) Rs. 80,000(c) Rs. 70,000 (d) Rs. 10,000


61. Which of the following is correct? When a minor has been supplied with necessaries oncredit.

(a) Minor is not liable (b) Minor’s estate is liable(c) Minor is personally liable (d) Minor is liable at his option

62. Which one of the following is not a wagering agreement?

(a) A lottery(b) An agreement to buy a ticket for a lottery(c) Commercial transaction, the intention of which is not to deliver the goods but only to pay

the difference in price(d) A contract of insurance

63. Which of the following persons are not competent to contract?

(a) Person of Indian origin (b) Person disqualified by law(c) Minor (d) Person of unsound mind


64. Which are the following elements that affect the consent of the party?

(a) Undue Influence (b) Representation(c) Fraud (d) Coercion

65. Which of the following agreements are void?

(a) Agreements the consideration of which is unlawful(b) Agreements made under the unilateral mistake of fact(c) Agreements made under the bilateral mistake of fact(d) Contingent agreement

66. Vindictive Damages are awarded

(a) For wrongful dishonour of cheque by a banker(b) For a breach of promise to marry(c) Neither (a) nor (b)(d) Either (a) or (b)

67. In which of the following situations specific performance can be granted?

(a) When there is no exact substitute or alternative to the subject matter of the contract(b) When it is probable that compensation in money cannot be got for non-performance(c) (a) or (b)(d) (a) and (b)

68. Which of the following statements is not correct?

(a) Ordinary damages are recoverable(b) Special damage are recoverable only if the parties knew about them(c) Remote or indirect damages are not recoverable(d) None of these statements is incorrect

69. An agreement between the bidders not to bid against each other is called

(a) Knock –out agreement (b) Auction agreement(c) Partnership agreement (d) By bidder agreement

70. Under Section 61 of the Sale of Goods Act, a court can award interest

(a) At the rate of 12% (b) At the rate of 8%(c) At the rate of 6% (d) At the rate as it thinks fit

71. An auction sale may be

(a) Conditional (b) Unconditional(c) voidable (d) None of the above

72. The bidder at an auction sale can withdraw his bid

(a) Any time during auction (b) Before fall of hammer(c) Before payment of price (d) None of these



73. Transfer of property in goods sent on approval take place when

(a) Buyer signifies his approval(b) When he makes the return by goods impossible(c) When he retains goods without signifying approval for unreasonably long time(d) All of the above

74. If the goods are not in existence (not produced at the time of agreement to sell), goods are tobe delivered at

(a) The place at which they are manufactured or produced(b) The buyer place(c) The sellers place(d) None of the above

75. A buyer is deemed to have accepted the delivery of goods

(a) When it is in accordance with the terms of the contract(b) When seller is ready but not willing for giving the possession of the goods(c) When the seller delivers the goods at the place at which they are at time of sale(d) All of the above

76. The property in the goods means the

(a) Ownership of goods (b) Possession of goods(c) Custody of goods (d) Both (b) and (c)

77. In case of a hire - purchase the hirer

(a) Can pass a goods title to a bona fide purchaser(b) Can choose whether to pass or not to pass the goods(c) Cannot pass a goods title to a bona fide purchaser(d) All of the above

78. Nemo-dat quad non habit means

(a) Result to pay the price of goods(b) Nobody can give that the himself does not have(c) Title is not clear(d) Delivery is not possible

79. If the consent is caused by coercion is to be proved by

(a) Both the parties (b) The aggrieved party(c) The party causing coercion (d) None of these

80. In case of reciprocal promise, first to do things which are legal are ________ and second todo things which are illegal are ________.

(a) Valid, void (b) Void, voidable(c) Valid, illegal (d) Void, void


81. All agreements in restraint of trade are ________.


82. Doctrine of restitution does not apply against a ________.

(a) Person of unsound mind (b) Fraud(c) Minor (d) None of the above

83. In the absence of a contract to contrary, the ___________ is under a duty to apply for deliveryof goods.

(a) Seller (b) Buyer(c) Bailee (d) No body

84. Compensation shall not be given for any remote and indirect loss sustained by reason ofbreach it is ___________.


85. The partner who does not take part in the conduct of the business is known as _______.

(a) Sub-partner (b) Nominal partner(c) Sleeping partner (d) All of the above

86. The term promisor and promisee has been defined in __________ of the Indian ContractAct.

(a) Section 2(a) (b) Section 2(b)(c) Section 2(c) (d) Section 2(d)

87. When all partners, or all but one partner, of the firm are declared insolvent then ______.

(a) Firm is automatically dissolved(b) Firm is also declared insolvent(c) Solvent partner has to repay the debts of the firm(d) None of the above

88. If the agreement contains a basis for ascertaining the meaning of vogue term, the agreementis ________ on the ground of its being vague.

(a) Valid (b) Void(c) Not Void (d) Voidable

89. Promissory estoppel is sometimes spoken of as a substitute for _______.

(a) Novation (b) Quasi contract(c) Consideration (d) Coercion



90. The property in the goods means _________.

(a) The possessing of goods (b) Custody of goods(c) Ownership of goods (d) Both (a) and (b)

91. Deliverable state is defined in Section_________.

(a) 2(1) (b) 2(2)(c) 2(3) (d) 2(4)

92. When buyer repudiates the contract before the date of delivery the seller may _________.

(a) Sue for damages (b) Sue for price(c) Rescind the contract (d) None of the above

93. A partnership at will is on __________.

(a) Which does not have any deed(b) Which does not have any partner(c) Which does not provide for how long the business will continue(d) Which cannot be dissolved

94. Partner by holding out is_________.

(a) A person representing himself to be a partner of the firm by words spoken or written or byhim conduct

(b) Partner of a firm but the outsiders do not know him as such(c) Partner of a partner of a firm(d) Partner of a firm but does not take part in the business of the firm

95. Active partner is one who _______.

(a) Actively takes part in the business of the firm(b) Actively participate in co-curricular activities(c) Actively shares the profits(d) Makes a show of authority

96. The term possession of goods refers __________.

(a) Ownership of goods (b) Custody of goods(c) Transfer of goods (d) Property in real estate

97. Right of unpaid seller, as to stoppage in transit has been provided in ___________ of the Saleof Goods Act.



98. Where a corporation enters into a contract beyond the scope of the objects, such a contractis said to be ___________.

(a) Intra Vires (b) Ultra Vires(c) Ultimo Vires (d) Infra Vires

99. ‘A’ and ‘B’ were two partners in a firm of sugar dealers. Unknown to ‘B’ ‘A’ supplies at aparticular time his own stock of sugar to the firm at market price and makes profit. Decidewhether

(a) ‘A’ can personally keep this profit(b) ‘A’ cannot keep this profit(c) A can keep half of profit(d) A can keep one fourth of profit

100. ‘A’ polished ‘B’ shoes without being accepted by ‘B’ to do so. ‘B’ does not make any attemptto stop ‘A’ from polishing the shoes. Decide.

(a) B is bound to pay(b) B is not bound to pay(c) B is bound to pay damages any incurred by A(d) None of these


101. In Micro Economics we study the Economic behaviour of:

(a) An Individual (b) Firm(c) Industry (d) All of the above

102. Which of the following statements is correct?

(a) As normative science, Economics involves value judgments(b) Robbins has made economics as a form of welfare economics(c) The Law of Demand is always true(d) None of the above

103. An economy achieves “ productive efficiency” when:

(a) The best quality goods are produced(b) The highly skillful resources in the country are fully employed(c) All resources are utilized and goods and services are produced at least cost(d) None of the above

104. Economic goods are goods which:

(a) Cannot be increased in quantity(b) Obey the law of Micro Economics(c) Are limited in supply and are scarce(d) Are limited to man-made goods.



105. Which of the following means an Economic activity?

(a) Production of Goods(b) Production of Services(c) Consumption of Goods and Services(d) All of the above

106. Which economy is now a myth only, as no country in the world is having that type of economy?

(a) Capitalist Economy (b) Socialist Economy(c) Mixed Economy (d) None of the above

107. If the proportion of income spent on a goods decreases as income rises then income elasticityis:

(a) Greater than one (b) Less than one(c) One (d) Zero

108. If two goods are totally unrelated, then cross elasticity between them is:

(a) Zero (b) One(c) Infinite (d) None of the above

109. The income of a household rises by 20 percent, the demand for computer rises by 50%, thismeans computer is a/an:

(a) Inferior good (b) Luxury good(c) Necessity (d) None of the above

110. Which of the following is considered production in Economics?

(a) Teaching CA students in CA Institute by a teacher(b) Singing a song before friends(c) Flying kite for pleasure(d) Teaching to friends in a library any concept of Economics

111. The following is not the characteristic of Land:

(a) Land varies in fertility and uses(b) Land is highly immobile(c) The supply of land is perfectly elastic from the point of view of the economy(d) The supply of land is perfectly inelastic from the point of view of the economy

112. Fiscal Policy is given by:

(a) Ministry of Finance (b) RBI(c) Planning Commission (d) Parliament

113. In India, except in the Election year, Budget is given on:

(a) Last day of March (b) 1st day of April(c) 1st January (d) Last day of February


114. SDR stands for:

(a) Security Drawing Rights (b) Super Drawing Rights(c) Systematic Drawing Rights (d) Special Drawing Rights

115. PTA stands for:

(a) Plurilateral Trade Agreements(b) Private Trade Agreements(c) Plurilateral Transaction Agreements(d) Public Trade Agreements

116. The number of members of WTO are (as on 11.1.2007)

(a) 177 (b) 184(c) 150 (d) 177

117. International Finance Corporation comes under:

(a) WTO(b) World Bank(c) IMF(d) United Nation Development Associations

118. Which of the following is not the function of World Bank?

(a) To help its member countries in the reconstruction and development of their territories(b) To provide finance for long-term purposes(c) To provide finance for short-term purposes(d) To encourage private foreign investment and credit by providing guarantee of repayment

of private industries

119. IBRD (World Bank) was set up in:

(a) 1946 (b) 1947(c) 1945 (d) 1919

120. Fiscal Deficit minus borrowings and other liabilities is equal to:

(a) Revenue Deficit (b) Primary Deficit(c) Capital Deficit (d) Budget Deficit

121. An increase in SLR will result in

(a) An increase in revenue deficit (b) A decrease in revenue deficit(c) An increase in fiscal deficit (d) No change in fiscal deficit

122. Under which of the following tax system, more tax is imposed on the lower income group?

(a) Regressive (b) Progressive(c) Value Added Tax (d) Proportional Tax



123. Open market purchase of government bonds by RBI will have the tendency to:

(a) Decrease interest rates, but increase money supply(b) Decrease interest rates, but decrease money supply(c) Increase interest rates, but increase money supply(d) Increase interest rates, but decrease money supply

124. Banks rate means:

(a) Rate of interest paid by banks to depositors(b) Rate below which banks cannot lend money to borrowers(c) Rate of interest charged by RBI on its loan to other commercial banks(d) Rate of interest charged by commercial banks for loan given to RBI

125. When prices are rising and there is unemployment and recession in the economy, then thephenomenon is called:

(a) Inflation (b) Stagflation(c) Deflation (d) Reflaction

126. When too much money chases too few goods the resulting inflation is called:

(a) Deflation (b) Cost-push inflation(c) Stagflation (d) Demand-pull inflation

127. NLM stands for:

(a) National Leprosy Mission (b) National Law Mission(c) National Logistic Mission (d) National Literacy Mission

128. Over the year, the incidence of malaria has _____________

(a) Increased (b) Reduced(c) Remained the same (d) Doubled

129. Who is regulatory authorities for securities market in India?

(a) RBI (b) SEBI(c) TRAI (d) BSE

130. Postal network in India is __________ in the world.

(a) Third largest (b) Second largest(c) Largest (d) Tenth largest

131. Which year is known as year of great divide for Indian population?

(a) 1911 (b) 1921(c) 1931 (d) 1941

132. India is passing through ___________ stage of Demographic Transition.

(a) Fourth (b) First(c) Second (d) Third


Use following table to answer questions 133-136.

Quantity Variable Cost Fixed Cost Total Cost AVC ATC MC

0

5 25

10 470

15 700

20 980

25 1350

30 1850

35 2520

40 3400

45 4530

50 5950

A firm operating in perfect competition sells as much as of its products as it chooses at a marketprice of Rs. 100 per unit. It Fixed cost is Rs. 300 and its Variable cost for different levels ofproduction are shown in the above table

133. When production is 40 units, the average cost is:

(a) Rs. 4.40 (b) Rs. 7.50(c) Rs. 85 (d) Rs. 92.50

134. In the table, marginal cost per unit that corresponds to 40 units of production is:

(a) Rs. 22 (b) Rs. 85(c) Rs. 176 (d) Rs. 880

135. To maximize profit the firm should produce:

(a) 15 units (b) 30 units(c) 35 units (d) 50 units

136. If the market price drops from Rs. 100 to Rs. 56 per unit, the firm’s short run responseshould be

(a) Shut down(b) Produce 5 units(c) Produce 20 units(d) Continue to produce the same number of units as before the drop in price



Use following table to answer questions 137 to 138

Hours of Labour Total Output Marginal Product

0

1 200 200

2 - 160

3 480 -

137. What is the total output when 2 hours of Labour are employed?

(a) 160 (b) 200(c) 360 (d) 400

138 What is the marginal product of the third hour labour?

(a) 120 (b) 160(c) 200 (d) 480

Use table to answer question 139-142

Mohan sweets is a small restaurant and a price taker. The table below provides the data of Mohan’sSandwich output and costs in Rupees

Quantity TC TFC TVC AVC AC MC

0 100

10 210

20 300

30 400

40 540

50 790

60 1060

139. If Sandwiches are being sold for Rs. 14 each, what is Mohan’s profit maximising level ofoutput?

(a) 10 Sandwiches (b) 40 Sandwiches(c) 50 Sandwiches (d) 60 Sandwiches

140. What is the total variable cost when 60 sandwich are produced?

(a) Rs. 690 (b) Rs. 960(c) Rs. 110 (d) Rs. 440


141. What is average fixed cost when 20 sandwiches are produced?

(a) Rs. 5 (b) Rs. 3.33(c) Rs. 10 (d) Rs. 2.5

142. Between 10 to 20 sandwiches, what is the marginal cost per sandwich?

(a) Rs. 11 (b) Rs. 13(c) Rs. 14 (d) Rs. 9

143. In July, 1991 Indian devalued the rupee by about:

(a) 19% (b) 29%(c) 13% (d) 9%

144. The marginal product of a variable input is best described as:

(a) Total product divided by the number of units of variable input(b) The additional output resulting from a one unit increase in the variable input(c) The additional output resulting from a one unit increase in both the variable and fixed

inputs(d) None of the above

145. Which of the following is the most profitable, but least liquid asset of a commercial bank?

(a) Loan and advances(b) Money at call and short notice(c) Bills discounted and purchased(d) Investment in Government securities

146. In the short run, when the output of a firm increases its average fixed cost:

(a) Increases(b) Decreases(c) Remains constant(d) First declines then rise

147. Contraction of demand is the result of:

(a) Decrease in the number of consumers(b) Increase in the price of the goods concerned(c) Increase in the price of other goods(d) Decrease in the income of purchases

148. The indifference curve approach assumes:

(a) Rationality (b) Consistency(c) Transitivity (d) All of the above



149. According to the 2001 census the total literacy rate is:

(a) 32.5% (b) 52.1%(c) 65.4% (d) 75.8%

150. The Telephone penetration rate in India is _________ per 100 population.

(a) 11.32 (b) 15.34(c) 25.56 (d) 19.22


151. If one-fifth of one-third of one-half of number is 15, then number is


152. Three-fourth of one–fifth of a number is 60. The number is


153. Four-fifths of three-eighths of a number is 24. What is 25% of that number?

(a) 100 (b) 160(c) 1120 (d) 200

154. If the sum of a number and its square is 182, what is the number?


155. The sum of the digits of a two digit number is 12. If the digits are reversed, the number isdecreased by 18. Find the number.

(a) 75 (b) 93(c) 84 (d) 57

156. A bag contains rupee, 50 paise and 25 paise coins in the ratio 10:14:18. If the total amount inthe bag is Rs. 430, find the number of coins of each kind.

(a) 200, 280, 360 (b) 280, 200, 360(c) 360, 280, 200 (d) None of these

157. Two vessels contain equal quantity of mixtures of milk and water in the ratio 5:2 and 6:1respectively. Both the mixtures are now mixed thoroughly. Find the ratio of milk to water inthe new mixture so obtained.



158. The vessels contain water and milk in the ratio 1:2 and 2:5 are mixed in the ratio 1:4. Theresulting mixture will have water and milk in the ratio.


159. The ratio of the incomes of two persons is 9:7 and the ratio of their expenditures is 4:3. Ifeach of them saves Rs. 200 per month, then their monthly incomes.

(a) Rs. 1,800, Rs. 1,400 (b) Rs. 1,600, Rs. 1,200(c) Rs. 1,400, Rs. 1,200 (d) None of these

160. An amount of Rs. 950 is distributed among A, B & C in the ratio of 5:11:3, what is thedifference between the share of B and A.


161. Evaluate − −

→

−−

x 1

x 1

e elim

x 1

(a)1

e(b)

1

e

−

(c) e (d) None of these

162. Evaluate →

−x

x 0

(1 + x) 1lim

x

(a)1

n(b) –n

(c) n (d) None of these

163. Evaluate 5/3 5/3

→

−−x 0

(x + 2) (a + 2)lim

x a

(a)2/35

(a 2)3

+ (b)1/35(a 2)

3

+

(c)1/25

(a 2)3

+ (d) None of these



165. Evaluate x x

→

−x 0

2 3lim

x

(a) log 6 (b) log 2

3⎛ ⎞⎜ ⎟⎝ ⎠

(c) log 3

2(d) None of these

166. If f’(x) = 3x2 + 2 & f(0) = 0 then find f(2).


167. Evaluate +

+ +∫ 2

x 3dx

x 6x 4

(a) ( )21log x 6x 4 c

2+ + + (b) ( )21

x log x 6x c c2− + + + +

(c) ( )1log x 3 c

2+ + (d) None of these

168. Evaluate ( )x

3e−+∫

x 1dx

x 1

(a) 2

exc

(x 1)+

+ (b) x2 + log (ex + 1) + c

(c) (x + 1)2 + log (ex + 1) + c (d) None of these

169. Evaluate ( +∫43x 5) dx

(a)5(3x 5)

c3

+ + (b)5(3x 5)

c15

+ +

(c)4(3x 5)

c15

+ + (d) None of these


170. Evaluate +∫ 7x 5 dx

(a)3/22

(7x 5) c21

+ + (b)3/21

(7x 5) c21

+ +

(c) (7x + 5)3/2 + c (d) None of these

171. Three gentlemen and three ladies are candidates for two vacancies. A voter has to vote fortwo candidates. In how many different ways can one cast his vote?


172. In a party of 40 people, each shakes hand with others. How many handshakes took place inthe party?


173. How many different triangles can be formed joining the angular points of a polygon of msides?

(a)m(m 1)(m 2)

6

− −(b)

m(m 1)

2

−

(c) m (d) None of these

174. How many different cricket teams of 11 players can be selected from 14 cricket players ofwhich only two can play as wicketkeeper? Given each team must have exactly onewicketkeeper?


175. Mr. X has 8 children of which he takes 3 at a time to the circus. Find, how many times aparticular child goes to the circus?


176. If ax = by = cz and x, y, z are in G.P. then log a, log b and log c are in

(a) A.P. (b) G.P.(c) A.P. and G.P. both (d) None of these



177. The 6th term from the end of the G.P. 8, 4, 2, 1, ………………………….,1

1,024 is

(a)1

64(b) 32

(c)1

32(d) None of these

178. In a finite G.P., the product of two terms equi distant from the beginning and from the end isequal to the product of the first and the last term of the G.P. This statement is

(a) True (b) False(c) Cannot say (d) None of these

179. If a, b, c are in G.P., a, x, b and b, y, c are both in A.P., then +a cx y is equal to


180. If a, b, c are in G.P., a, x, b and b, y, c are both in A.P., the value of +1 1x y is

(a)1

b(b)

2

b

(c)2

b− (d) None of these

181. The number of times a particular item occurs in a given data is called its

(a) Variation (b) Frequency(c) Cumulative frequency (d) None of these

182. The width of each of ten classes in a frequency distribution is 2.5 and the lower class boundaryof the lowest class is 10.6. Which one of the following is the upper class boundary of thehighest class?



183. Let L be the lower class boundary of a class in a frequency distribution and m be the midpoint of the class. Which one of the following is the higher class boundary of the class?

(a)m 2

m2

++ (b)m L

L2

++

(c) 2m – L (d) m – 2L

184. The mean of the values of 1, 2, 3 …………, n with respective frequencies x, 2x, 3x, ……… nxis

(a)n 1

2

+(b)

n

2

(c)2n 1

3

+(d)

2n 1

6

+

185. The mean of four observations is 10 and when a constant a is added to each observation, themean becomes 13. The value of a is


186. For the bivariate data [(x, y)] = [(20,5), (21,4), (22,3)], the correlation coefficient between xand y is

(a) 0 (b) 1(c) –1 (d) 0.5

187. For a (m×n) classification of bivariate data, the maximum number of conditional distributionsis

(a) q (b) p+q(c) pq (d) p

188. The regression of y on x is 2y + 3x = 4 and the correlation coefficient between x and y is 0.8.This statement is


189. The correlation coefficient of 3x and –2y is the same as the correlation coefficient Of x and y.This statement is


190. When the correlation coefficient r = ± 1, then the two repression lines are

(a) Perpendicular to each other (b) Coincide(c) Parallel to each other (d) Do not exist



191. In a binomial distribution with 6 independent trials, the probability of 3 and 4 successes isfound to be 0.2457 and 0.0819 respectively. Find the parameters p and q of the binomialdistribution.

(a)2 1

,13 13

(b)4 9

,13 13

(c)5 2

,13 13

(d) None of these

192. E (x.y) = E(x). E(y), where x and y are independent random variables. This is


193. Probability distribution is known as theoretical distribution. This is

(a) False (b) True(c) Either (a) or (b) (d) None of these

194. Mean of the probability distribution of random variable x is

(a) E(x) (b) E(x2)(c) E(x)2 (d) None of these

195. An attempt to produce a particular outcome which is neither certain nor impossible is called.

(a) Event (b) Trial(c) Sample Space (d) None of these

196. Which measure of dispersion has some desirable mathematical properties?

(a) Standard Deviation (b) Mean Deviation(c) Q.D. (d) None of these

197. If ;+ + +x 1 y y 1 x = 0 then 2( )

dy1 + x

dx is equal to


198. If y = x ( )+ +2 2x +1 log x x +1 then dydx

is equal to

(a) 2x 1+ (b) 2 x 1+(c) 22 x 1+ (d) None of these


199. If y = aemx + be–mx then 2

2

d ydx

is

(a) my (b) m2y2

(c) m2y (d) None of these of these

200. If 12C5 + 2 12C4 + 12C3 = 14Cx then the value of x is:

(a) 5 (b) 9(c) 5 or 9 (d) None of these

❖❖❖

BOARD OF STUDIES








163


1. Consignment Account is


(c) Nominal A/c (d) Both (a) & (b)

2. Bills receivable is….


(c) Nominal A/c (d) Both (a) and (b)

3. Return Inwards books records…….

(a) Purchase returns (b) Sales returns

(c) Cash Sales returns (d) Both (a) and (c)

4. Parties to Bills of exchange are

(a) Drawer (b) Drawee

(c) Payee (d) All of the above.

5. Contra entries are passed only when

(a) Single column Cash Book is prepared

(b) Double column Cash Book is prepared

(c) Three column Cash Book is prepared

(d) Petty Cash Book is prepared

Common Proficiency Test (CPT) Volume - II



6. Sale or return day book is a

(a) Personal A/c (b) Suspense A/c(c) Memorandum A/c (d) Nominal A/c

7. Goodwill is a

(a) Current Asset (b) Intangible asset(c) Personal asset (d) Tangible Asset

8. Prepaid insurance is….

(a) Nominal A/c (b) Real A/c(c) Personal A/c (d) None of the above

9. Cash column in Cash Book always has

(a) Credit Balance (b) Both (a) and (c)(c) Debit Balance (d) None of the above

10. Total of the sales day book is posted periodically to the credit of

(a) Sales Books (b) Purchases Books(c) Cash Book (d) None of the above

11. Outstanding Salaries given in the trial balance is recorded in

(a) Profit & Loss A/c (b) Balance Sheet(c) Trading A/c (d) P & L appropriation

12. Which reserve is not shown in balance sheet?

(a) Secret Reserve (b) General Reserve(c) Capital Reserve (d) All the above

13. Which Liability is not included in the total of Balance Sheet?

(a) Current Liability (b) Contingent Liability(c) Fixed Liability (d) All of the above

14. Errors are

(a) Undetected mistakes (b) Intentional mistakes(c) Frauds (d) Unintentional mistakes

15. Revenue expenditures are recorded in the

(a) Manufacturing A/c. (b) Trading A/c.(c) P & L A/c. (d) All the above


16. Goods purchased from Mohan for Rs. 4,000 passed through the Sales books.The rectification of this error will result in

(a) Increase in debtors (b) Increase in gross profit(c) Decrease in gross profit (d) None of the above.

17. In case of Credit Balance the word …..are written on the Credit side.

(a) By balance b/d (b) To balance b/d(c) By balance c/d (d) To balance c/d

18. Preliminary expenses are treated as

(a) Fixed Assets (b) Current Assets(c) Intangible Assets (d) Miscellaneous expenditure

19. Account payable normally has

(a) Credit balance (b) Debit balance(c) Unfavourable balance (d) Either (a) or (b)

20. Proposed dividend are debited to

(a) Balance Sheet (b) P & L Appropriation A/c(c) Trading A/c (d) P & L A/c

21. Narang purchased goods for Rs. 3,00,000 and sold 4/5 of goods amounting Rs. 5,00,000 andpaid expenses amounting Rs. 1,10,000 for the year 2006. Besides that he paid Rs. 7,000 foran electricity bill of March 2005 and advance salaries amounting Rs. 10,000 was paid for themonth of April 2007. He calculated net profit Rs. 1,50,000. The profit calculated by him iscorrect according to

(a) Conservatism concept (b) Matching concept(c) Periodicity concept (d) Entity concept

22. A trader purchased goods for Rs. 5,00,000 and sold 55% of such goods during the accountingyear ended 31st Dec. 2006. The market value of the remaining goods was Rs. 1,00,000. Hevalued the closing stock at cost. He violated the concept of

(a) Cost (b) Conservatism(c) Periodicity (d) Money measurement

23. Stock worth Rs. 20,000 (cost price Rs.15,000) taken by Naresh who is a clerk in the office.The same is to be deducted from his salary in the subsequent month. Journal entry will be

(a) Dr. Salary A/c Rs.15,000 and Cr. Purchases A/c Rs. 15,000(b) Dr. Naresh Rs.15,000 and Cr. Purchases A/c Rs. 20,000(c) Dr. Salary A/c Rs.15,000 and Cr. Purchases A/c Rs. 20,000(d) None of the above



24. Cost of goods sold Rs. 20,000

Closing stock Rs. 8,000

Opening Stock Rs. 6,000

Amount of purchases will be

(a) Rs. 24,000 (b) Rs. 18,000(c) Rs. 22,000 (d) Rs. 34,000

25. Opening debtors Rs.15,000

Bad debts during the year Rs.14,000

Cash received from customers Rs.1,60,000

Closing Debtors Rs.7,000

Cash sales Rs.20,000

Total sales will be -

(a) Rs. 1,50,000 (b) Rs. 1,60,000(c) Rs. 1,51,000 (d) Rs. 1,66,000

26. Bank overdraft as per Cash book is Rs. 15,000

Cheque deposited but not cleared Rs. 4,000

Cheque issued but not cashed Rs. 6,000

Bank overdraft as per Bank statement will be

(a) Rs. 13,000 (b) Rs. 5,000(c) Rs. 25,000 (d) Rs. 17,000

27. Bank balance as per pass book Rs 20,000

Cheque issued but not presented Rs 7,000

Cheque deposited but not cleared Rs 5,000

Bank balance as per cash book will be -:

(a) Rs 22,000 (b) Rs 32,000(c) Rs 18,000 (d) Rs 8,000

28. A company can issue redeemable preference share

(a) At discount (b) At par(c) At premium (d) All of the three

29. According to Companies Act, 1956 of table A interest on call in arrears is charged

(a) 4% (b) 6%(c) 5% (d) 7%


30. Credit purchases of goods worth Rs. 30,000 by a dealer will be recorded in

(a) Cash book (b) Journal Proper(c) Sales Book (d) Purchases book

31. Pooja and Pratibha are partners sharing profits and losses in the ratio of 3:2. Pallavi isadmitted for 1/5th share and brings Rs. 10,000 as capital and necessary amount for his shareof goodwill. The goodwill of the entire firm is value at Rs. 40,000.

Goodwill brought by Pallavi is

(a) Rs. 5,000 (b) Rs. 8,000(c) Rs. 10,000 (d) Rs. 6,000

32. Debentures issued as collateral security is ….

(a) Added in the total liability of the company(b) Deducted in the liability of the company(c) Added in the assets of the company(d) Both (a) and (c)

33. Debenture holders are

(a) Owners of the company (b) Lenders of the company(c) Debtors of the company (d) Trustee of the company

34. Cost of goods sold Rs. 15,000 were sold at 25% profit on selling price. The amount of saleswill be

(a) Rs. 20,000 (b) Rs. 11,250(c) Rs. 18,750 (d) Rs. 15,000

35. The securities premium account may be applied by the company

(a) In writing off the preliminary expenses of the company.(b) In writing off the expenses of or the commission paid or discount allowed on, any issue of

shares or debentures of the company.(c) In paying up un-issued shares of the company to be issued to members of the company as

fully paid bonus shares.(d) All of the above.

36. Bill is drawn on 20 January 2005 for 2 months. After sight date of acceptance is 29 January2005. The due date of the bill will be

(a) 1 April 2005 (b) 23 March, 2005(c) 20 March, 2005 (d) 29 March, 2005

37. Returns of Cash Sales is recorded in

(a) Purchase book (b) Sales book(c) Cash Book (d) Sales Returns book



38. Security premium is recorded in …..

(a) Trading A/c (b) P & L A/c(c) P & L appropriation A/c (d) Balance Sheet

39. MND & Company employs a team of 15 workers who were paid Rs. 2,000 each in the yearending March 31, 2006. At the start of the year April 2006, company raised salaries by 25%.The amount of salary for the year ended 31st March, 2007 will be

(a) Rs. 30,000 (b) Rs. 37,500(c) Rs. 22,500 (d) Rs. 35,000

40. Machinery costing Rs. 50,000 was purchased on 1st January 2006. The installation chargesamounting Rs. 5,000 were incurred. The depreciation at 25% p.a. by written down valueequal method for the year ended 31st Dec. 2006 will be

(a) Rs. 68,750 (b) Rs. 13,750(c) Rs. 41,250 (d) Rs. 12,500

41. Original cost Rs. 1,50,000, Salvage value Nil, Useful Life - 5 yearsDepreciation for the 3rd year under sum of digits method will be

(a) Rs. 20,000 (b) Rs. 35,000(c) Rs. 25,000 (d) Rs. 30,000

42. A company issued Rs. 50,000 10% debentures at a discount of 5% redeemable after 5 yearat a premium of 5%. Loss on issue of debentures will be

(a) Rs. 2,500 (b) Rs. 6,000(c) Rs. 5,000 (d) Rs. 7,000

43. Ramesh Ltd. purchases furniture for Rs. 20,000 payable as to Rs. 6500 in cash and thebalance by an issue of 6% debentures of Rs. 100 each at a discount of 10% discount amountwill be

(a) Rs.1,350 (b) Rs.2,000(c) Rs. 650 (d) Rs.1,500

44. Opening debtors - Rs. 50,000

Total sales - Rs.50,000

Cash received from debtors – Rs.30,000

Cash sales – Rs.15,000

Sales Returns – Rs.3,000

Bad debts – Rs.7,000

Bills received from customers – Rs.15,000

Debtors at the end will be

(a) Rs. 1,40,000 (b) Rs. 1,30,000(c) Rs. 1,20,000 (d) Rs. 1,50,000


45. Goods costing Rs. 3,00,000 sent out to consignee at cost plus 25%. Invoice value of goodswill be

(a) Rs. 3,75,000 (b) Rs. 3,50,000(c) Rs. 2,25,000 (d) Rs. 2,50,000

46. A manager gets 10% commission on sales. Cost price of goods sold is Rs.80,000 which hesold at a margin 20% on sale. Amount of commission will be

(a) Rs. 16,000 (b) Rs. 9,600(c) Rs. 10,000 (d) Rs. 6,000

47. Adjustment entry for interest earned but not received will be

(a) Dr. Cash A/c and Cr. Interest A/c(b) Dr. Accrued Interest A/c and Cr. Customer A/c(c) Dr. Accrued Interest A/c and Cr. Interest A/c(d) None of the above

48. General Manager gets 10% commission on net profit after charging such commission. Grossprofit Rs. 70,000 and General expenses other than manager commission are Rs. 12,000.Commission amount will be

(a) Rs. 5272.72 (b) Rs. 6072.72(c) Rs. 5372.72 (d) Rs. 5172.72

49. Goods sold Rs. 25,000 on approval or return basis were included in Sales Book. The profitincluded in the sales was at 25% on cost. At the year end, closing stock will increase by

(a) Rs. 5,000 (b) Rs. 20,000(c) Rs. 15,000 (d) Rs. 45,000

50. Balance as per Pass Book 27,400(i) Cheque issued but not presented Rs. 73,000(ii) Cheque deposited but not yet recorded by bank Rs. 47,700Balance as per cash book will be

(a) Rs. 52,700 (b) Rs. 93,300(c) Rs. 2100 (d) None of the above

51. Overdraft as per pass book Rs. 4501. Cheque drawn but not presented for payment Rs. 1052. Cheque sent for collection but not credited by bank Rs. 300

(a) Rs. 645 (b) Rs. 255(c) Rs. 855 (d) Rs. 45

52. If sales Rs. 70,000 and Cost of goods sold is Rs. 24,000. The gross profit is




53. 1. 50,000 equity share of Rs.100 each fully called up2. Calls in arrears Rs. 50,0003. Proposed dividend 20%

(a) Rs. 10,00,000 (b) Rs. 9,84,000(c) Rs. 9,90,000 (d) Rs. 9,80,000

54. Rs. 30,000 claim for workman compensation under dispute is a

(a) Fixed assets (b) Current liability(c) Current asset (d) Contingent liability

55. 12% loan Rs.17,000Interest on loan Rs. 700Outstanding interest on loan will be


56. Trial balance shows the following balanceCapital - Rs.30,000 (Cr.)Received Payment of advance income tax - Rs. 1,500Income tax paid - Rs. 4,000Capital A/c balance at the end of the year will be


57. Ashish’s acceptance to Mohit for Rs. 10,000 discharged by a cash payment of Rs. 2,000 anda new bill for the balance plus Rs. 300 for interest. The amount of new bill will be

(a) Rs. 8,000 (b) Rs.10,300(c) Rs. 12,300 (d) Rs. 8,300

58. On 1st April, 2006 Ram Ltd. issued Rs. 5,00,000 14% debentures at a discount of 10%repayable at the end of 5 years. Amount of discount to be written off every year will be


59. Sohan Ltd. forfeited 1000 shares of Rs. 10 each fully called up for non payment of final callof Rs. 4 per share. All of these shares were reissued as fully paid for Rs. 6 per share. Amounttransferred to capital reserve will be

(a) Rs. 6,000 (b) Rs. 4,000(c) Rs. 2,000 (d) NIL

60. A company cannot issue redeemable preference shares for the period exceeding




61. Only those agreements, which are valid are

(a) Contract (b) Proposal(c) Offer (d) None of the above

62. Contractual rights and duties are created by

(a) State (b) Statute(c) Parties (d) Custom

63. An agreement enforceable by law under the Indian Contract Act may be

(a) In writing (b) Oral(c) Both (a) and (b) (d) Either (a) or (b)

64. A voidable contract is one which

(a) Can be enforced at the option of aggrieved party(b) Can be enforced at the option of both the parties(c) Cannot be enforced in court of law(d) Courts prohibit

65. Which of the following is not the legal requirement of a valid acceptance?

(a) It must be communicable(b) It must be absolute and unconditional(c) It must be presumed(d)I It must be accepted by a person who has the authority to accept

66. Which are of the following is an essential element of a valid contract?

(a) Free consent (b) Consideration(c) Competent parties (d) All of the above

67. A contract to perform a promise could arise by

(a) Standard form of contracts by promise(b) Agreement and contract(c) Promissory Estoppel(d) All of the above

68. Contract which ceases to be enforceable by law becomes a

(a) Valid contract (b) Void agreement(c) Void contract (d) Voidable contract

69. An agreement without consideration is

(a) Valid (b) Void(c) Unenforceable (d) None of the above



70. The consideration must be at the desire of the

(a) Promisor (b) Promisee(c) Third party (d) None of the above

71. Contract will be valid, if the consideration is

(a) Inadequate (b) Real(c) Illusory (d) Illegal

72. Which of the following statement is true?

(a) Consideration may be past (b) Consideration may be present(c) Consideration may be future (d) All of the above

73. A wrong representation when made without any intention to decline the other partyamounts to

(a) Fraud (b) Undue Influence(c) Misrepresentation (d) Coercion

74. A contract with the minor, which is beneficial for him is

(a) Void ab initio (b) Voidable(c) Valid (d) Illegal

75. Where the consent of both the parties is given by mistake the contract is


76. To make a contract voidable coercion must have been exercised against

(a) Only the promisor (b) Any other person(c) (a) or (b) (d) (a) and (b)

77. Under Section 13 of the Indian Contract Act, consent means agreeing on the same thing

(a) At the same time (b) In the same sense(c) At different time (d) All of the above

78. Consideration and object of an agreement is unlawful if it

(a) Is fraudulent(b) is forbidden by law(c) Would defeat the provision of any law(d) All of the above

79. Which of the following agreements will not be declared expressly void

(a) If parties to it have no contractual capacity(b) If it is done by mutual mistake(c) If it is for lawful consideration(d) If its consent is not free


80. A ___________ agreement is one, which is enforceable at the option of one party.

(a) Voidable (b) Void(c) Valid (d) Illegal

81. A contract can be discharged ____________.

(a) By mutual Agreement(b) By impossibility of performance(c) By breach of contract(d) By all the above

82. __________ signifies that the parties are not further bound under the contract.

(a) Discharge of contract (b) Breach of contract(c) Waiver of contract (d) Recession of a contract

83. A contract can be discharged by performance in the ways of _____________.

(a) Offer to perform (b) Actual performance(c) (a) or (b) (d) (a) and (b)

84. A contract dependent on the happening or non happening of future uncertain event, is a_____________.

(a) Uncertain contract (b) Void Contract(c) Contingent contract (d) Voidable contract

85. A contingent contract dependant on the happening of future uncertain event can be enforcedwhen the event __________.

(a) Happens (b) Becomes impossible(c) Does not happen (d) Either of these

86. The term “goods” for the purpose of Sale of Goods Act, does not include__________.

(a) Money (b) Actionable claim(c) Immovable property (d) All of these

87. Under the Sale of Goods Act, 1930 existing goods are classified as ________.

(a) Specific goods (b) Ascertained goods(c) Unascertained goods (d) All of the above

88. __________ may or may not pass between bailee and bailer.

(a) Consideration (b) Ownership(c) Both (a) and (b) (d) None of the above

89. When a breach of condition is treated as a breach of warranty, the buyer can _________.

(a) Claim damages (b) Repudiate the contract(c) Reject the goods (d) None of the above



90. In case of sale of goods by sample as well as by description, the goods should correspondwith________.

(a) The sample (b) The description(c) Either (a) or (b) (d) Both (a) and (b)

91. The unpaid seller is required to give notice of resale to the buyer under _________.

(a) Section 54(4) (b) Section 54(3)(c) Section 54(2) (d) Section 54(1)

92. Duration of transit is given in the sale of Goods Act, 1930 in ____________.


93. The right of lien is available to the unpaid seller, only when __________.

(a) Seller is not in possession of goods(b) Seller is in possession of the goods(c) Seller delivered the goods to the carrier(d) Seller has delivered the goods to the buyer

94. In a partnership firm, the decisions can be made by rule of majority when decisions relatesto __________.

(a) Policy decisions (b) Fundamental decisions(c) Ordinary routine matters (d) Buying and selling of property

95. Section ___________ of the Partnership Act, 1932 deals with “Right of outgoing partner toshare subsequent profits in certain cases”.

(a) 34 (b) 37(c) 40 (d) 42

96. Every partner of a ____________ firm has implied authority to borrow money for the businessof the firm.

(a) Chartered Accountants (b) Broking(c) Lawyer’s (d) Trading

97. The registration of firm may be effected __________.

(a) At any time during life of partnership firm(b) At anytime after filing a suit(c) After dissolution of a firm(d) Either (b) or (c)

98. Section _____________ of the Partnership Act, 1932 deals with “Partnership Property”.

(a) 13 & 14 (b) 14 & 15(c) 16 & 17 (d) 17 & 18


99. A enters with a contract with B to sell him 100 bales of cotton and afterwards discovers that“B’ was acting as agent for “C’. Decide.

(a) A may sue B only(b) A may sue C only(c) A may sue either ‘B’ or C(d) A may sue either ‘B’ or ‘C’ or both for the price of cotton

100. A lends a book to B, for examinations. Before ‘B’ has taken his examination, A seeks returnof his book. Decide.

(a) ‘A’ must compensate ‘B’ for any loss occasioned to him(b) A will not compensate B for any loss occasioned to B(c) Both (a) and (b)(d) None of the above


101 We mainly study the following in micro economics:

(a) Location of a Industry (b) Study of firms(c) Factor pricing (d) All of the above

102 When we study why saving rates are high or low, we are studying:

(a) Macro Economics (b) Micro Economics(c) Econometrics (d) Both (a) and (b)

103 Which of the following is not a central problem of the economy?

(a) How to produce? (b) When to produce?(c) What to produce? (d) For whom to produce?

104 Effective Demand depends on:

(a) Desire(b) Means to purchase(c) Willingness to use those means for that purchase(d) All of above

105 Quantity demanded is a:

(a) Flow Concept (b) Stock Concept(c) Both (a) and (b) (d) None of the above

106 Inferior goods have:

(a) Positive Income elasticity (b) Negative Income elasticity(c) Zero (d) Both (a) and (b)



107 If two goods are substitutes like tea and coffee, then the cross elasticity is:

(a) Negative (b) Zero(c) Positive (d) less than one

108 If the price of Banana rises from Rs 30 per dozen to Rs. 40 per dozen and the supply increasesfrom 240 dozen to 300 dozens elasticity of supply is:

(a) .7 (b) -.67(c) .65 (d) .77

109 If as a result of 90 percent increase in all inputs, the output increase by 75 percent this is acase of

(a) Increasing return to a factor (b) Decreasing return to a factor(c) Diminishing returns to scale (d) None of the above

110 Under which market structure, average revenue of a firm is equal to its marginal revenue

(a) Monopoly (b) Monopolistic competition(c) Oligopoly (d) None of the above

111 Special Drawing Rights has link with:

(a) World Bank (b) WTO(c) IMF (d) ADB

112 Banking Regulation Act, of India pertains to the year:

(a) 1945 (b) 1949(c) 1943 (d) 1934

113 ______________ refers to that portion of total deposits which a commercial is required tokeep with itself in the form of liquid Assets.

(a) CRR (b) SLR(c) Both (a) and (b) (d) margin requirements

114 The present membership of IMF is:

(a) 148 (b) 177(c) 184 (d) 149

115 The WTO came into existence on:

(a) 1st January, 1995 (b) 1st January, 1991(c) 1st January, 2001 (d) 1st January, 1996

116 Which of the following is not the function of IMF?

(a) It functions as a short term credit institution.(b) It functions as a long term credit institution.(c) It is a reservoir of the currencies of all the member nations.(d) It grants loan for financing current transactions.


117 MTA stands for

(a) Mutual Trade Agreements(b) Multiple Trade Agreements(c) Mutilated Trade Union Agreements(d) Multilateral Trade Agreements

118 The predecessor of WTO was:

(a) IMF (b) GATT(c) IBRD (d) None of the above

119 NDP does not include:

(a) Payment made for direct taxes (b) Depreciation allowance(c) Undistributed profits (d) Corporate dividend tax

120 Which of the following would not be included in GNP?

(a) Mohan purchases a shirt to wear(b) Sai Ram purchases a new Mercedes – Benz of S-class(c) Yes bank purchases new computers for its shares business(d) Aditi grows Tulsi plant in her home

121 Full employment is the level at which there is:

(a) Normal rate of unemployment (b) Zero unemployment(c) Least supply of labour (d) None of the above

122 In which sector of the Indian Economy will we find a high rate of disguised unemployment?

(a) Transport Sector (b) Agricultural Sector(c) Service Sector (d) Mining

123 Balance of payments is a broader term than:

(a) Balance of Trade (b) Balance of Current Account(c) Balance of capital Account (d) All of the above

124 In the Balance of payment statement, current account includes:

(a) Goods and invisible items (b) Government Loans from abroad(c) Foreign Direct Investment (d) None of the above

125 Service Tax is an instrument of:

(a) Fiscal policy (b) Monetary policy(c) Revenue policy (d) None of the above

126 Transfer payments are:

(a) Payments made to factors of production(b) Payments made by one sector to another



(c) Payments made for no return service(d) Repayment of loan

127 In terms of overseas shipping tonnage, India ranks __________

(a) 17th (b) 10th

(c) 15th (d) 27th

128 Which of the following statements is incorrect?

(a) The Indian Road network is one of the longest in the world(b) The village road network connects around 65 percent of all weather roads(c) The National highways carry more than 40 percent of the total road traffic(d) Most of the State Electricity Boards are running on profits

129 Electricity generated from radio active elements is called:

(a) Thermal electricity (b) Hyder Electricity(c) Tidal Energy (d) Atomic energy

130 According to the latest data, PLF is lowest in:

(a) South eastern region (b) North eastern region(c) West eastern region (d) Eastern region

131 Plant load factor measures

(a) Operational efficiency of Hydel plant(b) Operational efficiency of Atomic plant(c) Operational efficiency of Thermal plant(d) Operational efficiency of Tidal plant

132 In the theory of demographic transaction in the first stage:

(a) Birth rate falls and death rate falls(b) Birth rate falls and death rate rises(c) Birth rate is high and death rate is high(d) Birth rate rises, death rate falls

133 Indian accomodates _____________ percent of world population.

(a) 10 (b) 50(c) 17 (d) 18

134 At shut down point:

(a) Price is equal to AVC(b) Total revenue is equal to TVC(c) Total loss of the firm is equal to TFC(d) All of the above


135 The indifference curve approach does not assume:

(a) Rationality on the parts of consumers(b) Ordinal measurement of satisfaction(c) Cardinal measurement of satisfaction(d) Consistent consumption pattern behavior of consumer

136 Which one of the following agencies in India is responsible for computation of Nationalincome?

(a) NCAER (b) CSO(c) NSS (d) RBI

137 Suppose the total cost of production of commodity x is Rs. 1,25,000. Out of this implicit costis Rs. 35,000 and normal profit is Rs. 25,000. What will be explicit cost of commodity x ?

(a) Rs. 90,000 (b) Rs. 60,000(c) Rs. 65,000 (d) Rs. 1,00,000

138 Over the planning period, the relative share of area under food grains in gross cropped areain India has:

(a) Decreased (b) Increased(c) Remained the same (d) Increased initially and then decreased

139 The LAC curve

(a) Falls when the LMC curve falls(b) Rises when the LMC curve rises(c) Goes through the lowest point of the LMC curve(d) Falls when LMC < LAC and rises when LMC > LAC

140 Over the planning period the share of industrial sector in the GDP of the India has:

(a) Increased (b) Decreased(c) Remained Constant (d) Remained above 40%

141 Which bank among the following is responsible for issuing currency notes in India?

(a) SBI (b) RBI(c) UTI (d) World Bank

142 Human Development Index is a composite index:

(a) Health, Literacy and employment(b) National Income, size of population and general price level(c) National Income, per capita Income and per capita consumption(d) Physical resource, monetary resource and population size



143 Excess Capacity is the essential characteristic of the firm in the market form of:

(a) Monopoly (b) Perfect competition(c) Monopolistic competition (d) Oligopoly

144 Which of the following is not including in the primary sector?

(a) fishery (b) Forestry(c) Animal Husbandry (d) None of the above

145 Which of the following is not a commercial crop?

(a) Sugar (b) Cotton(c) Oilseeds (d) None of the above

146 Which of the following was not prevailing in the country at the time of Independence?

(a) Zamindari System (b) Ryotwari system(c) Mahalwari system (d) None of the above

147 Agriculture provides employment to ______% of people living in the country

(a) 60 (b) 50(c) 55 (d) 48

148 UNDP stands for

(a) Unlimited National Developed Programme(b) United Nation Development Programme(c) United Nation Development Project(d) United National Development Programme

149 Which one is a direct tax among the following?

(a) Wealth Tax (b) Excise Duty(c) Service Tax (d) None of the above

150 The other name of Budget line is:

(a) Demand line (b) Price line(c) Supply line (d) None of the above


151. One third of a number is greater than one fourth of its successor by 1. Find the number



152. A student on being asked to multiply 1617

of a certain fraction made the mistake of dividing

the fraction by 1617

and so got an answer which exceeded the correct answer by 33

340 Find

the correct answer.

(a)64

85(b)

46

58

(c)64

58(d) None of these

153.57

of 4

15 of a number is 8 more than

25

of 49

of the same number. What is half of that

number?


154. The sum of two numbers is 14 and their difference is 10. Find the product of the two numbers.


155. The difference of two numbers is 11 and 15

th of their sum is 9. The numbers are:

(a) 31, 20 (b) 30, 19(c) 29, 18 (d) 28, 17

156. The sub duplicate ratio of 16:49 is


157. Duplicate ratio of 4:5 is

(a) 16:25 (b) 2: 5(c) 64:125 (d) None of these

158. Triplicate ratio of 3:5 is

(a) 27:125 (b) 9:25

(c)1 13 33 :5 (d) 125:27



159. The sub–triplicate ratio 8:125 is


160. The 4th proportion of 6, 8 and 15 is –


161. The ratio of two numbers is 4:1. If 5 is added to both the numbers, the ratio of the newnumbers obtained becomes 3:1. Then the numbers are


162. The ratio of the money with A and B is 3:4 and that with B and C is 4:5. If A has Rs. 300, howmuch money does C have?


163. Two numbers are in the Ratio 5:6. If 5 is subtracted from each number, the ratio becomes4:5. Then the number are:


164. If 1 add 1 to each of the two given numbers their ratio is 1:2. If 1 subtract 5 from each theratio is 5:11. Then the numbers are


165. What must be subtracted from each term of the ratio 27:43 to make it equal to 7:15?


166. Seven times a two digit number is equal to four time the number obtained by reversing theorder of digits, and the sum of the digits of number is 3. then the number is:


167. There are 7 man and 3 ladies. Find the numbers of ways in which a committee of 6 can beformed of them if the committee is to include atleast two ladies.



168. If 28C2r : 24C2r–4 = 225:11, then the value of r is


169. A two digit number is obtained by either multiplying sum of the digits by 8 and adding 1 orby multiplying the difference of the digits by 13 and adding 3. Then the number is:


170. A committee is to be formed of 3 persons out of 12. Find the number of ways of forming sucha committee.


171. A gentlemen invites 6 of his friends to a party. In how many different arrangements theyalong with the wife of the gentleman can sit at a round table for a dinner if the host and hiswife always sit side by side?

(a) 1440 (b) 144(c) 1445 (e) None of these

172. Evaluate x a

x 3l i m

x 9→

−−

(a)1

6(b)

1

3

(c)2

3(d) None of these

173. Evaluate x a

x a 2alim

x a→

+ −−

(a)1

2 a(b)

1

2 2a

(c)1

3 2a(d) None of these



174. Find

2

2x

6 5xlim

4 x 15x→∞

++

(a)1

2(b)

1

4

(c)1

3(d) None of these

175. Evaluate 2x

a b xlim

x→ ∞

−


176. Evaluate

x -x

x -x

dy e -e; if y =

dx e +e

(a) ( )2x x

4

e e−−

+ (b) ( )2x x

4

e e−+

(c) ( )2x x

1

e e−+ (d) None of these

177. Find ( )21 x+

dy x;if y =

dx

(a) ( )3

1 x

1 x

+− (b) ( )3

1 x

1 x

−+

(c) ( )4

1 x

1 x

−+ (d) None of these


178. Find dy

;if y = x + xdx

(a)2 x 1

4 x x x

+

− +(b)

2 x 1

4 x x x

−

−

(c)2 x 1

2 x 1

+− (d) None of these

179. Evaluate 2 +2xxdy

;if y =7dx

(a)2 xx 2(2x 1).7 .log7++ (b)

2 xx 22(x 1).7 .log7++

(c)2x 2x7 log 7+ (d) None of these

180. If y = log2 2 dy

(x + x +a then finddx

(a) 2 2

1

x a+ (b) 2 2

1

x a

−+

(c) 2 2

x

x a+ (d) None of these

181. If (x–y) x

x-ye = a; then y dy

+ xdx

is

(a) 2 (b) –2y(c) 2y (d) None of these

182. If the demand law is 2x = 10-p then the elasticity of demand at point p = 2




183. Evaluate :

3xdx

x 1+∫

(a) x + log (x+1) + c (b) x3 – log (x+1) + c

(c)3 2x x

x log (x 1) c3 2− + − + + (d) None of these

184. Evaluate ∫4x 2x

3x

e + edx

e

(a)2x

4x

1 1e c

2 4e− + (b) x xe e c−−

(c)2x

4x

1e c

e− + (d) None of these

185. Evaluate ∫4

2

x +1dx

x +1

(a)2

2xx 2 log (x 1) c

2+ − + + (b) 2 2x x 2log (x 1) c+ + + +

(c)3

1xx 2 tan x c

3−− + + (d) None of these

186. Evaluate ∫ log (x +1)dx

(a) x log (x+1) – x + log (x+1) + c

(b) 2 2 2x log (x 1) x log (x 1) c+ + + + -

(c) 2x log (x 1) x log (x 1) c+ + + + - (d) None of these

187. Evaluate ∫dx

x + 1+x

(a) { }2 23 32

(1 x) x c3

+ − + (b) { }3 32 2

2(1 x) x c

3+ − +

(d) { }2 23 32

(1 x) x c3

+ − + (d) None of these


188. Evaluate +∫2

3 2

x -x+ 2dx

x x + 2x

(a) –log x + 3/2 log (x–1) + 4/3 log (x2 + 2) + log c(b) –log x + 2/3 log (x2–1) + 3/4 log (x2 +2) + log c(c) –log x + 2/3 log (x–1) + 4/3 log (x + 2) + log c(d) None of these

189. Evaluate ∫ 2

1dx

3x +13x -10

(a)

2

2

1 3x 2log c

17 3x 15

⎛ ⎞− +⎜ ⎟+⎝ ⎠(b) 2

1 3x 2log c

17 3x 15

⎛ ⎞− +⎜ ⎟+⎝ ⎠

(c)1 3x 15

log c17 3x 2

⎛ ⎞+ +⎜ ⎟−⎝ ⎠(d) None of these

190. Evaluate: { }∫xe f(x) + f'(x) dx

(a) ex f(x) + c (b) -ex f(x) + c(c) ex f’(x) + c (d) None of these

191. Evaluate: ∫b

a

logxdx

x

(a)1 b

log(ba).log2 a

⎛ ⎞⎜ ⎟⎝ ⎠

(b)b

log(ba ). loga

⎛ ⎞⎜ ⎟⎝ ⎠

(c)a

log(b a).logb

⎛ ⎞+ ⎜ ⎟⎝ ⎠

(d) None of these

192. Evaluate: ∫ [f(x) + f(-x)][g(x) - g(-x)]dx




193. Evaluate: ∫b

23a

dx

(a+b-x)

(a)1 1

3 3b a− (b)

1 1

3 33 b a⎛ ⎞

−⎜ ⎟⎝ ⎠

(c)

1 1

3 33 b a⎛ ⎞

+⎜ ⎟⎝ ⎠

(d) None of these

194. Evaluate: ∫2

0

xdx

x + 2 - x


195. Evaluate: x⎛ ⎞−⎜ ⎟⎝ ⎠

∫1

0

1log dx

x


196. In how many ways can 7 departments be distributed among 3 ministers, if every ministersgets at least one but not more than 3 departments?


197. Find the number of words of three letters that can be formed with the letters of the word“CALCUTTA”.


198. How many number of numbers three digits can be made from the digits of the number1,2,3,4,3,2?



199. If Sn be the sum of n terms of an A.P.; the value of Sn – 2Sn–1 + Sn–2 is

(a) d (b) d2

(c) cannot calculated (d) None of these

200. here are n ARITHMETIC MEANs between 3 and 31 such that the ratio of 3rd mean to (n–1)th mean is 1:3, then the value of n is


❖❖❖

BOARD OF STUDIES









1. Financial statements are part of

(a) Book keeping (b) Accounting

(c) Management (d) None of the above

2. The following error do not affect the trial balance

(a) Error of partial omission (b) Error of principal

(c) Error of complete omission (d) All of the above

3. In which area different accounting policies are adopted

(a) Valuation of inventories (b) Valuation of investment

(c) Depreciation (d) All of the above

4. Income includes

(a) Income earned (b) Income received

(c) Income receivable (d) All of the above

5. Cash Account is…..


(c) Nominal A/c (d) None of the above




6. Total of Sales book is posted periodically to credit of

(a) Journal proper (b) Purchase Book(c) Sales Account (d) Cash Book

7. Advance received from Debtors is not taken as Sale is based on

(a) Conservatism concept (b) Accrual Concept(c) Money measurement concept (d) None of the above

8. Ram Motors will debit purchases of Motor in

(a) Motor A/c (b) Purchase A/c(c) General expenses (d) None of the above

9. General Manager attended a meeting held abroad to develop market; meeting was successful.This expenses is in the nature of

(a) Deferred revenue expenditure (b) Capital expenditure(c) Revenue expenditure (d) None of the above

10. Wages Rs. 1,000 payable to labour will be credited

(a) Cash A/c (b) Labour A/c(c) Salary A/c (d) None of the above

11. Heavy amount spent for the advertisement of new company product is

(a) Revenue expenditure (b) Deferred Revenue expenditure(c) Capital expenditure (d) Either (a) or (c)

12. Rs. 40,000 spent on repairs of newly purchased old machinery is debited to

(a) Repairs A/c (b) Cash A/c(c) General expenses A/c (d) Machinery A/c

13. Cost of goods sold can be calculated by

(a) Balance Sheet (b) Profit & Loss A/c(c) Trading A/c (d) P & L Appropriation A/c

14. Liability for bill discounted is a

(a) Contingent Liability (b) Fixed Liability(c) Current Liability (d) None of the above

15. Interest is calculated on

(a) Purchase value (b) Market value(c) Face value (d) All of the above


16. Income tax in case of a sole trader is treated as

(a) Personal expenses (b) Debtors expenses(c) Business expenses (d) None of the above

17. The parties to joint venture are called

(a) Friends (b) Principal and agent(c) Partner (d) Co-venturers

18. Dividend is usually paid as a percentage of

(a) Paid up capital (b) Called up capital(c) Authorized share capital (d) Net Profit

19. Goodwill is

(a) An Investment (b) A Current Assets(c) An Intangible fixed assets (d) A Tangible fixed assets

20. Unexpired rent given in trial balance is recorded in

(a) Balance Sheet (b) Trading A/c(c) Profit & Loss A/c (d) Either (b) or (c)

21. Mohan purchased a Motor Car costing Rs. 60,000 on 1st January 2006 transportation andrepairing charge were incurred amounting Rs. 5,000 and 200 respectively. Dismentalingcharge of old motor car in place of which new motor car was purchased amounted to Rs.20,000. Marked value of motor car was estimated at Rs. 70,000 on 31st Dec., 2006 whilefinalizing the annual accounts. Mohan values the motor car at Rs. 70,000 in his book. Whichof the following concepts was violated by the Mohan?

(a) Matching concept (b) Realisation concept(c) Cost Concept (d) Periodicity concept

22. AB Ltd. issued 50,000 equity shares of Rs. 100 each at a premium of Rs. 10 payable at Rs. 30on application Rs. 30 on allotment and balance in the first call. Application received for1,00,000 equity shares but the company issued to them only 50,000 shares. Excess moneywas refunded to them after adjustment for further calls. Last call on 1,000 shares were notreceived and were forfeited after due notice. The above is the case of

(a) Over subscription (b) Pro-rata allotment(c) Forfeiture of shares (d) All of the above

23. It purchases Rs. 30,000; Closing stock Rs. 5,000; Opening Stock Rs. 10,000; then cost ofgoods sold will be

(a) Rs. 25,000 (b) Rs. 30,000(c) Rs. 35,000 (d) Rs. 45,000



24. Total actual cost of machinery Rs. 50,000; salvage value Rs. 5,000; Useful life 9 years; thenannual depreciation under Straight line Method will be

(a) Rs. 5,000 (b) Rs. 6,111(c) Rs. 5,555 (d) Rs. 4,500

25. Rent Rs. 10,000; Provision for bad debts (old) Rs. 10,000Salaries Rs. 8,000 Apprentice Premium (credit) Rs. 12,000Gross profit Rs. 70,000Net profit of the firm will be

(a) Rs. 74,000 (b) Rs. 64,000(c) Rs. 54,000 (d) Rs. 52,000

26. When preparing a Bank Reconciliation Statement if you start with balance as per pass bookthen payments made by bank Rs. 4,000 recorded twice in pass book Rs. 4000 will be

(a) Not required to be adjusted (b) Added(c) Deducted (d) None of the above

27. If Goods purchased for Rs. 2,00,000; Sales Rs. 1,60,000; Margin 20% on sales, then closingstock is

(a) Rs. 72,000 (b) Rs. 40,000(c) Rs. 70,000 (d) Rs. 75,000

28. Ram paid Rs. 1,000 towards a debit of Rs. 3,000 which was written off as bad debt in theprevious year. Ram’s account will be credited with

(a) Rs. 1,000 (b) Rs. 3,000(c) Rs. 2,500 (d) NIL

29. Income tax liability of the owner Rs. 2,000 was paid out of petty cash. Journal entry will be

(a) Dr. Income tax A/c Rs.2,000 and Cr. Cash A/c Rs. 2,000(b) Dr. Drawings Rs.2,000 and Cr. Cash A/c Rs. 2,000(c) Dr. Drawings Rs.2,000 and Cr. Petty Cash A/c Rs. 2,000(d) None of the above

30. An old motor car was purchased for Rs. 1,00,000. It was repaired for Rs. 10,000 andRs. 15,000 spent on its painting. Machinery repairs A/c will be debited by

(a) Rs. 25,000 (b) Rs. 10,000(c) Rs. 15,000 (d) NIL

31. Shyam started business on 1.4.05 with a capital of Rs. 2,00,000 for which he borrowed Rs.30,000 from a friend. He earned a profit of Rs. 1,00,000 during the year and withdrew cashRs. 50,000 for private use. What is his capital at the end of the year?

(a) Rs. 2,80,000 (b) Rs. 2,50,000(c) Rs. 3,00,000 (d) Rs. 3,80,000


32. X & Y purchased a building of Rs. 1,00,000 and sold it for Rs. 1,20,000. X had contributedfor Rs.60,000 and Rs. 40,000. They decided to share profits in the ratio of their capitalcontribution. The profit on venture will be

(a) Rs. 12,500 & Rs. 7,500 (b) Rs. 8,000 & Rs. 12,000(c) Rs. 75,000 & Rs. 12,500 (d) Rs. 12,000 & Rs. 8,000

33. Goods costing Rs. 20,000 was sold to Mohan at the invoice price of 20% above cost with atrade discount of 10%. The amount of sales will be

(a) Rs. 22,000 (b) Rs. 24,000(c) Rs. 21,600 (d) Rs. 22,600

34. Z & Co. issued Rs. 10,000 10% Debentures at 5% discount redeemable at 5% premiumafter 10 years loss on issue of debentures will be

(a) Rs. 1,000 (b) Rs. 1,500(c) Rs. 500 (d) Rs. 2,000

35. X & Y are partners in a business sharing profits and losses in the ratio of 7:3. They admit Zas a partner. X sacrificed 1/7th of his share and Y sacrifice 1/3rd of his share in favour of Z.New profit sharing ratio will be


36. On 1st Jan., 2005 goods costing Rs. 40,000 were consigned by A to his agent B at a proformaprice which was cost plus one fifth of profit on invoice price. Invoice price of goods will be

(a) Rs. 48,000 (b) Rs. 35,000(c) Rs. 50,000 (d) Rs. 45,000

37. Ram of Mumbai sends out certain goods at cost plus 25%. Invoice value of goods sends outRs. 20,000. 4/5th of the goods were sold by consignee at Rs. 17,600. Commission 2% uptoinvoice value and 10% on any surplus above invoice value commission amount will be

(a) Rs. 320 (b) Rs. 400(c) Rs. 520 (d) Rs. 480

38. Opening Stock – Rs.40,000Purchase – Rs.1,00,000Closing stock –Rs.30,000Carriage inwards – Rs.5,000Carriage outwards – Rs.3,000Office rent – Rs.4,000Sales –Rs.2,00,000Gross profit will be

(a) Rs. 85,000 (b) Rs. 75,000(c) Rs. 95,000 (d) Rs. 65,000



39. Mohan sells goods at cost plus 50%; total sales were 2,00,000 Cost price of the goods will be

(a) Rs. 1,22,222 (b) Rs. 1,11,111(c) Rs. 1,33,333 (d) Rs. 1,44,444

40. A seller sells goods at a profit of 25% on sales. In a particular month, he sold goods costing45,000. Sales price of goods will be

(a) Rs. 56,250 (b) Rs. 65,000(c) Rs. 55,000 (d) Rs. 60,000

41. Opening balance of capital – Rs.15,000Income tax – Rs. 2,500Net profit – Rs.1,500Drawings – Rs.1,000Interest on capital – Rs.750Interest on drawings – Rs.300Capital at the end will be

(a) Rs. 13,500 (b) Rs. 13,450(c) Rs. 13,350 (d) Rs. 13,300

42. Cost of good sold – Rs.1,50,000Opening stock – Rs.20,000Closing stock – Rs.40,000Purchases amount will be

(a) Rs. 1,80,000 (b) Rs. 1,30,000(c) Rs. 1,70,000 (d) Rs. 1,75,000

43. Mohan and Sohan are partners sharing profits and losses in the ratio of 5:3. They admitShyam with 1/5th share in profit which he acquires equally from both 1/10 from Mohan and1/10 from Sohan. New profit sharing ratio will be

(a) 15:10:5 (b) 20:10:4(c) 21:11:8 (d) None of those

44. Share capital 50,000 shares of Rs. 15 eachRs. 10 called up - Rs. 5,00,000Calls in arrears - Rs. 20,000Call in advance - Rs. 30,000Board of directors decide to provide 15% for dividend on share capital.Amount of proposed dividend will be

(a) Rs. 65,000 (b) Rs. 70,000(c) Rs. 75,000 (d) Rs. 72,000


45. Under diminishing balance method, depreciation

(a) Is constant every year (b) Increases every year(c) Decreases every year (d) None of the above

46. The total of the purchases day book is posted periodically to the debit of

(a) Sales book (b) Purchases Account(c) Cash book (d) Journal

47. Which stock valuation method best matches the cost of goods sold with current replacementcost

(a) Specific identification method (b) Weighted average method(c) LIFO (d) FIFO

48. Actual total cost of plant - Rs 1,50,000Salvage value - Rs. 20,000Useful Life - 10 yearsAnnual depreciation under Straight line method will be

(a) Rs. 13,000 (b) Rs. 15,000(c) Rs. 12,000 (d) Rs. 17,000

49. Legal expenses incurred on a suit for breach of contract to supply goods is a

(a) Capital expenditure (b) Deferred expenditure(c) Revenue expenditure (d) Both (a) and (c)

50. No journal entry is required to be passed when there is

(a) Loss by theft (b) Normal loss(c) Loss of bad debts (d) Abnormal loss

51. A plant & machinery worth Rs. 1,00,000 is insured for Rs. 60,000. It is completely destroyedby fire. The loss to be admitted by the insurance company will be

(a) Rs. 1,00,000 (b) Rs. 1,60,000(c) Rs. 40,000 (d) Rs. 60,000

52. There must be a gap of atleast _______ month between two calls.

(a) 3 (b) 6(c) 1 (d) 2

53. Cost of goods sold Rs. 8,000. Closing stock Rs. 3,000 opening stock Rs. 2,500. WagesRs. 1,000 purchases will be

(a) Rs. 8,500 (b) Rs. 7,500(c) Rs. 6,500 (d) Rs. 9,500



54. Cost of goods sold - Rs. 80,000Sales - Rs. 1,60,000Closing stock - Rs. 30,000Gross profit will be

(a) Rs. 1,00,000 (b) Rs. 1,10,000(c) Rs. 80,000 (d) Rs. 1,20,000

55. Bill of Rs. 15,000 accepted by A was endorsed by B to C on account of final settlement ofRs. 18,000. The benefit of Rs. 3,000 earn by B was

(a) Credited to discount received A/c by Rs. 3,000(b) Credited to rebate account by Rs. 3,000(c) Credited to discount allowed A/c Rs. 3,000(d) Not shown in the books of B at all

56. Depreciation on plants machinery whose cost is Rs. 80,000 with an accumulated depreciationreserve of Rs. 12,000 at 30% p.a. on written down value will be

(a) Rs. 12,000 (b) Rs. 20,000(c) Rs. 24,000 (d) Rs. 20,400

57. Ram and Rahim have been sharing profit and losses in the ratio of 4:3 Rahman is admittedas a partner. He acquires his 1/7 share only from Rahim. New ratio will be

(a) 3:2:1 (b) 4:2:1(c) 5:2:1 (d) 2:2:1

58. Narain Ltd. invited application for 50,000 shares of Rs. 100 each at a discount of 8%. Discountper share will be

(a) Rs. 8.00 (b) Rs. 0.08 paise(c) 0.80 paise (d) Rs. 80.00

59. Salary has been paid for 9 months from April to December 2005 amounting Rs. 72,000. Theamount of outstanding salary shown in the balance sheet will be

(a) Rs. 48,000 (b) Rs. 8,000(c) Rs. 24,000 (d) Rs. 72,000

60. Forfeited shares can be re-issued at discount

(a) When the market value of the forfeited share is less than is nominal value(b) When the forfeited shares were originally issued at discount(c) When board of directors seems to issue it at discount(d) When the forfeited shares were originally issued at premiuim



61. The sources of Indian commercial law include

(a) English common law (b) Mercantile Usages(c) Principles of Equity & justice (d) All of the above

62. Every contract is an agreement but every agreement is not contract. This statement is

(a) Correct (b) Correct subject to certain exception(c) Partially correct (d) Wrong

63. An agreement enforceable by law amounts to

(a) Offer (b) Promise(c) Contract (d) Obligation

64. Agreement is defined in Section

(a) 2(b) (b) 2(e)(c) 2(f) (d) 2(g)

65. A proposal when accepted becomes a

(a) Offer (b) Acceptance(c) Contract (d) Lawful promise

66. Consent should be given

(a) By the person to whom offer is made(b) Without a Condition(c) In clear terms either oral or written(d) All of the above

67. In case of conflict of jurisdiction of the courts, the incidence of a contract shall be governedby the law of the place where the

(a) Accepter resides (b) Proposer resides(c) Contract is made (d) Contract is performed

68. Which one of the following statements is not correct?

(a) Oral acceptance is a valid acceptance(b) Acceptance must be in writing(c) Acceptance must be communicated(d) Acceptance must be in prescribed manner

69. Which one of the following falls into the category of offer?

(a) Newspaper advertisement regarding sale(b) Display of goods by a shopkeeper in his window with prices marked on them(c) An advertisement for a concert(d) Announcement of reward to the public



70. A counter offer is

(a) A rejection of the original offer (b) An acceptance of the offer(c) A bargain (d) An invitation to treat

71. When a person without expressing his final willingness, proposes certain terms on which heis willing to negotiate, he makes

(a) Counter offer (b) Standing offer(c) Offer (d) Invitation to offer

72. A notice in the newspapers inviting tenders is

(a) Proposal (b) An invitation to proposal(c) A promise (d) An invitation for negotiation

73. When goods are displayed in a shop window with price tags attached to them, the offercomes from

(a) Shop public (b) Shop owner(c) Customer (d) Officer

74. Acceptance in ignorance of the offer is

(a) Valid (b) Invalid(c) Void (d) Voidable

75. An agreement without consideration is

(a) Valid (b) Void(c) Unenforceable (d) None of the above

76. Consideration is defined in the Indian Contract Act, 1872 in Section

(a) 2(d) (b) 2(e)(c) 2(f) (d) 2(g)

77. The consideration may move from

(a) The promisor or any other person(b) The promisee or any other person(c) The promisee only(d) The promisor only

78. Inadequacy of consideration does not make a contract

(a) Void (b) Voidable(c) Unenforceable (d) None of the above

79. Consideration is unlawful when

(a) It is fraudulent (b) Immoral or opposed to public policy(c) It is forbidden by law (d) All of the above


80. Promissory estoppel is sometimes spoken of as a substitute for________.

(a) Novation (b) Quasi contract(c) Consideration (d) Coercion

81. Agreement which are in the nature of bets and gambling are called__________.

(a) Invalid agreements (b) Voidable contracts(c) Contingent contract (d) Wagering agreements

82. Illegality renders a contract________.

(a) Illegal (b) Punishable(c) Void (d) Voidable

83. An agreement to share the benefits of a public offer is ____________.

(a) Valid (b) Voidable(c) Void (d) None of the above

84. Recession of a contract means_________.

(a) The renewal of original contract(b) Cancellation of contract(c) Substitution of new contract(d) Alteration of contract

85. Novation means _______________.

(a) Frustration due to change of circumstances(b) Impossibility of contract sending it void(c) No frustration of executed contracts(d) Substitution of an existing contract with a new one

86. Injuction may be ___________.

(a) Temporary (b) Perpetual(c) (a) or (b) (d) None of the above

87. Caveat emptor means _________.

(a) Let the buyer aware (b) A jus in personam(c) A jus in rem (d) None of the above

88. In case of anticipatory breach the agreed party may treat the contract __________.

(a) As operative and wait till the time for performance arrives(b) As discharged and bring an immediate action for damages(c) Exercise option either (a) or (b)(d) Only option (a) is available



89. Compulsory dissolution is dealt with Section ____________ of The Partnership Act, 1932.

(a) 41 (b) 42(c) 43 (d) 45

90. According to Sale of Goods Act, 1930, seller means a person ____________.

(a) Who sells or agrees to sell goods(b) Who only sells goods(c) Who only agrees to sell the goods(d) None of these

91. According to the Sale of Goods Act, 1930, Buyer is a person who ________.

(a) Buys or agrees to buy goods (b) Buys goods(c) Agrees to buy goods (d) None of the above

92. Things attached to land, which are agreed to be severed before sale constitute ________.

(a) Movable property (b) Immovable property(c) Goods (d) Crops, Gross and other things

93. The term goods includes ________.

(a) Shares (b) Growing crops(c) Old coins (d) All the above

94. In a contract of sale, price of goods may be paid __________.

(a) In cash(b) Other than cash(c) Partly in cash and partly in goods valued in terms of money(d) (a) and (c)

95. The general rule of law is that the risk follows _________ of goods.

(a) Possession (b) Delivery(c) Ownership (d) Contract of sale

96. Where the goods are perishable in nature, unpaid seller can ___________.

(a) Resale the goods(b) Not resale the goods(c) Ask again the buyer(d) Take possession and mark goods as bad

97. When there is no reserve price, the auctioneer is ____________.

(a) not bound to accept the highest bid(b) bound to accept the highest bid(c) Can accept any price(d) None of the above


98. Partnership property vest in the ____________.

(a) Firm(b) Partner of the firm(c) Continuing partner of the firm(d) Retiring partners of the firm

99. ‘A’ borrows Rs. 500 from ‘B’ to pay to ‘C’, to whom ‘B’ has lost a bet. Contract between ‘A’and ‘B’ is

(a) Valid (b) Voidable(c) Void (d) None of these

100. A purchase a refrigerator on hire purchase from B and pledged with C. D purchased therefrigerator from C in good faith, on knowing the facts B wants to recover the refrigeratorfrom D. Which of the following statements is/are correct?

(a) B can recover the refrigerator from D(b) B can recover the refrigerator from A only(c) B cannot recover the refrigerator from D(d) D will get good title for the refrigerator as he bought it in good faith


101 When we are studying how a producer fixes the prices of his products we are studying.

(a) Macro Economics(b) Micro Economics(c) Both Micro and Macro Economics(d) None of the above

102 Macro economics doesn’t include one example from the following:

(a) National Income and output (b) Study of firms(c) General Price Level (d) Saving and Investment

103 If distribution of income is more equal, then the propensity to consumer of the country is

(a) Relatively High (b) Relatively Low(c) Unaffected (d) None of the above

104 Normal goods have:

(a) Positive income elasticity (b) Negative income elasticity(c) Fluctuating income elasticity (d) Zero income elasticity

105 If the goods are complementary like car and petrol, their cross elasticity is:

(a) Negative (b) Positive(c) Zero (d) Infinite



106 If demand for a good is elastic, an increase in its price will cause total expenditure of theconsumers of the good to:

(a) Increase (b) Decrease(c) Remain the same (d) None of the above

107 If a good is priced at Rs 180 p.u. and its price is increased to Rs. 240 p.u. Now supposequantity demanded previously was 100 units and as a result of price increase, the quantitydemanded fell to 80 units. What is the price elasticity?

(a) .777 (b) 1.4(c) 1 (d) .8

108 Monetary policy is given by:

(a) Commercial banks (b) Central bank(c) Both (a) and (b) (d) Ministry of Finance

109 Fiscal policy is the policy of the Government related to:

(a) Public Revenue(b) Public Expenditure(c) Both Public Revenue and Public Expenditure(d) Public welfare

110 Which of the following is not the objective of Monetary Policy?

(a) To regulate monetary growth(b) To ensure adequate expansion in credit to assist economic growth(c) To introduce measures for strengthening the banking system(d) To increase Public Revenue

111 FEMA stands for

(a) Fiscal Exchange Management Act(b) Foreign Exchange Monetary Act(c) Foreign Exchange Management Act(d) Foreign Exchange Money Act

112 __________________ refers to that portion of total deposits which a commercial bank has tokeep with the RBI

(a) CRR (b) SLR(c) Bank Rate (d) Margin Requirement

113 Which is the central bank of India?

(a) SBI (b) Indian Bank(c) NABARD (d) RBI


114 Which of the following is a commercial bank in India?

(a) SBI (b) Citi Bank(c) ABN Amro Bank (d) All of the above

115 The initial membership of IMF in the year 1947 was________.

(a) 31 (b) 51(c) 91 (d) 101

116 Macro economics is the study of:

(a) Inflation (b) Unemployment(c) Growth (d) All of the above

117 Net Factor Income from abroad is equal to:

(a) NDP at market price – Net Indirect Taxes(b) NNP at factor cast – NDP at factor cast(c) NDP

FC (+) Deprecation


118 Balance of Trade is:

(a) Difference between current and capital Account(b) Difference between export and import of goods(c) Difference between export and import of goods and services(d) Balance of current account

119 Which of the following is not included in the computation of GDP?

(a) Spending on guns and tanks(b) Purchase of Limca by a family(c) Services of a teacher(d) Price paid for a stolen car

120 In terms of capacity of power generation, the highest capacity is of:

(a) Thermal (b) Hydel(c) Nuclear (d) others

121 The highest user of commercial energy is

(a) Railways (b) Industry(c) Households (d) Agriculture

122 According to NSSO survey (latest):

(a) Unemployment rates on the basis of current daily status were same as those on the basis ofusual status

(b) Unemployment rates on the basis of current daily status were higher than those of thebasis of usual status



(c) Unemployment rates of the basis of current daily status were lower than those on the basisof usual status


123 Indian ranked _______ among top 10 debtor countries of the world according to the GlobalDevelopment Finance 2005

(a) 10th (b) 9th

(c) 8th (d) 7th

124 India’s external debt stood at more than __________crore 2005-06

(a) 5,48, 000 (b) 7,58,000(c) 8,48,000 (d) 9,48,000

125 Balance of payment consists of:

(a) Balance of current account and capital account(b) Only Capital account(c) Only Current Account(d) Only trade account.

126 Budget Deficit means:

(a) Total Receipts and total expenditure(b) Revenue receipts and revenue expenditure(c) Fiscal deficit – Interest(d) Total Budgetary receipts – revenue expenditure

127 The aim of FRBM bill is to reduce gross fiscal deficit by_____________ % of GDP.

(a) 2.5% (b) .5%(c) 1% (d) .25%

128 Non-plan revenue expenditure consists of :

(a) Defence (b) Interest Payment(c) Food and Fertilizer subsidy (d) All of the above

129 The Government now taps 91 days treasury bills from the market and shows them as partof:

(a) Revenue Receipt (b) Loan Receipt(c) Capital Receipt (d) None of the above


(a) In India, we mainly use the concept of relative poverty for measuring poverty(b) Gini coefficients are used to measure absolute poverty(c) Gini coefficients are often used for measuring poverty in relative sense(d) When poverty is related to the distribution of income or consumption expenditure, it is

absolute poverty


131 According to ______________measure, a person is said to be employed for the week even ifhe is employed only for a day during that week

(a) Current weekly status (b) Usual status(c) Current daily status (d) Current yearly status

132 The green revolution is also known as:

(a) Rice revolution (b) Wheat revolution(c) Bajra revolution (d) All of the above


(a) Tax on agriculture is a state subject(b) Under zamindari system, farmers directly paid land revenue to the state(c) Cooperative banks are giving loans to agricultural sector at zero interest rates(d) India has been a big importer of food grain especially since 1995

134 Agriculture sector faces the problem of:

(a) Slow and unplanned growth (b) Inadequate finance(c) Inadequate reforms (d) All of the above

135 Increasing returns imply:

(a) Constant average cost(b) Diminishing cost per unit of output(c) Optimum use of capital and labour(d) None of the above

136 _____________ is an implicit cost of production

(a) Wages of the labour(b) Charges for electricity(c) Interest on owned money capital(d) Payment for raw material

137 All of the following are U-shaped curves except the:

(a) AVC curve (b) AFC curve(c) AC curve (d) MC curve

138 Suppose that a sole proprietor is earning total revenue of Rs. 1,20,000 and is incurringexplicit cost of Rs. 90,000. If the owner could work for another company for Rs. 50,000 ayear, we would conclude that:

(a) The firm is incurring an economic profit(b) The firm is incurring an economic loss(c) Total economic cost is Rs 2,10,000(d) The firm is earning economic profit of Rs. 30,000



Use following table to answers questions 139-140

Hour of labour Total output Marginal product

0 0 01 300 3002 - 240

3 720 -

139 What is the total output when 2 hours of labour are employed?

(a) 160 (b) 200(c) 360 (d) 540

140 What is the marginal product of the third hour of labour?

(a) 120 (b) 160(c) 200 (d) 180

Use the following data to answer questions 141-143

Output Total Cast

0 240

1 330

2 410

3 480

4 540

5 610

6 690

141. The Average fixed cost of 2 units of output is:

(a) Rs. 80 (b) Rs. 85(c) Rs 120 (d) Rs. 205

142 The marginal cost of the sixth unit of output is:

(a) Rs. 133 (b) Rs. 75(c) Rs. 80 (d) Rs. 450

143 Diminishing marginal returns start to occur between units:

(a) 2 and 3 (b) 3 and 4(c) 4 and 5 (d) 5 and 6


144 Which cost increases continuously with the increase in production?

(a) Average cost (b) Marginal cost(c) Fixed cost (d) Variable cost

145 Before financial reforms, the banking system was characterized by all of the following except:

(a) Administered interest rate structure(b) Quantitative restriction on credit flow(c) High revenue requirements(d) Keeping very less lendable resources

146 The law of scarcity:

(a) Doesn’t apply to rich, developed countries(b) Applies only to the less developed countries(c) Implies that consumer wants will be satisfied in a mixed economy(d) Implies that consumer wants will never be completely satisfied

147 Money includes

(a) Currencies and demand deposits(b) Bonds, Government securities(c) Equity shares(d) All of the above

148 A horizontal supply curve parallel to the quantity axis implies that the elasticity of supply is:

(a) Infinite (b) Zero(c) Equal to one (d) Greater than zero but less than one

149 According to the Planning Commission, a person is said to be below the poverty line if he isearning less than Rs. __________ per month(December, 2005) for urban area.

(a) 559 (b) 225(c) 240 (d) 275

150 Lesser production of ______would lead to lesser production in future

(a) Public goods (b) Consumer goods(c) Agricultural goods (d) Capital goods


151. How many numbers between 100 and 200 are divisible by 2 & 8?

(a) 12 (b) 13(c) 9 (d) 16



152. The sum of first n odd numbers is

(a) n2 (b) (2n–1)2

(c) (n+1)2 (d) None of these

153. Find the number which when multiplied by 36 is increased by 1050.


154. Find the value of 13 + 23 + 33 + ……………. + 123


155. Find the sum of n terms of the series 1 + 9 + 24 + 46 + 75 + .................

(a)n(n 1) (7n 4)

6

+ −(b)

n(2n 1) (4n 3)

6

+ −

(c)n(2n 1) (2n 3)

6

+ −(d) None of these

156. What must be added to each term of 83:263 to make it equal to 1:3?


157. An employer reduces the number of employees in the ratio of 9:8 and increases their wagesin the ratio of 14:15. In what ratio is the wages bill decreased?


158. Divide Rs. 680 among A, B and C such that A gets 23

of what B gets and B gets 14

th of what

C gets. What is C’s share


159. What must be added to each of the four numbers 10, 18, 22, 38. So that they become inproportion?


160. Find two numbers, such that the mean proportion between them is 24 and the third proportionto them is 192.



161. Evaluate x x 2

x 0

e + elim

x

−

→

−

(a) 1 (b) 0(c) log

x(d) None of these

162. Evaluate

1x

1x

1

1x 0

elim

e

−

−→

−

+

(a) 1 (b) –1(c) does not exist (d) None of these

163. Evaluate →

−−x 0

3x | x |lim

7x 5 | x |

(a) 2 (b) 1(c) does not exist (d) None of these

164. Evaluate ax bx

x 0

e elim

x→

−

(a) a–b (b) ab(c) 0 (d) None of these

165. Evaluate

x

x 0

e 1lim

log(1+ x)→

−


166. If y = 1 x

1 x

−+

then dydx

is

(a)2 / 3

(1 x)(1 x)+ − (b) 3/2

1

(1 x) (1 x)

−+ −

(c) 2

3 / 2

(1 x) (1 x)

−+ − (d) None of these



167. If y = 2

x

1 + x, then

3.dy

xdx

is

(a) y2 (b) y(c) y3 (d) None of these

168. If xy = ex–y; then dydx

is

(a) 2

log x

(1 log x)+ (b) 2

log x

(1 log x)−

(c) 2

1

(1 log x)+ (d) None of these

169. if y3 . x5 = (x+y)8, then dydx

is

(a)y

x(b)

y

x

−

(c)5

3

y

x(d) None of these

170. If y = x......xx∞ ; then x.

dydx

is

(a)

2y

1 y log x+ (b)

2y

1 y log x−

(c)

2y

1 y log x

−− (d) None of these

171. Evaluate ( )1

1

x xe e dx−

−∫

(a) 1 (b) 0(c) –1 (c) None of these


172. Evaluate:

e

1

1 log xdx

x+

∫

(a)3

2(b)

3

2−


173. Evaluate:

log3

0

x

x

edx

1+ e∫

(a) log 3 (b) log 2(c) 1 (d) None of these

174. Evaluate:

1

02

xdx

1+ 1 x+∫

(a) ( )22 1

3+ (b) ( )2

2 13

− +

(c) ( )22 1

3− (d) None of these

175. Evaluate:

1

0

dx(1+ x)(2 + x)∫

(a) log 4

3(b) log

3

4(c) 0 (d) None of these

176. The sum of the first two terms of an infinite geometric series is 15 and each term is equal tothe sum of all the terms following it; then the sum of the series is


177. If x and y are positive intigers such that x + y = 1 and a = 1 + x + x2 + ………….. to ∞∞∞∞∞ , b = 1

+ y + y2 +…………….. to ∞∞∞∞∞ then the value of 1 1a b+ is




178. At what rate, will a person who invests Rs. 2,000 will receive Rs.2, 090 as simple interest in9 months?


179. The time required for Rs. 5,400 to yield Rs. 216 at 6% simple interest.

(a) 7 months (b) 8 months(c) 10 months (d) None of these

180. A person deposited a sum of Rs. 10,000 in a bank. After 2 years, he withdrew Rs. 4,000 andat the end of 5 years, he received an amount of Rs. 7,900; then the rate of simple interest is:


181. If the values of all observations are equal then the Standard Deviation of the given observationsis


182. The Standard Deviation of a set of 50 items is 10. Find the Standard Deviation if every itemis increased by 5.


183. Find the coefficient of variation if the sum of squared deviations taken from mean 40 of 10observations is 360.


184. If the coefficient of mean deviation is 0.44 and the mean deviation from mean is 5.77; thenthe mean is –

(a) 14 (b) 13.11(c) 16 (4) None of these

185. The Standard Deviation of two values is equal to half their difference. This statement is

(a) True (b) false(c) cannot say (d) None of these


186. Find the correlation coefficient between the following set of observation.

x: 50 50

y: 40 40


187. The value of Spearman’s rank correlation coefficient of a certain number of observations

was to be23

. The sum of the squares of differences between the corresponding ranks was 55.

Find the number of Pairs.


188. The equation of two lines of regression is 4x + 3y + 7 = 0 & 3x + 4y + 8 = 0. The correlationcoefficient between x & y is

(a) 1.25 (b) 0.25(c) –0.75 (d) None of these

189. The co–variance between the two variables is

(a) always positive(b) always negative(c) always 0(d) Either positive or negative or Zero

190. The coefficient of regression of Y on X is byx = 1.2. If U = x 100

2−

and V=2−Y 00

3 find bvu


191. A bag contains 5 red & 3 black balls and the second one 4 red and 5 black balls. One of theseis selected at random and a draw of two balls is made from it. What is the chance that one ofthem is red and the other is black?

(a)275

504(b)

273

504

(c)175




192. A purse contains 3 silver and 4 Gold coins and a second purse contains 4 silver and 3 Goldcoins. If a coin is selected at random from one of the two purses, what is chance that it is asilver coin.

(a)1

2(b)

1

4

(c)3

4(d) None of these

193. Find mean of the probability distribution of “number of sixes” in two tosses of unbiaseddice.

(a)1

3(b)

2

3

(c)1

4(d) None of these

194. Find the probability distribution (when x = 2) of the number of sixes in a single throw ofthree dice.

(a)75

216(b)

1

216

(c)15


195. A Chartered Accountant applies of a job in two firms X and Y. He estimates that theprobability of his being selected in firm X is 0.7, and being rejected at Y is 0.5 and theprobability of atleast one of his applications being rejected is 0.6. What is the probabilitythat he will be selected in one of the firms?


196. Evaluate ( )( )2

1log log x dx

log x

⎡ ⎤+⎢ ⎥

⎢ ⎥⎣ ⎦∫

(a) x log (log x) – x

clog x

+ (b) x (log x)2 – x

clog x

+

(c) x log (log x) + x

clog x

+ (d) None of these


197. “Is equal to” is a

(a) Symmetric relation (b) Reflexive relation(c) Transitive relation (d) Equivalence relation

198. If f(x) = x2 + 2, then the given function is

(a) odd function(b) even function(c) Neither odd nor even function(d) None of these

199. For the function f(x) = 121+x, the domain of real values of x where 0 < x < 9 the range is

(a) 12 < f(x) < 1210 (b) 0 < f(x) < 1210

(c) 0 < f(x) < 12 (d) None of these

200. “Is greater than” over the set of real number s is

(a) Transitive relation (b) Symmetric relation(c) Reflexive relation (d) Equivalence relation

❖❖❖

BOARD OF STUDIES








219


1. Carriage inwards is debited to

(a) Trading A/c (b) P & L A/c

(c) P & L appropriation A/c (d) Balance Sheet

2. A bill was drawn on 20.1.2006 payable after 60 days the due date of the bill will be

(a) 24.4.2006 (b) 21.3.2006

(c) 24.3.2006 (d) None of the above

3. Amount spent for the construction of temporary huts which were necessary for construction

of the overbridge (flyover) and demolished when the flyover was ready is a

(a) Capital expenditure

(b) Deferred Revenue expenditure

(c) Revenue expenditure

(d) Both (a) and (c)

4. Difference of total of debit and credit side of the trial balance is transferred to

(a) Suspense A/c (b) Difference A/c

(c) P & L A/c (d) Trading A/c




5. In the absence of any partnership agreement, profits and losses are shared among the partners

(a) Equally(b) In the ratio of capital(c) In the ratio of loan given by them to the partnership firm(d) Either (a) or (b)

6. Which of the following statement is not true?

(a) Petty cash is an assets(b) In case of debt becoming bad the amount should be credited to bad debts A/c(c) Plant & Machinery is a fixed assets(d) Goods distributed as sample is credited to Purchases A/c

7. Returns inward is debited to

(a) P & L A/c (b) Balance Sheet(c) Trading A/c (d) None of the above

8. Carriage outward is debited to

(a) Balance Sheet (b) P & L A/c(c) P & L appropriation (d) All of the above


(a) Liabilities = Capital + Assets(b) Capital = Assets – Liabilities(c) Capital = Assets + Liabilities(d) Assets = Liabilities – Capital

10. Material costing Rs. 4,000 and labour charges Rs. 3,000 paid for the erection of the buildingis debited to

(a) Purchases A/c (b) Material A/c(c) Building A/c (d) Wages A/c

11. Fundamental accounting assumptions are

(a) Consistency concept (b) Going concern concept(c) Accrual concept (d) All of the above

12. Writing of transaction in the Ledger is called

(a) Casting (b) Balancing(c) Posting (d) Journalizing

13. Municipal tax Rs. 6,000 under dispute is a

(a) Contingent Liability (b) Revenue expenditure(c) Current Liabilities (d) Current assets


14. Purpose of accommodation bill is

(a) To facilitate trade transaction(b) When both parties are in need of support of fund(c) Provide loan for actual purchases or sales of goods(d) All of the above

15. In the Journal there are

(a) 4 columns (b) 5 columns(c) 6 columns (d) 7 columns

16. In the ledger there are

(a) 5 columns (b) 6 columns(c) 7 columns (d) 8 columns

17. Joint Venture account is a

(a) Nominal A/c (b) Personal A/c(c) Real A/c (d) Dummy A/c

18. Freight charges paid on purchase of a new motor will be debited to

(a) Carriage A/c (b) Motor A/c(c) Freight A/c (d) Freight & Motor A/c

19. Capital expenditure provides benefit

(a) Very short-term (b) Long term(c) Short term (d) All of the above

20. Capital expenditures are recorded in the

(a) Trading A/c (b) P & L A/c(c) Balance sheet (d) All of the above

21. Arjun purchased goods for Rs. 10,00,000 and sold 70% of such goods during the year ended31st December 2006. The market value of the remaining goods was Rs. 2,00,000. He valuedthe closing stock at cost. He violated the concept of

(a) Periodicity (b) Money measurement(c) Conservatism (d) Cost

22. A building was purchased for Rs. 4,00,000 on 1.04.2005. 31st March, 2006, its net realizablevalue was Rs. 5,00,000. The value of building to be shown in the books as on 31st March,2006 will be

(a) Cost price(b) Net realisable value(c) Cost or Net realisable value which ever is less(d) Cost or Net realisable value which ever is more



23. Cash sales Rs. 70,000Cash collected from debtors Rs. 2,00,000Bad debts Rs. 7,000Opening Debtors - Rs. 30,000Closing Debtors Rs. 16,000Total sales will be

(a) Rs. 2,33,000 (b) Rs. 2,63,000(c) Rs. 2,43,000 (d) Rs. 2,60,000

24. A cheque of Rs. 6,000 received from X was dishonoured and had been posted to debit ofSales returns account. Rectifying journal entry will be

(a) X A/c Dr. 6,000To Sales Returns A/c 6,000

(b) Sales Return A/c Dr. 6,000To X A/c 6,000

(c) Sales Return A/c Dr. 6,000To Suspense A/c 6,000

. (d) None of the above

25. Ram and Shyam entered into a joint venture. Ram purchased goods costing Rs. 52,500.Shyam sold goods costing Rs. 45,000 at Rs. 60,000. Balance goods were taken over by Ramat Rs. 10,000. The profit on Joint Venture is

(a) Rs. 15,000 (b) Rs. 17,500(c) Rs. 7,500 (d) Rs. 25,000

26. K and L are equal partners. They admitted M for 1/4 share in future profit. New profitsharing ratio will be

(a) 2:2:1 (b) 3:3:1(c) 3:3:2 (d) none of the above

27. X, Y and Z are partners sharing profits in the ratio of 4:3:2. Y retires, X and Z decide toshare future profits in the ratio of 5:3. Gaining ratio between X and Z will be

(a) 12:10 (b) 10:12(c) 13:11 (d) None of the above

28. A machinery is purchased for Rs. 60,000. Depreciation is to be provided annually on thebasis of fixed instalment method. Useful life of the asset is 8 years and the residual value isRs. 10,000. Rate of depreciation will be

(a) 10.416% (b) 10%(c) 9.416% (d) 11%

29. Goods worth Rs. 7,000 given as charity should be credited to

(a) Trustee A/c (b) Sales A/c(c) Purchases A/c (d) Charity A/c


30. Perpetual inventory valuation system entails

(a) Maintenance of detailed records of receipts and issues.(b) Continuous physical verification(c) Reconciliation of physical stocks with the stock as per records.(d) All of the above

31. Ram, Shyam and Mohan are partners sharing profits in the ratio of 4:3:2. Sohan is admittedfor 1/3 share in future. Profit sacrificing ratio will be


32. Y and Z are partners sharing profit in the ratio of 3:2. X is admitted as a partner. The newprofit sharing ratio among Y, Z and X is 5:3:2. Sacrificing ratio will be

(a) 2:3 (b) 1:1(c) 3:2 (d) None of the above

33. On admission of a partner, unrecorded investment worth Rs. 10,000 and unrecorded liabilitytoward suppliers for Rs. 4,000 will be recorded in

(a) Capital A/c (b) Realization A/c(c) Revaluation A/c (d) None of the above

34. M, N and O are partners with capitals of Rs. 10,000, Rs. 7,500 and Rs. 5,000 respectively. OnO’s retirement his share is acquired by M and N in the ratio of 3:2 respectively. Gainingratio will be

(a) 2:2 (b) 2:3(c) 1:2 (d) 3:2

35. Goodwill is to be calculated at one and half years purchases of average profit of last 6 years.The firm earned profit during the first 3 years as Rs. 30,000, 20,000 and 20,000 and sufferedlosses of Rs. 5000, 3000 and 2000 in the last 3 years. Goodwill amount will be

(a) Rs. 10,000 (b) Rs. 15,000(c) Rs. 20,000 (d) Rs. 25,000

36. X started business with cash Rs. 1,00,000 cash and furniture Rs. 20,000. He bought goodsworth Rs.3,00,000 on credit basis. Sales amount to Rs. 5,00,000 including Rs 50,000; cashsales Rs 1,00,000 sales were outstanding at the end of the year. Cash balance after givingaffect of above transactions will be

(a) Rs 4,50,000 (b) Rs 3,50,000(c) Rs 5,00,000 (d) Rs 2,00,000



37. An old furniture appearing in the books at Rs. 10,000 is to be exchanged for a new furnitureof Rs. 10,000. The old furniture has been valued at Rs. 2,000 for exchange purpose. Loss onexchange will be

(a) Rs. 18,000 (b) Rs. 22,000(c) Rs. 8,000 (d) Rs. 7,000

38. Goods of Rs. 30,000 ( sales price ) sent on approval or return basis were included in the salesbook. The profit included in the sales was 20% on cost stock with the party will increaseclosing stock by

(a) Rs. 25,000 (b) Rs. 30,000(c) Rs. 20,000 (d) Rs. 24,000

39. Which of the following is a non cash expense

(a) Depreciation (b) Salary paid(c) Rent paid (d) Carriage

40. Salary paid to employee Rs. 10,000 debited to Employee A/c by Rs. 1,000. Rectifying entrywill be

(a) Salary A/c Dr 10,000To Employee A/c 10,000

(b) Salary A/c Dr 10,000To Employee A/c 1,000To Suspense A/c 9,000

(c) Salary Dr 10,000To Employee A/c 1,000


41. In the trial balance of joint stock company the following balances are given

i. 10% Mortgage debenture 4,00,000

(payable after 4 years)

ii. Discount allowed on issue of debenture 10,000

Amount of discount written off per year will be

(a) Rs. 2,400 (b) Rs. 2,500(c) Rs. 3,000 (d) Rs. 2,600

42. Recovery of bad debt is a

(a) Revenue expenditure(b) Revenue receipt(c) Deferred revenue expenses(d) Capital receipt


43. Capital on April 1, 2006 20,000Capital on April 1, 2007 25,000Drawings during the year 5,000Additional capital introduced 6,000during the yearNet Profit of the year will be

(a) Rs. 6,000 (b) Rs. 5,000(c) Rs. 4,000 (d) Rs. 3,000

44. Raj draw a bill on Rohan for Rs. 1,00,000 for mutual accommodation. Raj discounted thebill for Rs. 98,000 from Bank and remitted Rs. 49,000 to Rohan. On the due date Raj willsend to Rohan

(a) Rs. 49,000 (b) Rs. 42,000(c) Rs. 47,000 (d) Rs. 50,000

45. In bank reconciliation statement, when balance as per cash book is taken as the startingpoint, then interest collected by the bank Rs.9,000 and direct deposit by a customer into hisbank Rs. 18,000 will be

(a) Ignored (b) Added(c) Subtracted (d) deducted

46. The expired portion of capital expenditure is

(a) An Asset (b) A Liability(c) An Income (d) An Expense

47. On 10.05.2006, A draw a bill on B for Rs. 50,000 for 40 days. June 22 is a public holiday. Thedue date of the bill will be

(a) 21 June, 2006 (b) 23 June, 2006(c) 22 June, 2006 (d) 19 June, 2006

48. Which of the following errors will effect the trial balance

(a) Repairs to motor plant wrongly debited to motor plant(b) Total of purchases journal is short by 70,000(c) Wages paid on purchases of new motors plant debited to wages a/c(d) None of three

49. Rohit acceptance to Sumit for Rs. 15,000 renewed at 6 month on the condition that Rs.10,000 be paid in cash immediately and a new bill of 6 months will be drawn for the remainingamount which will carry interest @ 10% p.a. The amount of interest will be

(a) Rs. 100 (b) Rs. 150(c) Rs. 250 (d) Rs. 200



50. Goods destroyed by fire Rs. 80,000 and insurance company admitted 50% claim. Thisadjustment will be entered in

(a) Balance Sheet (b) Trading A/c(c) P & L A/c (d) All of the above.

51. Following balances are given in trial balance10% loan on (1.04.06) Rs. 70,000 (Cr.)Interest on loan 3,500Interest outstanding at the end of the year will be

(a) Rs. 3,500 (b) Rs. 10,500(c) Rs. 7,000 (d) Rs. 3,000

52. Furniture bought on 1st October 2005 for Rs. 40,000 was sold on 31st March, 2007 forRs. 30,000. Depreciation is charged @ 10% original cost. Accounting year closes on 31stMarch every year . Profit on sales will be

(a) Rs. 3,000 (b) Rs. 1,000(c) Rs. 4,000 (d) Rs. 2,000

53. Following figures have been taken from the book of a trader

Purchases 1,00,000 Purchases returns 9,000

Sales returns 8,000 Sales 1,60,000

Carriage outward 5,000

Office rent 4,000

Amount of gross profit will be

(a) Rs. 60,000 (b) Rs. 61,000(c) Rs. 52,000 (d) Rs. 70,000

54. The profit for the last four years are given as follows

Years Rs.

2003 10,000

2004 15,000

2005 20,000

2006 15,000

The value of goodwill on the basis of three years purchases of average profit based on lastfour years will be

(a) Rs. 15,000 (b) Rs. 60,000(c) Rs. 20,000 (d) Rs. 45,000


55. Which of the following is a fixed asset?

(a) Cash (b) Building(c) Stock (d) Debtors

56. General Reserve at the time of admission of a new partner is transferred to

(a) Capital A/c of partners (b) Trading A/c(c) P & L adjustment (d) Balance Sheet

57. Which of the following is a current asset?

(a) Plant & Machinery (b) Land & Building(c) Debtors (d) Furniture

58. Preliminary expenses in connection with flotation of a new company is

(a) Miscellaneous capital expenditure(b) Current assets(c) Fixed assets(d) All of the above

59. Goods costing Rs. 30,000 were sold at 25% profit on selling price. Sales price will be

(a) Rs. 7,500 (b) Rs. 22,500(c) Rs. 37,500 (d) Rs. 40,000

60. On April, 2006, Gita invested capital of Rs. 60,000. She withdrew Rs. 5,000 on the first dayof each month interest on drawing is provided @ 20%. The amount of interest on drawingsdeducted from capital will be

(a) Rs. 6,000 (b) Rs. 12,000(c) Rs. 6,500 (d) Rs. 1,000


61. Actual breach may be

(a) During the course of performance(b) On the date of performance(c) (a) and (b)(d) (a) or (b)

62. A contract implied by law is known as

(a) Contingent contract (b) Alternation(c) Quasi contract (d) Implied contract

63. Specific performance may be ordered by court if

(a) There is no standard for ascertain actual damage(b) Pecuniary compensation is not adequate relief



(c) The act is done wholly on part of trust(d) (a) or (b) or (c)

64. Performance or offer to the contract is provided in the Indian Contract Act, 1872 in


65. A contract can be performed by

(a) An agent of the promisor (b) The promisor himself(c) (a) or (b) (d) Both (a) and (b)

66. Which of the following statement is false? Consideration

(a) Must be of some value(b) Must not of the desire of the promisor(c) May move from any person(d) Must be illusory

67. An executory consideration

(a) Is a promise for a promise(b) Consists of a promise in future(c) Is an outstanding liability on both the parties(d) All of the above

68. “Specific goods” are defined in


69. Deliverable state is defined in


70. Following is not a mode of delivery

(a) Statutory delivery (b) Constructive delivery(c) Actual delivery (d) Symbolic delivery

71. Buyer’s right against the seller in case of breach of contract deals with

(a) Sections 55 and 56 (b) Sections 53 and 54(c) Sections 57 – 59 (d) None of the above

72. Section 41 of the Sale of Goods Act deals with examination of goods by the

(a) Buyer (b) Seller(c) (a) or (b) (d) (a) and (b)


73. Risk prima facie passes with

(a) Payment of price(b) Property or ownership(c) Completed agreement(d) Verification and delivery of goods

74. When the seller fails to give notice to the buyer under Section 39(3), the risk during sea-transit lies with the

(a) Seller (b) Buyer(c) Carrier (d) Insurer

75. A pen or pencil that will not write, a watch that will not keep time, a rubber that will not helpto erase cannot be considered as

(a) Presentable (b) Whole some(c) Merchantable (d) None of the above

76. Audit of a partnership firm’s account is compulsory under the Partnership Act, 1932

(a) Yes (b) Partly yes(c) No (d) Partly No

77. Seller has right of resale where

(a) Goods are perishable. (b) Seller has reserved such right(c) Seller gives notice (d) All of these.

78. To form a partnership, the minimum capital contribution should be

(a) Rs. 1 Lakhs (b) Rs. 2 Lakhs(c) Rs. 10 Lakhs (d) No minimum limit

79. A contingent contract is

(a) Void from beginning(b) Void if based on happening of an impossible event(c) Enforceable if the contingent event is under the control of the promisor(d) Wagering agreement

80. Champerty and maintenance are the ____________agreement.

(a) Lawful (b) Void(c) Valid (d) Unlawful

81. The decision in Mohori Bibi Vs. Dharamdas Ghose was related to the _________.

(a) Offer and its communication(b) Acceptance and its communication(c) Undue Influence(d) Capacity of a minor to enter into contract



82. _________cannot enter with a contract.

(a) Partner (b) Agent(c) Lunatic (d) Sole Trader

83. The objects of an agreement shall not be unlawful if ___________.

(a) It is forbidden by law (b) It defines the provisions of law(c) It is for legal consideration (d) It is fraudulent

84. A __________ agreement is one, which is enforceable at the option of one party.

(a) Voidable (b) Void(c) Valid (d) Illegal

85. Under Section 18 of the Sale of Goods Act, 1930, the property in goods passes when________.

(a) Payment is made (b) Goods are ascertained(c) The contract is made (d) None of the above

86. Privity of contract is subject to the exception ___________.

(a) Where a trust or charge is created(b) Where payment is made to a third party(c) Where payment is made by a third party(d) None of the above

87. Section ___________ of the Indian Contract Act declares that an agreement made withoutconsideration is void.

(a) 24 (b) 26(c) 28 (d) 30

88. Partnership deed is also called________.

(a) Partnership Agreement (b) Constitution of Partnership(c) Articles of Partnership (d) All of the above

89. Property of the firm shall be held by use of the partners ___________.

(a) For charitable purposes(b) For private purposes of the partners(c) For business purposes as well as private purposes(d) Exclusively for business purposes

90. Section 10 of the Sale of Goods Act 1930 deals with fixation of price of goods by __________.

(a) The Judge(b) The Arbitrator(c) The Central Government(d) The valuation of a third party.


91. In an agreement to sell the property (ownership) in the goods passes __________.

(a) Immediately(b) At a future date(c) Either immediately or future date(d) Never

92. A contract of sale may be__________.

(a) Conditional (b) Absolute(c) Written (d) All of the above

93. Under the Sale of Goods Act, 1930, goods may be _________.

(a) Existing (b) Future(c) Contingent (d) All of the above

94. Where the unpaid seller has attained a decree for the price of the goods, the right of lien_________.

(a) Is lost(b) Is at the optioning the court(c) Is at the optioning the seller(d) Can be exercised

95. The rights available to an unpaid seller against the buyer are right to sue for ________.

(a) Price (b) Damages(c) Interest (d) All of the above

96. An agreement to sell in respect of goods is an executory contract which creates ___________.

(a) A just in personam (b) A just in rem(c) Both (a) and (b) (d) Neither (a) nor (b)

97. A contract of sale of contingent goods is _________.

(a) Sale (b) Agreement to sell(c) Unlawful (d) All of the above

98. The term “Property” is defined under section __________.

(a) 2(11) (b) 2(12)(c) 2(13) (d) 2(14)

99. ‘A’ buys a readymade shirt for his son, The shirt does not exactly fit his son. Decide.

(a) A has no right to return or exchange the same(b) A has right to return the same(c) He will demand for damages(d) He may file a suit for exchange



100. ‘A’ buys a T.V. set from ‘B’. ‘B’ agrees to deliver the set to ‘A’. After some time during theday, B sells the same to ‘C’ at a higher price. Decide title of the good.

(a) ‘C’ gets a good title (b) A gets a good title(c) Nobody gets a goods title (d) None of these


101. If budget deficit is Rs. 11,350 crore and borrowings are Rs. 33,300 crore, what is fiscaldeficit?

(a) Rs. 11,350 crore (b) Rs. 44,650 crore(c) Rs. 33,300 crore (d) Rs. 21,950 crore

102. Sir Robert Giffen was surprised to find out relationship of price with two other goods, whichwere:

(a) Bread and Rice (b) Meat and Rice(c) Bread and Meat (d) Cheese and meat

103. If the proportion of income spent on a good remains the same as income increases, thenincome elasticity for the good in:

(a) More than one (b) One(c) Less than one (d) Zero

104. Marginal utility analysis was mainly propounded by:

(a) J.B. Say (b) Robbins(c) Adam Smith (d) Alfred Marshall

105. Indifference curve analysis is propounded by:

(a) Alfred Marshall (b) Adam Smith(c) Hicks and Allen (d) None of the above

106. Cardinal Measurability of utility means:

(a) Utility can be measured(b) Utility cannot be measured(c) Utility can be ranked(d) Utility can be measured in some case

107. Which of the following statements is false?

(a) An indifference curve is concave to the origin(b) An indifference curve is convex to the origin(c) A higher indifference curve is better than a lower indifferent curve(d) An indifference curve is a curve which represents all those combinations of two goods

which give same satisfaction to the consumer.


108. Identify the factor which generally keeps the price-elasticity of a demand for a good high.

(a) Its very high price (b) Its very low price(c) Large number of substitutes (d) None of the above

109. Suppose price of fashionable Shirts rises from Rs. 400 per piece to Rs. 700 per piece. TheShopping Mall manager observes that the rise in price causes demand for shirts to fall from500 shirts per week to 300 shirts per week. What is the price elasticity of demand for shirts?

(a) 0.916 (b) 1.5(c) 1 (d) 1.667

110. The basic distinction between M1 and M2 is in the:

(a) Treatment of post office deposits(b) Treatment of time deposits of banks(c) Treatment of saving deposits of banks(d) Treatment of currency

111. After 1950, commercial banks in India were nationalized:

(a) Once in 1969(b) Twice in 1969 and 1980(c) Thrice in 1969, 1980 and 1991(d) None of the above

112 In order to increase money supply in the country, the RBI may:

(a) Reduce CRR(b) Increase CRR(c) Sell securities in the open market(d) Increase Bank Rate

113 Monetary Policy is given by:

(a) RBI (b) Planning Commission(c) Finance Minister (d) Monetary Bank of India

114 Which of the following is incorrect?

(a) The shape of the average cost and marginal cost curve is ‘U’(b) The AR and MR curves of a firm under perfect competition are parallel to X-axis.(c) At Equilibrium AR=MR(d) At Equilibrium MC=MR

115 The slope of indifference curve indicates:

(a) Price ratio between two commodities(b) Marginal rate of substitution(c) Factor substitution(d) Level of indifference



116 If the quantity of Banana demanded in 100 kg and quantity supplied is 50 kg, then price perkg of Banana is:

(a) Rs.18(b) Rs.24(c) Less than equilibrium price(d) Greater than equilibrium price

117. Suppose Mohan & Co. produces 10 units of output and incurs Rs. 30 per unit of variablecost and Rs. 5 per unit of fixed cost. In this case, total cost is:

(a) Rs. 300 (b) Rs. 35(c) Rs. 305 (d) Rs. 350

118. A condition needed for a perfectly competitive industry to exist is that:

(a) Buyers are able to influence the price of the commodity(b) Any units of commodity are considered by buyers to be different(c) Buyer discriminates in their purchases based on non-price factors.(d) There are no obstacles to the free mobility of resources.

119. If the price of petrol rises by 25% and demand for car falls by 40% then, cross elasticitybetween petrol and car is:

(a) -1.6 (b) 1.6(c) -2.6 (d) 2.6


(a) Economic laws are mere statement of tendencies(b) Economics laws are as exact as physical lows(c) Economics laws are permanent(d) All of the above

121. If after selling 10 units, a seller realises Rs. 12, 000 and after selling 15 units he realisesRs. 20, 000 what is the marginal revenue here?

(a) Rs. 1500 (b) Rs. 1600(c) Rs. 8000 (d) Rs. 2000

122. Under which market structure, the control of firm over price is nil?

(a) Perfect competition (b) Monopoly(c) Oligopoly (d) Monopolistic Competition

123. If as a result of 80 percent increase in all inputs, the output increases by 25 percent, this is acase of:

(a) Increasing return to scale (b) Decreasing return to factor(c) Decreasing returns to scale (d) Diminishing return to factor


124. When marginal product is negative, then total product is:

(a) Maximum (b) Decreasing(c) Constant (d) None of the above

125. In the long run, a firm in monopolistic competition:

(a) Always earns super profits(b) Incurs losses(c) Earns normal profit only(d) May earn normal profits, super normal profits or incur losses.

126. Assume that when price is Rs.40 quantity demanded is 9 units, and when price is Rs. 38,quantity demanded is 10 units. Based on this information, what is the marginal revenueresulting from an increase in output from 9 units to 10 units?

(a) Rs.20 (b) Rs.40(c) Rs.38 (d) Rs.1

127. Suppose a firm is producing at level of output, such that MR>MC what should be the firmdo to maximise profit?

(a) The firm should increase output(b) The firm should do nothing(c) The firm should hire less labour(d) The firm should decrease price

128. Marginal Revenue is equal to

(a) Change in quantity, divided by the change in price(b) Change in price divided by change in output(c) The change in PxQ due to a one unit change in output(d) None of above

129. Suppose that an owner is earning total revenue of Rs.1, 00,000 and is increasing explicit costof Rs.60, 000. If the owner could work for another company for Rs.30, 000 a year, we wouldconclude that:

(a) The firm is earning economic profit or Rs.10, 000(b) The firm is earning accounting profit or Rs.40, 000(c) The firm is earning economic profit of Rs.40, 000(d) Both (a) and (b)

130. Which is not the essential condition of pure competition?

(a) Large number of buyers and sellers(b) Homogeneous product(c) Freedom of entry(d) Perfect knowledge among buyers and sellers



131. What is the shape of A R curve faced by a firm under perfect competition?

(a) Horizontal(b) Vertical(c) Positively sloped(d) Negatively sloped

132. Which of the following is the condition for equilibrium of a firm?

(a) AC = AR (b) MR = AR(c) MC = MR (d) AC = MR

133. ___________________ measure estimates the number of persons who may be said to bechronically unemployed.

(a) Usual status(b) Current weekly status(c) Current daily status(d) Current yearly status

134. When due to introduction of new equipments, some workers tend to be replaced byequipments; their unemployment is termed as __________

(a) Structural (b) Seasonal(c) Frictional (d) Technological

135. Every__________ person in the world is an Indian

(a) Second (b) Sixth(c) Fifth (d) Ninth

136. __________ measures generally gives the lowest estimate of unemployment.

(a) CWS (b) Usual Status(c) CDS (d) CMS


(a) Countries which are industrially well-developed generally have higher per-capital incomethan countries which are not.

(b) India is a capital surplus economy(c) Agriculture sector need not depend upon industrial sector for its growth(d) None of the above

138. Mahalanobis model stressed upon the establishment of:

(a) Consumer goods industries(b) Export oriented industries(c) Agro-based industries(d) Capital and basic goods industries


139. If income elasticity of the household for good X is 3 then it is a:

(a) Normal Good (b) Necessity Good(c) Luxury Good (d) Inferior Good

140. Which of the following is not included in foreign exchange reserves?

(a) Foreign currency assets held by RBI(b) Gold holding of the RBI(c) Special Drawings Rights(d) None of the above

141. Based II framework is for:

(a) Banks (b) Insurance Companies(c) RBI (d) None of the above

142. The total area under the demand curve of good measures:

(a) Marginal utility (b) Total utility(c) Consumers surplus (d) Producer surplus

143. Which of the following is not a quantitative measure of credit control?

(a) Bank rate policy (b) Open market operation(c) Margin requirement (d) Variable reserve requirement

144. Integration of the domestic economy with the world economy is called____.

(a) Liberalisation (b) Globalisation(c) Privatisation (d) Disinvestment

145. Which of the following is not an indirect Tax Reform?

(a) Reducing the peak rate of custom duties(b) Rectifying anomalies like inverted duty structure(c) Introduction of VAT for achieving harmonized taxation regime(d) The tax rate on foreign companies has also been reduced from 55% to 40%

146. Occupational structure refers to the:

(a) Number of workers living in a country.(b) Size of working population in the industrial sector(c) Distribution of working population among different occupations(d) Nature of different occupation in the economy

147. Which of the following is not a characteristic of a price taker?

(a) Negatively Sloped Demand Curve(b) TR = P x Q(c) AR = Price(d) MR = AR



148. All are features of monopoly except:

(a) There is a single seller(b) The firm is a price taker(c) The firm produces a unique product(d) The existence of some advertising

149. A monopolist is able to maximize his profits when:

(a) His output is maximum(b) He charges a higher price(c) His average cost is minimum(d) His marginal cost is equal to marginal revenue

150. ___________ is the difference between total receipts and total expenditure

(a) Fiscal Deficit (b) Budget Deficit(c) Capital Deficit (d) Revenue Deficit


151. If x 17

x y 23=

+ , what is x + yx y− equal to

(a)11

23(b)

17

32

(c)23

11(d) None of these

152. If 25 x

1 1144 12

+ = + , then x is


153. If (4)3 × ( )82 = 2n, then n is


154. A number of men went to a hotel and each spent as many rupees as there were men. If themoney spent was Rs. 15625; find the number of men.



155. A, B and C have to distribute Rs. 1,000 between them, A and C together haveRs. 400 and B and C Rs. 700. How much does C have?


156. If log a + b 1

2 2= (log a + log b), the value of a2 + b2 is

(a) 6ab (b) 8ab(c) 6a262 (d) None of these

157. If log10x = 4, then the value of x is


158. If log 2 = 0.301 and log 3 = 0.477, then the value of log 225 is:


159. If log 2 = 0.3010, find the number of digits in 2100


160. If nP3 = 60, then the value of n is


161. Evaluate x x

x 0

a b 2lim

x→

+ −

(a) log ab (b) log a

b(c) log (a – b) (d) None of these

162. Evaluate 1x x x

x 0

10 5 2lim

x→

− − +

(a) 1 (b) 0(c) log 5 × log 2 (d) None of these



163. Evaluate x x x

2

10 5 2 1x

− − +

(a) log 5 × log 2 (b) log 5 + log 2(c) 0 (d) None of these

164. Evaluate 5x 3x 2x

x 0

e e e 1lim

x→

− − +


165. Evaluate 5x 3x 2x

x 0

e e e 1lim

x→

− − +


166. Evaluate: 2 2

1dx

x a+∫

(a) log ( )2 2x x a c+ + + (b) log ( )2 2x x a c+ − +

(c) log ( )2 2x x a c− − + (d) None of these

167. Evaluate: 2 2

1dx

x a−∫

(a) log ( )2 2x x a c− − + (b) log ( )2 2x x a c+ + +

(c) log ( )2 2x x a c+ − + (d) None of these

168. Evaluate 2

1dx

9x 1−∫

(a)1 3x 1

log c6 3x 1

+⎛ ⎞ +⎜ ⎟−⎝ ⎠(b)

1 3x 1log c

6 3x 1

−⎛ ⎞ +⎜ ⎟+⎝ ⎠

(c)1 3x 2

log c3 3x 2

+⎛ ⎞ +⎜ ⎟+⎝ ⎠(d) None of these


169. Evaluate 2

x -1dx

x 1+∫

(a) ( )2 2x 1 log x x 1 c+ − + + +

(b) ( )x 1 log x x 1 c− − + − +

(c) ( )2x 1 log x x 1 c+ − + − +

(d) None of these

170. Evaluate (1-x2) log x

(a) ( )2

2 x1 x x log x 1 c

9

⎛ ⎞− − − +⎜ ⎟

⎝ ⎠

(b) ( )2

2 x1 x log x 1 c

9

⎛ ⎞− − + +⎜ ⎟

⎝ ⎠

(c)

2 3x x1 x log x x c

3 9

⎛ ⎞ ⎛ ⎞− − − +⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠

(d) None of these

171. From a panel of 4 doctors, 4 officers and one doctor who is also an officer, how many committeeof 3 can be made if it has to contain at least one doctor and one officer?


172. In an election, there are five candidates contesting for three vacancies; an elector can voteany number of candidates not exceeding the number of vacancies. In how many ways canone cast his votes?


173. In how many ways can 12 different things be equally distributed among 4 groups?

(a) 15,400 (b) 15,000(c) 14,400 (d) None of these



174. The number of factors of 420 is


175. Five balls of different colours are to be placed in three boxes of different sizes. Each box canhold all the five balls. In how many different ways can we place the balls so that no boxremains empty?


176. Find the sum of the series. 243 + 324 + 432 + …………………. to n terms

(a)

n6

n

43 1

3

⎛ ⎞−⎜ ⎟

⎝ ⎠(b)

n4

n

43 1

3

⎛ ⎞−⎜ ⎟

⎝ ⎠

(c)

n6

n

33 1

4

⎛ ⎞−⎜ ⎟

⎝ ⎠(d) None of these

177. The sum of the first eight terms of a G.P. is five times the sum of the first four terms; then thecommon ratio is –

(a) 2 (b) – 2

(c) ± 2 (d) None of these

178. The sum of the following series 4 + 44 + 444 + ………… to n term is:

(a)

n4 10(10 1)n

9 9

⎡ ⎤− −⎢ ⎥⎣ ⎦

(b)

n4 10(10 1)n

9 9

⎡ ⎤− +⎢ ⎥⎣ ⎦

(c)n10(10 1)

n9


179. The Arithmetic Mean between two numbers is 15 and their G.M. is 9; then the numbers are–

(a) 27,3 (b) 9, 9(c) 16, 9 (d) None of these

180. The product of n G.M.s between the two given numbers is equal to the n power of the singleG.M. between them. This statement is –



181. The weighted arithmetic mean of first n natural numbers whose weights are equal to thecorresponding numbers is equal to:

(a)2n 1

3

+(b)

2(2n 1)

2

+

(c)n(n 1)

2

+(d) None of these

182. The mean weight of 15 persons is 110 kg. The mean weight of 5 of them is 100 and another 5is 125 kgs. What is the mean weight of the remainder?

(a) 110 kgs. (b) 105 kgs.(c) 100 kgs. (d) None of these

183. The sum of diviations of certain number of items measured from 2.5 is 50 and the sum ofdeviations of the same series measured from 3.5 is –50. Find the number of observations andtheir mean?


184. The most reliable central value is

(a) Mean (b) Median(c) Mode (d) (a) and (b) both

185. In which Central value arranging is required.

(a) Mean (b) G.M.(c) Median (d) H.M.

186. The chance of 53 Tuesdays in a year is

(a)2

7(b)

1

7

(c)3

7(d) None of these

187. Two unbiased dice are thrown. Find the probability that sum of the faces is not less than 10.

(a)1

6(b)

5

6

(c)2

3(d) None of these



188. The probability that a person travels by a plane is 1

5 and that he travels by train is

2

3 Find

the probability of his traveling neither by plane nor by train?

(a)13

15(b)

2

15

(c)1

15(d) None of these

189. A card is drawn from a well shuffled pack of playing cards. Find the probability that it iseither a diamond or a king.


190. A problem in statistics is given to two students A and B. The odd in favour of A solving theproblem are 6 to 9 and against B Solving the problem are 12 to 10. If both A and B attempt,find the probability of the problem being solved.


191. For a binomial distribution is 7 and its Standard Deviation is 8 . This statement is


192. The mean and variance of a binomial distribution and 3 and 2 respectively. Find theprobability that the variate takes values less than or equal to 2.


193. Two digits are selected at random from the digits 1 through 9. Find the probability that theirsum is even.

(a)2 7

,9 18

(b)5 5

,9 18

(c)4 5

,9 18

(d) None of these


194. A die is thrown twice and the sum of the number appearing is observed to be 6. What is theconditional probability that the number 4 has appeared at least once?

(a)3

5(b)

2

5

(c)4

5(d) None of these

195. It is observed that 80% of television viewers watch “Kahani Ghar Ghar Ki” Programme.What is probability that at least 80% of the viewers in a random sample of five watch thisprogramme?


196. A simple random sample of size 36 is drawn from a finite population consisting of 101 units.If the population Standard Deviation is 12.6, find the Standard Error of sample mean whenthe sample is drawn with replacement.


197. A simple random sample of size 36 is drawn from a finite population consisting of 101 units.If the population Standard Deviation is 12.6, find the Standard Error of sample mean whenthe sample is drawn without replacement.


198. A random sample of size 9 is drawn without replacement from a finite population consistingof 25 units. If the number of defective units in the population be 5, find the Standard Errorof the sample proportion of defectives.


199. A population consists of 4 numbers. Find the number of sample of size 2 for with replacementcondition.


200. A population consists of 4 numbers. Find the number of sample of size two for withoutreplacement condition.


❖❖❖

BOARD OF STUDIES


COMMON PROFICIENCY TESTModel Test Paper – BOS/CPT –10 / 2007





247 247Common Proficiency Test (CPT) Volume - II


1. Cash discount allowed to a debtors should be credited to

(a) Debtor A/c (b) Purchase A/c(c) Discount A/c (d) Sales A/c

2. On 31st December, 2005 Ashok Ltd. purchased a machine from Mohan Ltd., for Rs. 1,75,000.This is

(a) A transaction(b) An event(c) None of these(d) A transaction as well as an event

3. Prepaid commission has a

(a) Negative balance (b) Debit balance(c) Credit balance (d) None of these

4. The following account will have debit balance

(a) Loan to other party(b) Capital A/c(c) Outstanding salary(d) Reserve for doubtful debts



5. A sum of Rs. 50,000 was spent on painting the new plant. It is a

(a) Revenue expenditure(b) Capital expenditure(c) Deferred revenue expenditure(d) None of these

6. Bills receivables is a

(a) Intangible assets (b) Tangible assets(c) Current assets (d) Investment

7. Prepaid insurance account is a

(a) Nominal A/c (b) Personal A/c(c) Real A/c (d) None of the above

8. Under annuity method, interest is calculated on

(a) Written down value (b) Original cost(c) Scrap value (d) None of the above

9. Stock should be out of godown in the sequence in which they arrive is based on

(a) HIFO (b) FIFO(c) Weighted overage (d) LIFO

10. All the expenditures of revenue nature go to

(a) Balance Sheet (b) Trading A/c(c) Profit & Loss A/c (d) Either (b) or (c)

11. Memorandum joint venture account is prepared

(a) When each co-venturer keeps records of their own joint venture transactions(b) When separate set of joint venture books is prepared(c) When each co-venture keep records of all the joint venture transaction himself(d) None of the three

12. The party who sends the goods for sales on fixed commission basis is known as

(a) Drawer (b) Drawee(c) Payee (d) Consignor

13. Endorsement, discounting and collection of bills of exchange is made by

(a) Debtors (b) Creditors(c) Drawee (d) Drawer

14. Returns Inward, appearing in the trial balance are deducted from

(a) Purchases (b) Capital(c) Sales (d) None of the above


15. Drawings is deducted from

(a) Capital (b) Sales(c) Purchases (d) None of the above

16. Purchase of Plant & Machinery on credit basis is recorded in

(a) Cash book (b) Journal proper(c) Purchases (d) Both (a) and (b)

17. The trial balance of Rajesh Ltd. shows closing inventories of Rs. 90,000. It will be recordedin

(a) Profit & Loss A/c (b) Trading A/c(c) Balance Sheet (d) None of the above

18. Loss on issue of debentures is treated as

(a) Miscellaneous capital expenditure(b) Current assets(c) Intangible assets(d) Current Liabilities

19. A proforma invoice is sent by

(a) Debtors to consignee (b) Debtors to consignor(c) Consignor to consignee (d) None of three

20. Noting charges are paid at the time of

(a) Renewal of the bill (b) Retirement of the bill(c) Dishonour of the bill (d) None of the three

21. Accounting has certain norms to be observed by the accountants in recording of transactionsand preparation of financial statement. These norms reduce the vagueness and chances ofmisunderstanding by harmonizing the varied accounting practices. These norms are

(a) Accounting Standards(b) Accounting framework(c) Accounting regulations(d) Accounting guidance notes

22. An undervaluation of previous year’s opening inventory will

(a) Cause current year’s net income to be overstated(b) Cause previous years net income to be understated(c) Cause previous years net income to be overstated(d) None of the above



23. Parul accepted a bill for 90 days of Rs. 10,000 drawn by Rahul on 10 Feb., 2006. On 18thMarch, 2006, Parul wished to retire the bill, Rahul offered rebate @ 12% p.a. consideringthe year of 360 days rebate amount will be

(a) Rs. 184 (b) Rs. 150(c) Rs. 180 (d) None of the above

24. Sohan draws a 40 days bill on Rohan on 20th Jan 2007. The bill falls due on

(a) March 4, 2007 (b) February 29, 2007(c) March 1, 2007 (a) None of these

25. The trial balance checks

(a) Valuation of closing stock(b) valuation of assets(c) valuation of liabilities(d) Arithmetical accuracy of books of accounts.

26. If total sales during the year Rs. 1,00,000; Cash sales Rs. 20,000 and outstanding debtors atthe end of the year Rs. 30,000 then cash received from debtors during the year will be

(a) Rs. 70,000 (b) Rs. 50,000(c) Rs. 1,10,000 (d) Rs. 90,000

27. Cost of goods sold Rs. 1,50,000

Closing stock Rs. 40,000

Opening stock Rs. 60,000

Amount of purchases will be

(a) Rs. 1,30,000 (b) Rs. 1,70,000(c) Rs. 50,000 (d) None of the above

28. If a bill of exchange will mature on 15th August but it is a public holiday then the bill willmature on

(a) 15 August (b) 16 August(c) 14 August (d) 18 August

29. A, B and C are partners in a firm sharing profits and losses in the ratio of 2:3:5. The firmseparate took life policy of Rs. 50,000, Rs. 1,00,000 and Rs. 1,50,000 for A, B and C respectively.The share of B in the policy will be

(a) Rs. 90,000 (b) Rs. 1,50,000(c) Rs. 3,00,000 (d) Rs. 60,000

30. A company purchased a motor car for Rs. 5,00,000. Estimated useful life of the motor caris 15 years and residual value is Rs. 50,000. Rate of depreciation will be

(a) 9% (b) 6%(c) 10% (d) 15%


31. A company issued Rs. 20,000 15% debentures at a discount of 10% redeemable after 15 yearat a premium of 5%. Loss on issue of debentures will be


32. Raj Ltd. purchased machinery for Rs. 20,000 payable Rs. 6500 in cash and the balance byan issue of 10% debentures of Rs. 100 each at a discount of 10%. Discount on issue ofdebentures will be


33. A firm had an unrecorded investment of worth Rs. 50,000. Entry in the firms journal onadmission of a partner will be

(a) Partner Capital A/c Dr. 50,000To Revaluation A/c 50,000

(b) Revaluation A/c Dr. 50,000To Partner’s capital 50,000

(c) Unrecorded investment A/c Dr. 50,000To Revaluation A/c 50,000

(d) Revaluation A/c Dr. 50,000To Unrecorded investment A/c 50,000

34. Gaining ratio is applied when

(a) A partner is insolvent (b) A partner is admitted(c) A partner retires (d) All of the above

35. Interest on capital at 12% p.a. is to be allowed. Capital in the beginning was Rs. 6,00,000.Interest amount will be

(a) Rs. 70,000 (b) Rs. 72,000(c) Rs. 60,000 (d) Rs. 75,000

36. Lal & Co. issued 10,000 debentures of Rs. 100 each at a discount of 4% redeemable after 5years at a premium of 6%. Loss on issue of debentures will be

(a) Rs. 60,000 (b) Rs. 1,60,000(c) Rs. 1,00,000 (d) Rs. 40,000

37. Dismantling and demolition charges is a

(a) Deferred Revenue expenditure(b) Capital expenditure(c) Revenue expenditure(d) None of the above



38. On equity share of Rs.20, the company has called up Rs.18 but actually received Rs.18. Theshare capital would be credited by

(a) Rs. 20 (b) Rs. 18(c) Rs. 16 (d) Rs. 10

39. Net salary paid to employees Rs. 5,00,000 in cash after deducting income tax Rs. 50,000professional tax Rs. 10,000. Salary A/c will be debited with

(a) Rs. 5,00,000 (b) Rs. 4,40,000(c) Rs. 5,60,000 (d) Rs.4,50,000

40. Ram and Mohan are partners sharing profits equally. They admitted Sohan for 1/3 share inthe firm. The new profit sharing ratio will be

(a) 2:2:1 (b) 1:1:1(c) 1:2:3 (d) 3:2:1

41. A, B and C are partners sharing profits and losses in the ratio of 5:4:3. C retires and if A andB share profits of C in 4:3 then new profit sharing ratio will be

(a) 5:4 (b) 4:3(c) 5:3 (d) 47:37

42. Following figures have been taken from the trial balance of a trader:

Cost of goods sold 45,000

Sales 60,000

Closing Stock 10,000

The amount of profit will be

(a) Rs. 15,000 (b) Rs. 25,000(c) Rs. 5,000 (d) None of those

43. In January 2003, a trader purchased machinery for Rs. 1,00,000 depreciation is charged @20% by diminishing balance method. At the end of the third year it was sold for Rs. 31,000.Profit or loss on sale will be

(a) Loss Rs.20,200 (b) Loss Rs.40,000(c) Profit Rs.20,000 (d) Profit Rs.20,200

44. Net profit before charging manager’s commission is Rs. 24,000 and the manager is to beallowed a commission of 20% on the profit after charging such commission. Commissionamount will be

(a) Rs. 4,000 (b) Rs. 4,800(c) Rs. 4444.44 (d) None of the above


45. Amount spent on “Structural alteration” under pressure of law is a

(a) Capital loss (b) Revenue expenditure(c) Capital expenditure (d) Deferred revenue expenditure

46. M, N and O share profit and losses in the ratio of 3:2:1. Upon admission of D, they agreed toshare 5:4:2:1. The sacrificing ratio will be

(a) Nil : Nil : 1/l2 (b) Nil : 1/12 : Nil(c) 1/12 : Nil : Nil (d) None of the above

47. A was holding 100 shares of Rs. 10 each of a company on which he had paid Rs. 4 onapplication and Rs. 3 allotment, but could not pay Rs. 2 on first call. Forfeited share A/c willbe credited with

(a) Rs. 500 (b) Rs. 400(c) Rs. 700 (d) Rs. 600

48. The following information pertains to Arjun Ltd.

(1) Equity share capital called up Rs. 1,00,000(2) Calls in arrear Rs. 10,000(3) Calls in advance Rs. 10,000(4) Proposed dividend 15%The amount of proposed dividend payable is


49. Ram Ltd. purchased the business of Rahim Ltd. for Rs. 9,00,000 payable in fully paidshares of Rs. 100 each. Shares were issued at a premium of 25%. Number of shares issuedagainst purchased consideration will be

(a) 7200 shares (b) 10800 shares(c) 2250 shares (d) 6750 shares

50. Credit balance in the ledger will be

(a) A revenue or an asset (b) A revenue or a liability(c) An expenses or an asset (d) None of the above

51. Gross profit is the difference between

(a) Sales and cost of goods sold (b) Sales and total expenses(c) Sales and purchases (d) None of the above

52. Closing entry for transfer of net profit Rs. 6,300 to the capital a/c will be

(a) Trading A/c 6,300 Dr. To Balance sheet 6,300(b) Trading A/c 6,300 Dr. To Profit & Loss A/c 6,300(c) P & L A/c 6,300 Dr. To Capital A/c 6,300(d) Capital A/c 6,300 Dr. To P& L A/c 6,300



53. The total of “Discount allowed” column in the Cash book for the month of July, 2007amounting to Rs. 10,000 was not posted. Rectifying entry for the same will be

(a) Discount A/c Dr. 10,000 To Suspense A/c 10,000(b) Suspense A/c Dr. 10,000 To Discount A/c 10,000(c) Customer A/c Dr. 10,000 To Discount A/c 10,000(d) None of the above

54. After preparing the trial balance the accountant find that the total of the credit side is shortby Rs. 2,000. This difference will be

(a) Debited to Suspense A/c(b) Credited to suspense A/c(c) Adjusted to any of the credit balance A/c(d) Adjusted to any of the debit balance A/c

55. Goods purchased for Rs. 2,00,000 and were sold for Rs., 1,60,000. Margin 20% on sales.Closing stock is ….


56. Journal entry for wages paid Rs. 3,000 for installation of plant will be

(a) Dr. Plant repairs A/c and Cr. Cash A/c 3,000(b) Dr. Wages A/c and Cr. Cash A/c 3,000(c) Dr. Plant A/c and Cr. Cash A/c 3,000(d) None of the above

57. On June 1, Sahil paid salary amounting Rs. 20,000. This is

(a) A transaction (b) An event(c) Both (a) and (b) (d) None of the above

58. Ram sells goods at cost plus 40%. Total sales were Rs. 21,000. Cost price of the goods will be

(a) Rs. 8,400 (b) Rs. 15,000(c) Rs. 12,600 (d) Rs. 20,000

59. Bright stationery used stationery for business purposes Rs. 500. Amount will be credited to

(a) Purchases A/c (b) Sales A/c(c) Cash A/c (d) None of the above

60. Goods destroyed by fire Rs. 50,000 and insurance company admitted full claim. Claimreceivable will be recorded in

(a) Trading A/c (b) P & L Appropriation A/c(c) P & L A/c (d) Balance Sheet



61. Under Section 2(10) of the Sale of Goods Act, price means

(a) Consideration in money(b) Transfer value of goods(c) Revenue consideration(d) Economic Exchange Value

62. An agreement to share the benefits of a public office

(a) Valid (b) Voidable(c) Void (d) None of the above

63. Agreement which are in nature of bets and gambling are called

(a) Invalid agreements (b) Voidable contracts(c) Contingent contracts (d) Wagering agreements

64. Offer implied from conduct of parties or from circumstances of the case is called

(a) General offer (b) Specific offer(c) Express offer (d) Implied offer

65. Consideration without agreement are valid in case

(a) Out of love and affection(b) Compensation for past voluntary series(c) Promise to pay time barred debt(d) All of the above

66. In case of sale on approval, the ownership is transferred to the buyer when he

(a) Accepts the goods (b) Adopts the transaction(c) Fails the return goods (d) In all the above cases

67. Novation may take place between

(a) Different parties (b) The same parties(c) (a) or (b) (d) (a) and (b)

68. Recission of a contract means

(a) The renewal of original contract(b) Cancellation or termination of contract(c) Substitution of new contract(d) Alteration of contract

69. Discharge of contracts by implied consent does not include

(a) Novations (b) Actual performance(c) Merger (d) Waiver



70. On the valid performance of the contractual obligation by the parties, the contract

(a) Is discharged (b) Becomes enforceable(c) Becomes void (d) None of above

71. A contract is discharged by alteration which means the

(a) Acceptance of loser performance(b) Cancellation of the existing contract(c) Change in one or more terms of contract(d) abandonment of rights by a party

72. A change in nature of obligation of contract known as

(a) Alteration (b) Repudiation(c) Innovation (d) Rescission

73. Which of the following persons can perform the contract?

(a) Promisor alone(b) Agent of the promisor(c) Legal representatives of promisor(d) All of these

74. Which of the remedies not available to a defrauded party?

(a) Consideration of the contract(b) Rescind the contract(c) Insistence on specific performance(d) Suit for damages

75. A seller is an unpaid seller

(a) When only a part of the price has been paid(b) When a cheque has been issued and the payment of the same is stopped(c) When whole of the price has not been tendered(d) Any one of the above

76. When property in goods has not passed to the buyer, the unpaid seller has a right of

(a) With holding delivery (b) Stoppage in transit(c) (a) and (b) (d) (a) or (b)

77. The definition of unpaid seller is given in the Sale of Goods Act, in


78. A notice given to a partner is deemed to be a notice given to the firm when notice is given to

(a) Any active partner (b) Any partner(c) Sleeping partner (d) All the partner


79. On the insolvency of a partner, the insolvent ceases to be a partner in the firm whether thefirm is dissolved or not

(a) Yes (b) No(c) Practically dissolved (d) Dissolve in capital ratio

80. Section _______ of the Partnership Act, 1932 deals with “General duties of partners”.

(a) 7 (b) 9(c) 11 (d) 14

81. For loss caused to the firm by his fraud in the conduct of the business, every partner shallidentify as a ________.

(a) Firm(b) The other partners(c) Only the working partners(d) All the retiring partners

82. A partner may be expelled from the firm by any majority of the partners ________.

(a) In good faith(b) Based on the contract between partners(c) Either (a) or (b)(d) Both (a) and (b)

83. Rules regarding delivery of goods deals by_________.

(a) Section 33 – 39 (b) Section 30 – 32(c) Section 40 – 42 (d) None of the above

84. On the valid performance of the contractual obligations by the parties, the contract__________.

(a) Becomes enforceable (b) Is discharged(c) Becomes void (d) None of these

85. A partnership firm cannot use ___________ the words as part of its name.

(a) Limited (b) Co-operative(c) Enterprises (d) Both (a) and (b)

86. The maximum number of partners in a banking firm is _____________.

(a) 10 (b) 15(c) 20 (d) 25

87. Death of a partner deals with Section ___________.

(a) 36 (b) 35(c) 38 (d) 37



88. A contract of sale is a contract for sale by sample if it is__________.

(a) By operation of law(b) By way of custom or usage of trade(c) By way of an express or implied term in the contract, to that effect(d) By decision of the seller

89. An agreement not enforceable by law is said to be void under Section _________ of theIndian Contract Act.

(a) 2(a) (b) 2(b)(c) 2(d) (d) 2(g)

90. Consent should be given ___________.

(a) By the person to whom offer is made(b) Without condition(c) In clear terms either oral or written(d) All of the above

91. Revocation of offer can be done by __________.

(a) Lapse of time (b) Death of the offeror(c) Counter offer (d) All of the above

92. The terms of offer must be _____________.

(a) Definite (b) Certain(c) Unambiguous (d) All the above

93. A proposal when accepted becomes a _____________.

(a) Promise (b) Agreement(c) Contract (d) None of the above

94. Offer has been defined in the Indian Contract Act, 1872 in __________.

(a) Section 2(a) (b) Section 2(b)(c) Section 2(c) (d) Section 2(d)

95. Communication of offer may be by ___________.

(a) Words only (b) Conduct only(c) Words or conduct (d) None of the above

96. In case letter of acceptance is lost in transit, it will be deemed to be a valid acceptance if it isproved that the letter___________.

(a) Sufficiently stamped (b) Correctly addressed(c) Posted (d) All the above


97. The juristic concept of contract consists of __________.

(a) Offer and acceptance(b) Consideration and coercion(c) Agreement and obligation(d) Free consent and capacity

98. Advertisement inviting tender is __________.

(a) An offer (b) A counter offer(c) An agreement (d) An invitation to offer

99. ‘A’, as surety ‘B’, makes a bond jointly with ‘B’, to ‘C’, to secure a loan from ‘C’ to ‘B’,afterwards, ‘C’ obtains from ‘B’ a further security for the same debt. Subsequently, ‘C’gives up the further security. Decide.

(a) A is discharged (b) A is not discharged(c) B cannot file a suit (d) None of the above

100. ‘A’ and ‘B’ bet as to whether it would rain on a promising to pay Rs. 100 to ‘B’, if it rained,and, ‘B’ promising an equal amount to ‘A’, if it did not. Decide the type of agreement.

(a) Contingent contract (b) Quasi contract(c) Wagering contract (d) Implied contract


101. If the proportion of income spent on a good increase as income increases, then income elasticityfor the good is:

(a) Greater than one (b) Less than one(c) One (d) Infinite

102 Which is not the assumption of marginal utility analysis?

(a) Cardinal measurability of utility(b) Constancy of the marginal utility of money(c) Rationality of human behaviour(d) Ordinal Measurability of utility

103 Law of diminishing marginal utility may not apply to:

(a) Money (b) Butter(c) Pepsi, Coke etc. (d) Ice cream

104 Which is not the assumption of the law of diminishing marginal utility?

(a) The different units consumed should be identifiable in all respects(b) The different units consumed should consist of standard units(c) There should be time gap or interval between consumption of one unit and another unit(d) The law may not apply to hobbies, music etc.



105 Concept of consumer surplus was evolved by:

(a) Allen and Hicks (b) Adam Smith(c) Alfred Marshall (d) Robbins

106 Contraction of demand is the result of:

(a) Increase in the price of other good(b) Increase in the price of substitute goods(c) Decrease in the income of the consumer(d) Increase in the price of the good concerned

107 Which of the following method is not used for measuring elasticity of supply?

(a) Arc Method (b) Percentage Method(c) Total outlay Method (d) Point Method

108 If the local ice-cream shop raises the price of a ice cream cup from Rs 10 per cup to Rs. 15per cup, and quantity demanded falls from 500 cups per day to 300 cups per day, the priceelasticity of demand for ice-cream cup is:

(a) 1 (b) 2.5(c) 2 (d) 1.25

109 SGSY stands far:

(a) Self Gram Swarozgar Yojna(b) Swarnajayanti Gram Swarozgar Yojna(c) Swarnajayanti Gram Sadak Yojna(d) Swarna Gram Swarozgar Yojna

110 Which of the following is not included in M1?

(a) Currency(b) Demand Deposits(c) Other deposits with RBI(d) Other deposits with post office

111 In order to increase money supply in the country RBI may:

(a) Buy securities in the open market(b) Sell securities in the open market(c) Increase CRR(d) Increase Bank rate

112 Which is not near money?

(a) Balance in saving account(b) Balance in current account(c) Both (a) and (b)(d) Time deposits


113 Monopoly power refers to the firm’s ability to:

(a) Earn economic Profit(b) Restrict entry into the industry(c) Set prices above marginal cost(d) Possess economies of scale

114 In the long run monopolistic competitive firm has:

(a) Excess Capacity (b) Excess Profits(c) Zero Fixed cost (d) All of the above

115 Which of the following is a normative statement?

(a) Planned economies allocate resources via government departments(b) Reducing inequality should be a major priorities for mixed economies(c) There is greater degree of consumer sovereignty in market economies(d) Most economies have experienced problems of falling output and rising prices

116 The market of computers is not in equilibrium, then which of the following statements isdefinitely true?

(a) The prices of computer will rise(b) The prices of computer will fall(c) The prices of computers will change, but not enough information is given to determine the

direction of the change(d) None of the above

117 As the price of Bananas rises:

(a) The quantity demanded for bananas increases(b) The demand curve for bananas shifts to the right(c) The quantity demanded for bananas decreases(d) The demand curve far bananas shifts to the left

118 Suppose the short run cost function can be written as TC=250+10Q. Average Fixed costequals:

(a) 250/Q (b) 250(c) 10 (d) 250/Q+10

119 Gopal inherited 1 acre of land from his father in 1960. Today the value of that land is Rs 90lakh per acre. What is the opportunity cost to Gopal for keeping that land? His father paidRs. 50, 000 for this land.

(a) Nothing, since the land was inherited(b) Rs.50, 000 which his father paid(c) Rs.90 lakh, since this amount Gopal is getting now if he sells it(d) Both (b) and (c)



120 Suraj is a high school senior thinking about becoming an economic research assistant. Shyamjust graduated from college with an economic degree and is looking for a job as an economicresearch assistant. For whom is the college tuition an opportunity cost?

(a) Suraj(b) Shyam(C) Both Suraj and Shyam(d) Neither Suraj nor Shyam

121 Which of the following is incorrect?

(a) The shape of average cost is U-shaped(b) MC Curve cuts AC curve at the minimum level of AC(c) The AR and MR curves of the industry under perfect competition are parallel to X- axis

(d) MC curve cuts AVC curve at the minimum level of AVC

122 Other things remaining constant, the law of supply states:

(a) Supply for commodities is directly related to its price(b) Price is not related to supply(c) As supply rises, price also rises(d) Supply is not related to factors other than price

123 Kinked demand curve in oligopoly market explains:

(a) Price and output determination(b) existence of very few firms in the market(c) Price rigidity(d) Price leadership

124 Right to own private property is found in:

(a) Socialism (b) Capitalism(c) Mixed Economy (d) Both (b) and (c)

125 Which of the following is not a factor of production?

(a) Man (b) Labour(c) Capital (d) Entrepreneurs

126 ___________ shows the relationship of output with given inputs.

(a) Demand Function (b) Production Function(c) Cost function (d) PPC function

127 TCn –TCn-1= which cost function?

(a) Marginal Cost (b) Average Cost(c) Total Cost (d) None of the above


128 Shares traded in the stock market depict characteristics close to_________.

(a) Perfect competition(b) Oligopoly(c) Monopolistic Competition(d) Monopoly

129 Assume that when price is Rs.20, quantity demanded in 10 units, and when price is Rs. 19quantity demanded in 11 units. Based on this information, what is the marginal revenueresulting from an increase in output from 10 units to 11 units.

(a) Re.1 (b) Rs.9(c) Rs.19 (d) Rs.10

130 Which of the following is not a characteristic of a price taker?

(a) Positively sloped demand curve(b) TR = PxQ(c) AR = Price(d) Marginal Revenue = Price

131. The cost of one thing in terms of the alternative given up is known as

(a) production cost (b) real cost(c) opportunity cost (d) physical cost

132 With a given supply curve, a decrease in demand causes:

(a) an overall decrease in price but an increase in equilibrium quantity(b) an overall increase in price but a decrease in equilibrium quantity(c) No change in overall price but a reduction in equilibrium quantity(d) An overall decrease in price and a decrease in equilibrium quantity

133 ___________ measure generally gives the highest estimate of unemployment especially forpoor economy

(a) CDS (b) CMS(c) Usual Status (d) CWS

134 VAMBAY stands for:

(a) Vikas Ambedkar Awas Yojna(b) Valmiki Aged Awas Yojna(c) Valmiki Ambedkar Awas Yojna(d) None of the above

135 The measure of absolute poverty is:

(a) Used only by India(b) Not related to the income or consumption expenditure distribution(c) Related to the distribution of income or consumption expenditure(d) None of the above



136 National Population Policy was announced in:

(a) 2001 (b) 1999(c) 2000 (d) 2005

137 Unproductive consumers consist of:

(a) Children upto 15 years (b) Adults above 60 years(c) Both (a) and (b) (d) Adults above 65 years


(a) Agriculture occupies 20% population of India(b) Merely 15% population is below the poverty line(c) The production techniques in India are very advance(d) None of the above

139 ______________ is the top most bank for agricultural loans in India.

(a) NABARD (b) RBI(c) SIDBI (d) SBI

140 MR curve and AR curves coincide in

(a) Monopoly (b) Monopolistic Competition(c) Oligopoly (d) Perfect Competition

141 Law of increasing return operates due to:

(a) Indivisibility of Fixed Factors(b) Division of Labour and specialization(c) Both (a) and (b)(d) Misuse of machinery

142 Law of variable proportion is applicable in:

(a) Short run(b) Long run(c) Both Short run and Long run(d) Very Short run

143 Which of the following statements is incorrect?

(a) Both AP and MP can be calculated from T.P.(b) When AP rises then MP>AP(c) When AP is maximum then MP = AP(d) When AP falls, MP also falls but MP>AP

144 Supply of a Commodity is a :

(a) Flow concept (b) Stock concept(c) Both stock and flow concepts (d) None of these


145 If two goods are perfect substitutes to each other, then is necessarily follows that.

(a) An indifference curve relating to the two goods will be curvilinear(b) An indifference curve relating to the two goods will be linear(c) An indifference curve relating the two goods will be concave to the origin(d) An indifference curve relating the two goods will be convex to the origin

146 When the price of a substitute of X commodity falls, the demand for X commodity:

(a) Falls (b) Rises(c) Remains unchanged (d) Any of the above

147 Generally supply curve of industrial products is

(a) Positively sloped (b) Negatively sloped(c) Both (a) and (b) (d) Parallel of to Y axis

148 Which of the following is not a fixed cost?

(a) Payment of interest on loan(b) Cost of electricity and fuel(c) Depreciation on building(d) Rent of go down.

149 The relationship between the AC and MC is that

(a) MC will always be less than the AC(b) MC will be more than AC when MC is falling(c) AC may be more than MC when MC is rising(d) None of the above

150 Which of the following is not included in M2?

(a) M1(b) Time liabilities portion of saving deposits with bank(c) Certificate of deposits issued by banks(d) Term deposits with banks with maturity over one year


151. The value of 33 + 43 + 53 + …………..+ 113

(a) 4356 (b) 4348(c) 4347 (d) 4374

152. The sum of two numbers is 75 and their difference is 20. Find the difference of their squares.




153. The sum of two numbers is 13 and the sum of their squares is 85. Find the numbers.


154. The difference between the squares of two consecutive numbers is 37. Find the numbers.


155. The denominator of a fraction is 3 more than its numerator. If the numerator is increasedby 7 and the denominator is decreased by 2, we obtain 2. The fraction is –

(a)3

8(b)

5

8

(c)7

8(d) None of these

156. If log 1x 3

6= find the value of x


157. The value of log xaa is

(a) x (b) logax

(c) x2 (d) None of these

158. The value of 2-log 633 is

(a)9

5(b)

3

2

(c)9

4(d) None of these

159. If log 2 = 0.3010, log 3 = 0.04771 and log 5 = 0.6990, there log 30


160. If log10 12.45 = 1.0952 and log10 3.79 = 0.5786, find the value oflog10 124.5 + log10 379.



161. If np5 : np3 = 2:1; then the value of n is


162. A room has 10 doors. In how many ways can a man enter the room by one door and come outby a different door.


163. How many numbers greater than 1000 can be formed with the digits of the number 23416;if the digits are not repeated in the same number.


164. How many numbers can be formed with the digits of the number 112321 that are greaterthan one lakh?


165. In how many different ways can 17 billiard balls be arranged, if 7 of them are black, 6 redand 4 white.


166. Evaluate ( )x

2

xedx

x 1+∫

(a) ( )2

1ex c

x 1+

+ (b)x1

e cx 1

++

(c) ( )2x

2

2xe c

x 1+

+ (d) None of these

167. Evaluate ( )x

3

x -1e dx

x 1+∫

(a) ( )2x

3

ec

x 1+

+ (b) ( )x

3

ec

x 1+

+

(c) ( )x

2

e

x 1+ (d) None of these



168. Evaluate ( )2

1dx

x 4 x 1− +∫

(a)11 x 1 3 1

log tan x 1 c24 3 x 1 3

−⎛ ⎞+ − − + +⎜ ⎟⎜ ⎟+ +⎝ ⎠

(b)

21 2

2

1 x 4 3 1log tan x 4 c

4 2x 4 3

−⎛ ⎞+ − − − +⎜ ⎟⎜ ⎟+ +⎝ ⎠

(c) ( ) ( )2 1 21 1log x 4 x 1 tan x 1 c

2 2−⎡ ⎤− + − + +⎣ ⎦

(d) None of these

169. Evaluate: 2 2

dxx a−∫

(a)1 x a

log c2a x a

− ++ (b)

1 x alog c

2a x a

+ +−

(c)1 x a

log c2a x a

−− ++ (d) None of these

170. Evaluate: 2 2

1dx

a x−∫

(a)1 a x

log c2a a x

+ +− (b)

1 a xlog c

2a a x

− − ++

(c)1 x a

lo g2 a x a

−+ (d) None of these

171. If ex–y + log xy + xy = 0, then dydx

is

(a)y

x(b)

–y

x


(c)–x

y (d) None of these

172. if y = x log (log x); then dydx

is

(a) ( )ylog log x 1

x+⎡ ⎤⎣ ⎦ (b) ( )x

log log x 1y

+⎡ ⎤⎣ ⎦

(c) ( )xlog log x 1

y− +⎡ ⎤⎣ ⎦ (d) None of these

173. If y =

1x + ,

1x +

x then

dydx

is

(a)

4 2

2 2

x x 2

(x 1)

+ ++ (b)

4 2

2

x x 2

x 1

+ ++

(c)

4 2 2

2

(x x 2)

x 1

+ ++ (d) None of these

174. If y x dy

+ =6,then isx y dx

(a)x 17y

17x y

++ (b)

x 17y

17x y

−+

(c)x 17y

17x y

−− (d) None of these

175. Evaluate : 3

474 3

j=0

c + 50- jc∑




176. The first term of an A.P. is 100 and the sum of whose first 6 terms is 5 times the sum of thenext 6 terms, then the c.d. is –

(a) –10 (b) 10(c) 5 (d) None of these

177. The sum of n terms of an A.P. is 3n2+n; then its pth term is

(a) 6P + 2 (b) 6P – 2(d) 6P – 1 (d) None of these

178. The sum of first m terms of an A.P. is same as the sum of first n terms, wherem¹ n; then the sum of first (m+n) terms is:


179. Which term of the sequence, -9 -7

, -2, ,4 4

................ is zero.

(a) 9th term (b) 10th term(c) 12th term (d) None of these

180. If 6 times of 6th term of an A.P. is equal to 15 times the 15th term, then its 21st term.


181. The average of n numbers is x. If each of the numbers is multiplied by (n+1); then theaverage of new set of numbers is

(a) x (b)x

n 1+(c) (n + 1).x (d) None of these

182. The average weight of 8 person increases by 1.5 kg, if a person weighing 65 kg replaced by anew person, what would be the weight of the new person?

(a) 76 kg (b) 80 kg(c) 77 kg (d) None of these

183. The average of marks obtained by 120 students in a certain examination is 135. If the averagemarks of passed students is 39 and that of the failed students is 15; what is the number ofstudents who passed in the examination?



184. The average of 17 numbers is 45. The average of first 9 of these numbers is 51 and the last 9of these numbers is 36. Find the 9th number?


185. The average of 11 results is 30, that of the first five is 25 and that of the last five is 28. Findthe value of the 6th number?


186. There are ……………. Tests for Index Number

(a) Four (b) Three(c) Five (d) None of these

187. Laspeyre’s & Paasche’s Index Number satisfy the time reversal test.


188. If one card is drawn at random from a pack of playing cards; find the probability it isneither a hearts nor a club:

(a) 12 (b) 3

4


189. Three balls are drawn at random from a bag containing 6 blue and 4 red balls. What is thechance that 2 balls are blue and 1 is red?

(a) 14 (b) 3

4


190. Find the probability of 53 Mondays in a leap year?

(a)2

7(b)

3

7

(c)4

7(d) None of these



191. If A & B are independent events and P(A) = 1

3 & P(B) =

3

4 ; then P( AUB ) is

(a)2

6(b)

5

6

(c)1

6(d) None of these

192. Two letters are drawn at random from the word “HOME” Find the probability that boththe letters are vowel?

(a)1

6(b)

5

6

(c)2

3(d) None of these

193. Two letters are drawn at random from the word “HOME” Find the probability that at leastone is vowel?

(a)5

6(b)

1

6

(c)1

3(d) None of these

194. Two letters are drawn at random from the word “HOME” Find the probability that one ofthe letters selected should be M.

(a)1

4(b)

1

2

(c)3

4(d) None of these

195. A and B are two mutually exclusive events of an experiments. If P (‘not A’) = 0.65, P (AYB)= 0.65 and P(B) = p. Then the value of p is


196. Find the sum of n terms of the given series

(a) 2n–n–1 (b) 1–2–n

(c) n+2–n–1 (d) 2n–1


197. Let f(x) be a polynomial function of second degree and a1, a2, a3 are in A.P. then f’ (a2) and f’ (a3) are in

(a) A.P. (b) G.P.(c) Either A.P. or G.P. (d) None of these

198. A man borrows Rs. 20,000 at interest rate 4% per annum compounded annually and agreesto pay both the principal and the interest in 10 equal instalments at the end of each year.Find the value of each instalment (approx.) (Given log 104 = 2.0170 and log 6761 = 3.8300).

(a) Rs. 2,470 (b) Rs. 3,470(d) Rs. 5,470 (d) None of these

199. Two regression coefficient bxy and byx are 1.2 and –0.5. This is


200. The mean of Poisson distribution is 1.6 and variance is 2. This is


❖❖❖


SECTION – A : FUNDAMENTALS OF ACCOUNTING

1. (d) 2. (d) 3. (b) 4. (a) 5. (d)

6. (a) 7. (b) 8. (a) 9. (c) 10. (b)

11. (c) 12. (a) 13. (d) 14. (b) 15. (a)

16. (d) 17. (b) 18. (a) 19. (b) 20. (d)

21. (c) 22. (c) 23. (b) 24. (c) 25. (a)

26. (b) 27. (b) 28. (d) 29. (b) 30. (c)

31. (b) 32. (c) 33. (a) 34. (a) 35. (c)

36. (d) 37. (a) 38. (c) 39. (b) 40. (a)

41. (b) 42. (b) 43. (c) 44. (a) 45. (c)

46. (b) 47. (d) 48. (a) 49. (c) 50. (b)

51. (c) 52. (a) 53. (b) 54. (a) 55. (b)

56. (d) 57. (a) 58. (c) 59. (d) 60. (b)


61. (c) 62. (d) 63. (a) 64. (b) 65. (a)

66. (a) 67. (d) 68. (c) 69. (c) 70. (b)

71. (a) 72. (a) 73. (a) 74. (b) 75. (a)

76. (c) 77. (d) 78. (c) 79. (b) 80. (b)

81. (a) 82. (a) 83. (c) 84. (d) 85. (d)

86. (a) 87. (b) 88. (b) 89. (a) 90. (a)

91. (a) 92. (d) 93. (b) 94. (b) 95. (b)

96. (b) 97. (c) 98. (d) 99. (b) 100. (a)

Answer of Model Test PapersModel Test Paper – BOS/CPT – 1 / 2007


ANSWERS


101 (b) 111 (d) 121 (b) 131 (c) 141 (b)

102 (a) 112 (d) 122 (a) 132 (b) 142 (c)

103 (c) 113 (a) 123 (c) 133 (d) 143 (b)

104 (a) 114 (c) 124 (d) 134 (c) 144 (a)

105 (a) 115 (b) 125 (b) 135 (b) 145 (b)

106 (b) 116 (c) 126 (c) 136 (a) 146 (b)

107 (c) 117 (b) 127 (b) 137 (b) 147 (d)

108 (a) 118 (a) 128 (d) 138 (c) 148 (b)

109 (d) 119 (b) 129 (c) 139 (b) 149 (a)

110 (b) 120 (c) 130 (c) 140 (c) 150 (d)


151. (a) 152. (c) 153. (d) 154. (b) 155. (a)

156. (a) 157. (c) 158. (a) 159. (b) 160. (c)

161. (b) 162. (d) 163. (b) 164. (a) 165. (a)

166. (b) 167. (c) 168. (a) 169. (c) 170. (b)

171. (c) 172. (a) 173. (c) 174. (a) 175. (b)

176. (a) 177. (c) 178. (d) 179. (b) 180. (a)

181. (a) 182. (c) 183. (b) 184. (a) 185. (a)

186. (a) 187. (b) 188. (a) 189. (b) 190. (a)

191. (b) 192. (a) 193. (b) 194. (c) 195. (b)

196. (b) 197. (a) 198. (b) 199. (a) 200. (c )




1. (c) 2. (d) 3. (a) 4. (b) 5. (c)

6. (a) 7. (c) 8. (b) 9. (a) 10. (c)

11. (b) 12. (d) 13. (c) 14. (b) 15. (c)

16. (a) 17. (a) 18. (c) 19. (b) 20. (b)

21. (c) 22. (d) 23. (d) 24. (a) 25. (c)

26. (b) 27. (c) 28. (a) 29. (d) 30. (b)

31. (c) 32. (a) 33. (b) 34. (a) 35. (b)

36. (b) 37. (c) 38. (d) 39. (c) 40. (a)

41. (a) 42. (b) 43. (d) 44. (c) 45. (a)

46. (c) 47. (d) 48. (a) 49. (b) 50. (a)

51. (c) 52. (a) 53. (d) 54. (b) 55. (c)

56. (a) 57. (b) 58. (d) 59. (a) 60. (c)


61. (a) 62. (b) 63. (a) 64. (a) 65. (b)

66. (a) 67. (c) 68. (d) 69. (d) 70. (c)

71. (a) 72. (d) 73. (c) 74. (a) 75. (c)

76. (c) 77. (c) 78. (c) 79. (c) 80. (b)

81. (a) 82. (d) 83. (b) 84. (b) 85. (a)

86. (c) 87. (d) 88. (a) 89. (b) 90. (c)

91. (a) 92. (a) 93. (d) 94. (a) 95. (c)

96. (a) 97. (d) 98. (a) 99. (c) 100. (c)



ANSWERS


101 (a) 111 (b) 121 (a) 131 (b) 141 (a)

102 (c) 112 (d) 122 (b) 132 (c) 142 (c)

103 (c) 113 (b) 123 (d) 133 (a) 143 (d)

104 (d) 114 (b) 124 (d) 134 (c) 144 (a)

105 (b) 115 (a) 125 (c) 135 (a) 145 (c)

106 (c) 116 (d) 126 (d) 136 (d) 146 (c)

107 (d) 117 (c) 127 (a) 137 (a) 147 (d)

108 (d) 118 (d) 128 (b) 138 (b) 148 (b)

109 (d) 119 (b) 129 (a) 139 (d) 149 (d)

110 (d) 120 (a) 130 (b) 140 (a) 150 (a)


151. (a) 152. (b) 153. (a) 154. (a) 155. (c)

156. () 157. (c) 158. (b) 159. (a) 160. (c)

161. (a) 162. (b) 163. (b) 164. (a) 165. (b)

166. (b) 167. (b) 168. (c) 169. (b) 170. (b)

171. (c) 172. (a) 173. (c) 174. (d) 175. (b)

176. (a) 177. (a) 178. (b) 179. (a) 180. (a)

181. (b) 182. (b) 183. (a) 184. (c) 185. (b)

186. (b) 187. (a) 188. (c) 189. (a) 190. (b)

191. (b) 192. (a) 193. (a) 194. (b) 195. (c)

196. (a) 197. (b) 198. (a) 199. (c) 200. (b)




1. (a) 2. (c) 3. (c) 4. (c) 5. (a)

6. (a) 7. (b) 8. (b) 9. (a) 10. (b)

11. (d) 12. (d) 13. (d) 14. (c) 15. (a)

16. (a) 17. (a) 18. (a) 19. (a) 20. (c)

21. (b) 22. (a) 23. (c) 24. (d) 25. (a)

26. (c) 27. (a) 28. (d) 29. (b) 30. (b)

31. (b) 32. (a) 33. (c) 34. (d) 35. (a)

36. (d) 37. (d) 38. (a) 39. (c) 40. (a)

41. (b) 42. (c) 43. (c) 44. (c) 45. (c)

46. (b) 47. (a) 48. (c) 49. (d) 50. (b)

51. (b) 52. (a) 53. (b) 54. (b) 55. (d)

56. (b) 57. (d) 58. (a) 59. (b) 60. (c)


61. (c) 62. (d) 63. (d) 64. (d) 65. (c)

66. (b) 67. (d) 68. (a) 69. (c) 70. (a)

71. (a) 72. (c) 73. (c) 74. (d) 75. (a)

76. (a) 77. (b) 78. (a) 79. (b) 80. (c)

81. (b) 82. (a) 83. (b) 84. (c) 85. (c)

86. (c) 87. (b) 88. (c) 89. (d) 90. (b)

91. (b) 92. (a) 93. (c) 94. (c) 95. (c)

96. (a) 97. (c) 98. (b) 99. (b) 100. (a)



ANSWERS


101 (d) 111 (a) 121 (d) 131 (d) 141 (b)

102 (b) 112 (d) 122 (c) 132 (a) 142 (d)

103 (b) 113 (c) 123 (b) 133 (c) 143 (d)

104 (c) 114 (c) 124 (c) 134 (a) 144 (a)

105 (c) 115 (b) 125 (a) 135 (d) 145 (b)

106 (a) 116 (d) 126 (c) 136 (a) 146 (c)

107 (b) 117 (a) 127 (a) 137 (a) 147 (b)

108 (b) 118 (c) 128 (d) 138 (b) 148 (d)

109 (c) 119 (a) 129 (c) 139 (d) 149 (b)

110 (d) 120 (d) 130 (b) 140 (c) 150 (c)


151. (b) 152. (c) 153. (a) 154. (b) 155. (c)

156. (c) 157. (a) 158. (b) 159. (b) 160. (c)

161. (b) 162. (a) 163. (b) 164. (a) 165. (b)

166. (c) 167. (b) 168. (c) 169. (a) 170. (b)

171. (d) 172. (a) 173. (c) 174. (b) 175. (a)

176. (a) 177. (c) 178. (a) 179. (c) 180. (a)

181. (a) 182. (a) 183. (a) 184. (d) 185. (c)

186. (b) 187. (a) 188. (c) 189. (a) 190. (a)

191. (c) 192. (b) 193. (a) 194. (b) 195. (a)

196. (a) 197. (c) 198. (b) 199. (a) 200. (c)




1. (b) 2. (d) 3. (b) 4. (c) 5. (d)

6. (b) 7. (d) 8. (d) 9. (b) 10. (a)

11. (c) 12. (c) 13. (b) 14. (b) 15. (c)

16. (a) 17. (a) 18. (c) 19. (a) 20. (d)

21. (a) 22. (d) 23. (c) 24. (a) 25. (c)

26. (a) 27. (d) 28. (b) 29. (b) 30. (d)

31. (c) 32. (c) 33. (c) 34. (a) 35. (d)

36. (a) 37. (d) 38. (c) 39. (b) 40. (c)

41. (a) 42. (c) 43. (a) 44. (a) 45. (c)

46. (b) 47. (c) 48. (b) 49. (b) 50. (b)

51. (a) 52. (c) 53. (b) 54. (a) 55. (b)

56. (b) 57. (b) 58. (d) 59. (a) 60. (b)


61. (d) 62. (c) 63. (a) 64. (c) 65. (c)

66. (a) 67. (d) 68. (d) 69. (b) 70. (c)

71. (b) 72. (d) 73. (c) 74. (c) 75. (b)

76. (b) 77. (d) 78. (a) 79. (c) 80. (d)

81. (c) 82. (b) 83. (c) 84. (b) 85. (b)

86. (a) 87. (c) 88. (b) 89. (b) 90. (a)

91. (c) 92. (b) 93. (b) 94. (a) 95. (c)

96. (d) 97. (b) 98. (a) 99. (b) 100. (b)



ANSWERS


101 (c) 111 (d) 121 (d) 131 (a) 141 (a)

102 (c) 112 (c) 122 (c) 132 (a) 142 (c)

103 (a) 113 (c) 123 (b) 133 (b) 143 (b)

104 (c) 114 (d) 124 (a) 134 (a) 144 (c)

105 (c) 115 (d) 125 (c) 135 (b) 145 (b)

106 (c) 116 (a) 126 (b) 136 (d) 146 (c)

107 (d) 117 (b) 127 (d) 137 (b) 147 (b)

108 (a) 118 (b) 128 (d) 138 (c) 148 (a)

109 (a) 119 (d) 129 (b) 139 (c) 149 (a)

110 (d) 120 (a) 130 (a) 140 (b) 150 (c)


151. (a) 152. (c) 153. (a) 154. (c) 155. (c)

156. (b) 157. (a) 158. (a) 159. (b) 160. (a)

161. (a) 162. (b) 163. (a) 164. (a) 165. (a)

166. (a) 167. (d) 168. (d) 169. (a) 170. (b)

171. (b) 172. (b) 173. (a) 174. (b) 175. (a)

176. (c) 177. (a) 178. (c) 179. (a) 180. (b)

181. (c) 182. (a) 183. (a) 184. (a) 185. (b)

186. (a) 187. (b) 188. (c) 189. (a) 190. (b)

191. (a) 192. (a) 193. (b) 194. (a) 195. (b)

196. (b) 197. (a) 198. (b) 199. (b) 200. (b)




1. (a) 2. (d) 3. (c) 4. (d) 5. (b)

6. (a) 7. (d) 8. (a) 9. (c) 10. (b)

11. (d) 12. (b) 13. (a) 14. (c) 15. (d)

16. (a) 17. (d) 18. (c) 19. (c) 20. (d)

21. (a) 22. (b) 23. (c) 24. (b) 25. (a)

26. (c) 27. (d) 28. (c) 29. (a) 30. (b)

31. (c) 32. (a) 33. (d) 34. (d) 35. (a)

36. (c) 37. (b) 38. (c) 39. (c) 40. (b)

41. (b) 42. (d) 43. (a) 44. (a) 45. (d)

46. (c) 47. (a) 48. (b) 49. (c) 50. (b)

51. (a) 52. (d) 53. (a) 54. (b) 55. (c)

56. (c) 57. (b) 58. (b) 59. (b) 60. (d)


61. (a) 62. (b) 63. (d) 64. (d) 65. (b)

66. (b) 67. (b) 68. (d) 69. (c) 70. (b)

71. (a) 72. (c) 73. (a) 74. (b) 75. (b)

76. (d) 77. (a) 78. (c) 79. (d) 80. (b)

81. (a) 82. (c) 83. (a) 84. (c) 85. (c)

86. (a) 87. (c) 88. (b) 89. (c) 90. (b)

91. (b) 92. (d) 93. (d) 94. (c) 95. (a)

96. (a) 97. (a) 98. (b) 99. (b) 100. (b)



ANSWERS


101 (b) 111 (b) 121 (c) 131 (b) 141 (d)

102 (c) 112 (b) 122 (a) 132 (a) 142 (a)

103 (d) 113 (d) 123 (a) 133 (a) 143 (a)

104 (c) 114 (b) 124 (a) 134 (b) 144 (d)

105 (d) 115 (c) 125 (c) 135 (a) 145 (c)

106 (a) 116 (a) 126 (c) 136 (b) 146 (c)

107 (b) 117 (b) 127 (b) 137 (b) 147 (a)

108 (a) 118 (b) 128 (a) 138 (a) 148 (b)

109 (b) 119 (b) 129 (d) 139 (d) 149 (b)

110 (d) 120 (a) 130 (d) 140 (a) 150 (d)


151. (c) 152. (a) 153. (b) 154. (a) 155. (b)

156. (b) 157. (b) 158. (c) 159. (a) 160. (b)

161. (a) 162. () 163. (a) 164. (a) 165. (a)

166. (b) 167. (b) 168. (a) 169. (c) 170. (a)

171. (a) 172. (c) 173. (a) 174. (b) 175. (c)

176. (a) 177. (b) 178. (a) 179. (c) 180. (a)

181. (a) 182. (b) 183. (b) 184. (a) 185. (d)

186. (c) 187. (c) 188. (b) 189. (a) 190. (b)

191. (a) 192. (a) 193. (b) 194. (b) 195. (c)

196. (c) 197. (b) 198. (b) 199. (b) 200. (b)




1. (d) 2. (b) 3. (a) 4. (c) 5. (b)

6. (a) 7. (a) 8. (a) 9. (a) 10. (c)

11. (a) 12. (d) 13. (c) 14. (b) 15. (d)

16. (b) 17. (c) 18. (b) 19. (c) 20. (a)

21. (a) 22. (b) 23. (d) 24. (a) 25. (a)

26. (b) 27. (c) 28. (a) 29. (a) 30. (b)

31. (a) 32. (d) 33. (c) 34. (b) 35. (c)

36. (a) 37. (b) 38. (a) 39. (c) 40. (d)

41. (b) 42. (a) 43. (c) 44. (a) 45. (d)

46. (c) 47. (c) 48. (b) 49. (a) 50. (a)

51. (c) 52. (a) 53. (b) 54. (a) 55. (a)

56. (d) 57. (d) 58. (a) 59. (c) 60. (a)


61. (b) 62. (d) 63. (d) 64. (b) 65. (a)

66. (d) 67. (d) 68. (d) 69. (a) 70. (d)

71. (b) 72. (b) 73. (d) 74. (a) 75. (b)

76. (a) 77. (c) 78. (b) 79. (b) 80. (a)

81. (a) 82. (c) 83. (b) 84. (a) 85. (d)

86. (c) 87. (a) 88. (c) 89. (c) 90. (c)

91. (b) 92. (c) 93. (c) 94. (a) 95. (a)

96. (b) 97. (b) 98. (b) 99. (b) 100. (a)



ANSWERS


101 (d) 111 (c) 121 (d) 131 (b) 141 (a)

102 (a) 112 (a) 122 (a) 132 (c) 142 (d)

103 (c) 113 (d) 123 (a) 133 (d) 143 (a)

104 (c) 114 (d) 124 (c) 134 (c) 144 (b)

105 (d) 115 (a) 125 (b) 135 (b) 145 (a)

106 (b) 116 (c) 126 (d) 136 (c) 146 (b)

107 (b) 117 (b) 127 (d) 137 (c) 147 (b)

108 (a) 118 (c) 128 (b) 138 (a) 148 (d)

109 (b) 119 (c) 129 (b) 139 (b) 149 (c)

110 (a) 120 (d) 130 (c) 140 (b) 150 (a)


151. (b) 152. (b) 153. (d) 154. (a) 155. (a)

156. (a) 157. (b) 158. (a) 159. (a) 160. (a)

161. (b) 162. (c) 163. (a) 164. () 165. (b)

166. (c) 167. (a) 168. (a) 169. (b) 170. (a)

171. (c) 172. (a) 173. (a) 174. (b) 175. (c)

176. (b) 177. (c) 178. (a) 179. (c) 180. (b)

181. (b) 182. (a) 183. (c) 184. (c) 185. (c)

186. (c) 187. (b) 188. (b) 189. (b) 190. (b)

191. (b) 192. (a) 193. (b) 194. (a) 195. (b)

196. (a) 197. (c) 198. (c) 199. (c) 200. (c)




1. (c) 2. (c) 3. (b) 4. (d) 5. (c)

6. (c) 7. (b) 8. (c) 9. (c) 10. (a)

11. (b) 12. (a) 13. (b) 14. (d) 15. (d)

16. (c) 17. (a) 18. (d) 19. (a) 20. (b)

21. (b) 22. (b) 23. (a) 24. (c) 25. (d)

26. (a) 27. (c) 28. (d) 29. (c) 30. (d)

31. (b) 32. (d) 33. (b) 34. (a) 35. (d)

36. (a) 37. (c) 38. (d) 39. (b) 40. (b)

41. (d) 42. (c) 43. (d) 44. (b) 45. (a)

46. (c) 47. (c) 48. (a) 49. (b) 50. (c)

51. (b) 52. (c) 53. (c) 54. (d) 55. (b)

56. (b) 57. (d) 58. (a) 59. (c) 60. (b)


61. (c) 62. (c) 63. (d) 64. (a) 65. (c)

66. (d) 67. (d) 68. (c) 69. (b) 70. (a)

71. (b) 72. (d) 73. (c) 74. (c) 75. (c)

76. (c) 77. (b) 78. (d) 79. (c) 80. (a)

81. (d) 82. (a) 83. (c) 84. (c) 85. (a)

86. (d) 87. (d) 88. (a) 89. (a) 90. (d)

91. (c) 92. (b) 93. (b) 94. (c) 95. (b)

96. (d) 97. (a) 98. (b) 99. (d) 100. (a)



ANSWERS


101 (d) 111 (c) 121 (a) 131 (c) 141 (b)

102 (a) 112 (b) 122 (b) 132 (c) 142 (a)

103 (b) 113 (b) 123 (d) 133 (c) 143 (c)

104 (d) 114 (c) 124 (a) 134 (d) 144 (d)

105 (a) 115 (a) 125 (a) 135 (c) 145 (d)

106 (b) 116 (b) 126 (c) 136 (b) 146 (d)

107 (c) 117 (d) 127 (a) 137 (c) 147 (a)

108 (d) 118 (b) 128 (d) 138 (a) 148 (b)

109 (c) 119 (b) 129 (d) 139 (d) 149 (a)

110 (d) 120 (d) 130 (b) 140 (a) 150 (b)


151. (c) 152. (a) 153. (d) 154. (a) 155. (d)

156. (a) 157. (a) 158. (a) 159. (b) 160. (c)

161. (b) 162. (c) 163. (c) 164. (b) 165. (a)

166. (c) 167. (a) 168. (b) 169. (b) 170. (c)

171. (a) 172. (a) 173. (b) 174. (c) 175. (a)

176. (b) 177. (b) 178. (a) 179. (b) 180. (a)

181. (c) 182. (a) 183. (c) 184. (b) 185. (c)

186. (a) 187. (b) 188. (c) 189. (b) 190. (a)

191. (a) 192. (a) 193. (b) 194. (a) 195. (c)

196. (a) 197. (b) 198. (b) 199. (a) 200. (c)




1. (b) 2. (a) 3. (d) 4. (d) 5. (b)

6. (c) 7. (b) 8. (b) 9. (a) 10. (d)

11. (b) 12. (d) 13. (c) 14. (a) 15. (c)

16. (a) 17. (d) 18. (a) 19. (c) 20. (a)

21. (c) 22. (d) 23. (c) 24. (a) 25. (a)

26. (b) 27. (a) 28. (d) 29. (c) 30. (d)

31. (b) 32. (d) 33. (c) 34. (a) 35. (b)

36. (c) 37. (d) 38. (a) 39. (c) 40. (d)

41. (b) 42. (c) 43. (c) 44. (d) 45. (c)

46. (b) 47. (c) 48. (a) 49. (c) 50. (b)

51. (d) 52. (c) 53. (b) 54. (c) 55. (a)

56. (d) 57. (b) 58. (a) 59. (c) 60. (b)


61. (d) 62. (a) 63. (c) 64. (b) 65. (c)

66. (d) 67. (c) 68. (d) 69. (d) 70. (b)

71. (d) 72. (c) 73. (c) 74. (b) 75. (b)

76. (a) 77. (b) 78. (a) 79. (b) 80. (c)

81. (d) 82. (c) 83. (b) 84. (b) 85. (d)

86. (c) 87. (a) 88. (c) 89. (a) 90. (a)

91. (a) 92. (c) 93. (d) 94. (d) 95. (c)

96. (a) 97. (a) 98. (a) 99. (c) 100. (a)



ANSWERS


101 (b) 111 (c) 121 (b) 131 (a) 141 (c)

102 (b) 112 (a) 122 (b) 132 (b) 142 (c)

103 (a) 113 (d) 123 (c) 133 (a) 143 (c)

104 (a) 114 (d) 124 (a) 134 (d) 144 (d)

105 (a) 115 (a) 125 (a) 135 (b) 145 (d)

106 (b) 116 (d) 126 (a) 136 (c) 146 (d)

107 (a) 117 (b) 127 (b) 137 (b) 147 (d)

108 (b) 118 (b) 128 (d) 138 (b) 148 (a)

109 (c) 119 (d) 129 (c) 139 (d) 149 (a)

110 (d) 120 (a) 130 (c) 140 (d) 150 (d)


151. (b) 152. (a) 153. (b) 154. (c) 155. (a)

156. (c) 157. (c) 158. (c) 159. (a) 160. (b)

161. (b) 162. (c) 163. (c) 164. (a) 165. (b)

166. (b) 167. (c) 168. (a) 169. (a) 170. (b)

171. (b) 172. (a) 173. (b) 174. (d) 175. (a)

176. (a) 177. (c) 178. (b) 179. (b) 180. (b)

181. (a) 182. (c) 183. (a) 184. (b) 185. (a)

186. (c) 187. (a) 188. (c) 189. (d) 190. (b)

191. (a) 192. (a) 193. (a) 194. (c) 195. (a)

196. (a) 197. (d) 198. (b) 199. (a) 200. (a)




1. (a) 2. (c) 3. (a) 4. (a) 5. (a)

6. (b) 7. (c) 8. (b) 9. (b) 10. (c)

11. (d) 12. (c) 13. (a) 14. (b) 15. (b)

16. (d) 17. (a) 18. (b) 19. (b) 20. (c)

21. (c) 22. (a) 23. (b) 24. (a) 25. (b)

26. (c) 27. (c) 28. (a) 29. (c) 30. (d)

31. (b) 32. (b) 33. (c) 34. (d) 35. (b)

36. (c) 37. (c) 38. (a) 39. (a) 40. (b)

41. (b) 42. (b) 43. (c) 44. (d) 45. (b)

46. (d) 47. (a) 48. (b) 49. (c) 50. (c)

51. (a) 52. (d) 53. (b) 54. (d) 55. (b)

56. (a) 57. (c) 58. (a) 59. (d) 60. (c)


61. (b) 62. (c) 63. (d) 64. (c) 65. (c)

66. (a) 67. (d) 68. (b) 69. (c) 70. (a)

71. (c) 72. (b) 73. (b) 74. (a) 75. (c)

76. (c) 77. (d) 78. (d) 79. (b) 80. (d)

81. (d) 82. (c) 83. (c) 84. (a) 85. (b)

86. (a) 87. (a) 88. (d) 89. (d) 90. (d)

91. (b) 92. (d) 93. (d) 94. (d) 95. (d)

96. (a) 97. (b) 98. (a) 99. (a) 100. (a)



ANSWERS


101 (b) 111 (b) 121 (b) 131 (a) 141 (a)

102 (c) 112 (a) 122 (a) 132 (c) 142 (b)

103 (b) 113 (a) 123 (c) 133 (a) 143 (c)

104 (d) 114 (c) 124 (b) 134 (d) 144 (b)

105 (c) 115 (b) 125 (c) 135 (b) 145 (d)

106 (a) 116 (c) 126 (a) 136 (b) 146 (c)

107 (a) 117 (d) 127 (a) 137 (a) 147 (a)

108 (c) 118 (d) 128 (c) 138 (d) 148 (b)

109 (a) 119 (a) 129 (d) 139 (c) 149 (d)

110 (b) 120 (a) 130 (d) 140 (d) 150 (b)


151. (c) 152. (a) 153. (a) 154. (b) 155. (a)

156. (a) 157. (c) 158. (a) 159. (b) 160. (c)

161. (a) 162. (b) 163. (a) 164. (b) 165. (a)

166. (a) 167. (c) 168. (b) 169. (a) 170. (c)

171. (a) 172. (c) 173. (a) 174. (b) 175. (b)

176. (a) 177. (c) 178. (a) 179. (a) 180. (a)

181. (a) 182. (b) 183. (a) 184. (a) 185. (c)

186. (b) 187. (a) 188. (b) 189. (a) 190. (b)

191. (b) 192. (a) 193. (c) 194. (b) 195. (b)

196. (a) 197. (b) 198. (b) 199. (a) 200. (b)




1. (a) 2. (d) 3. (b) 4. (a) 5. (b)

6. (c) 7. (b) 8. (b) 9. (b) 10. (d)

11. (a) 12. (d) 13. (d) 14. (c) 15. (a)

16. (b) 17. (c) 18. (a) 19. (c) 20. (c)

21. (a) 22. (c) 23. (c) 24. (a) 25. (d)

26. (b) 27. (a) 28. (c) 29. (a) 30. (b)

31. (c) 32. (b) 33. (c) 34. (c) 35. (b)

36. (c) 37. (c) 38. (b) 39. (c) 40. (b)

41. (d) 42. (a) 43. (a) 44. (a) 45. (b)

46. (c) 47. (c) 48. (b) 49. (a) 50. (b)

51. (a) 52. (c) 53. (a) 54. (b) 55. (b)

56. (c) 57. (a) 58. (b) 59. (a) 60. (d)


61. (a) 62. (a) 63. (d) 64. (a) 65. (d)

66. (d) 67. (b) 68. (b) 69. (b) 70. (a)

71. (c) 72. (c) 73. (d) 74. (b) 75. (d)

76. (c) 77. (a) 78. (a) 79. (a) 80. (b)

81. (a) 82. (d) 83. (a) 84. (d) 85. (a)

86. (a) 87. (b) 88. (c) 89. (d) 90. (d)

91. (d) 92. (d) 93. (a) 94. (a) 95. (c)

96. (d) 97. (a) 98. (d) 99. (a) 100. (c)



ANSWERS


101 (a) 111 (a) 121 (c) 131 (c) 141 (c)

102 (d) 112 (d) 122 (a) 132 (d) 142 (a)

103 (a) 113 (b) 123 (c) 133 (a) 143 (d)

104 (c) 114 (a) 124 (d) 134 (c) 144 (a)

105 (c) 115 (b) 125 (a) 135 (b) 145 (b)

106 (d) 116 (c) 126 (b) 136 (c) 146 (a)

107 (c) 117 (c) 127 (a) 137 (c) 147 (a)

108 (d) 118 (a) 128 (a) 138 (d) 148 (b)

109 (b) 119 (c) 129 (b) 139 (a) 149 (c)

110 (d) 120 (a) 130 (a) 140 (d) 150 (d)


151. (c) 152. (a) 153. (a) 154. (a) 155. (b)

156. (b) 157. (a) 158. (b) 159. (c) 160. (b)

161. (b) 162. (a) 163. (c) 164. (a) 165. (b)

166. (b) 167. (c) 168. (a) 169. (a) 170. (b)

171. (d) 172. (a) 173. (a) 174. (c) 175. (a)

176. (a) 177. (b) 178. (a) 179. (b) 180. (c)

181. (c) 182. (c) 183. (a) 184. (a) 185. (b)

186. (a) 187. (b) 188. (a) 189. (c) 190. (a)

191. (b) 192. (a) 193. (a) 194. (b) 195. (c)

196. (C) 197. (a) 198. (a) 199. (b) 200. (b)



SECTION – D : QUANTITATIVE APTITUDE

Suggested Answers/ Hints


151. ( ) ( ) 54

3264641 2/1

0

−++⎟⎠

⎞⎜⎝

⎛ − = ( ) ( )54

54

3216411 −++

= ( )54

52811 ++

= 42811 ++

= 8

1378

1281816811 =++=++

= 8117

152. Given 45ba 22 =+ → (1)

18ab = → (2)

(2) a=b

18 → (3)

Substitute a = b

18 in (1)

45bb

18 22

=+⎟⎠

⎞⎜⎝

⎛

45bb324 2

2 =+

24 b45b324 =+

0324b45b 24 =+−

Let xb 2 =

0324x45x2 =+−

295


ANSWERS

( ) ( ) 09x36x =−−

9x,36x ==

When x = 36, b = 6 When x = 9, b = 3

When, b = 6, (3) ⇒ a = 6

18 = 3

When b = 3, (3) ⇒ a = 3

18 = 6

When a = 3, b = 6

∴ 21

63

612

61

31

b1

a1 ==+=+=+

When a = 6, b = 3 ⇒ 21

31

61

b1

a1 =+=+

∴ Ans (c) = 21

a1a1

a1aa 2

121

21

+−+

−+

−−

= a1a

11

a1a

1a

+

−+

−

+

= ( ) ( )a1a1a

a1a1a

+−+

−+

= ( )( ) ( )( )( ) ( ) ⎥

⎥⎦

⎤

⎢⎢⎣

⎡

+−−−+++

a1a1a11aa11a

a1

= ( ) ( ) ⎥⎥⎦

⎤

⎢⎢⎣

⎡

+−+−−++++

a1a1a1aaaa1aaa

a1

= ( ) ( )⎥⎥⎦⎤

⎢⎢⎣

⎡

+−+

a1a1a2a2

a1

= ( )( )( )a1a1a

1aa2+−+

153. Given

296

= a1

2−


e

44

e

2

log10log.

10log2log

xlog5log

loglog =

or, 2log4

)5log4(2log = logx

∴x = 5

Ans.(b)

highest score = x92

The next highest = ⎟⎠

⎞⎜⎝

⎛ − x92x

92 According the third condition of the problem

8x92x

92

9x2 =⎟

⎠

⎞⎜⎝

⎛ −−

8x814x

92

9x2 =+−

x = 162481x8 =

Ans. (a) 156. Let three proportionals are a, b, c

Then the third proportional = c = [ ]acba

b 2=∴

∴ 3

8015400

1520c

2===

Ans. (a)

157. Let a, b, c be the three proport ional then the mean proportional = b = ac

i.e. b = 259 × = 3 × 3

= 15

or, log 5 = log x

155. Let the total score = x. Given the condition

154. The given equation may be written as

297

Ans. (c)


ANSWERS

158. Let the boys Ratio 2x and the girls ratio 5x Given 2x + 5x = 280 7x = 280

x = 407

280 =

∴ Boys Ratio = 2 × 40 = 80

Girls Ratio = 5 × 40 = 200 159. Let x be the number of coins available in a bag

Given 35x41x

21x =++

354

xx2x4 =++

7 x = 35 × 4

x = 207

435 =×

Ans. (b) 160. Let the number be x. Then according to the given condition of the problem.

14

1x3x ++=

( ) 14

1x3x =+−

112

3x3x4 =−−

x = 15 Ans. (c)

161. Let log3 ⎟⎠

⎞⎜⎝

⎛

811 = x

i.e. 8113 x =

−

x 3 = 12 −

298


= ( )431

4x 33 −=

Ans. (b)

162. Let 22log ⎟⎠

⎞⎜⎝

⎛

2561 = x

i.e. ( )x22 =

2561

( )x½22 × = 821

( )x2/32 = 2

x

23

2 = 2

∴ 8x23 −=

316x −=

Ans. (d)

163. Given 1512log 3

x =

i.e. 3151

2x =

( )31

151

2x =

Taking power 15 on both sides

15

3115

151

2x⎟⎟

⎠

⎞

⎜⎜

⎝

⎛=

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

x = 2 5 x = 32 Ans. (b)

∴ x = 4 −

− 8

8−

299


ANSWERS

164. Given 0xlog243 =

i.e. 3° = log 4 (log 2 x) 1 = log4 (log 2 x) 4 1 = log 2x log 2 x = 4 2 4 = x 16 = x Ans. (a)

165. Given ( ) 500001.0logx −=

i.e. 00001.0x 5 =−

00001.0x15 =

5x00001.0

1 =

i.e. 100000x5 =

( )55 10x =

∴ x = 10

Ans. (a) 166. Suppose the x and y baskets were loaded in the first two trucks. Total number of baskets = 1230

∴

According to the question,

∴ 15)yx(1230

5x−+−

− = 53

⇒

⇒ 8x + 3y = 3670 → (1)

and 15)yx(1230

10y−+−

− = 54

⇒

[log log ( )]

x 5; y 10; 1230 (x+y) 15 = 3:4:5

Number of baskets initially loaded in the third basket = 1230 (x+y)

−− − −

5x 25 = 3690 3x 3y 45 − − − −

5y 50 = 4920 4x 4y 60 − − − −

300


⇒ 4x + 9y = 4910 → (2)

Multiply equation (1) by 3,

24x + 9y = 11010 → (3)

Subtracting equation (2) from equation (3), we get 20x = 6100

⇒ x = 20

6100 = 305

(1) ⇒ 8(305) + 3y = 3670

⇒ 2440 + 3y = 3670

y = 3

1230 = 410

Hence number of baskets loaded in first truck = 305. Number of baskets loaded in Second Truck = 410 and the number of baskets loaded in third truck.

= 515 Ans. (b) 167. The given equations are:

94x

1415y

1021x

+=

−=

+

⇒ 13z

1y

31x ==

⇒ x : y : z = 31 : 1 : 13 Ans. (c)

3y = 3670 2440 = 1230 −

= 1230 (x+y) −

= 1230 (305 + 410) −= 1230 715 −

2x + 3y 5z = 0 −

3x + 2y + 7z = 0 −By Gross-multiplication method, we have

301


ANSWERS

168. log a An = log a (A1/n)

= Alogn1

a

ans. (a)

169. 8log4log

10

10 = 310

210

2log2log

= 2log22log2

10

10

= 32

Ans. (c)

170. 10log 124.5 + 10log 379 = 10log (12.45×10) + 10log (3.79×100)

= 10log 12.45 + 10log 10 + 10log 3.79 + 10log 100

= 1.0952 + 0.5786 + 2

10log 124.5 + 10log 379 = 4.6738

Ans. (b) 171. No. of ways to fill unit place = 2 No. of ways to fill to the place = 4 No. of ways to fill 100 th place = 3

∴ Total no. of 3 digit even Nose 2 × 4 × 3 = 24

If 0 comes at 100th place then 3 digit no. 3P3 = 3

Ans. (c) 20

172. Total no. of 3 digits nos. are = 3P6 = 120

3P

∴ Total nos. greater than 100 and less than 1000 by using (2, 3, 4, 0, 8, 9) are

= 100 Ans. (a) 100

Total Nos. greater than 100 = 24 (3+1) −

Nos. of 3 digit if 0 comes at hundredth place = 5 = 20

= 120 20 −

302


173. No. of ways to arrange consonants = 4!

No. of ways to arrange vowels = !2!3

∴ Total no. of words without changing order of vowels

= 72!2

!3!4 =× words.

Ans. (c) 72 words

174. No. of ways in which vowels can be arranged = !2!4 = 12

No. of ways in which 4 vowels taken as together 6 consonants are arranged = 7!

∴Total no. of words in which 4 vowels and 6 consonants are arranged = 7! × 12 = 60480

Ans. (a) 60480

175. Total words without any restriction = !2!8

= 20160

Total words if vowels comes together = !2

!3!6 ×

= 2160

∴ Total words if vowels never

= 18000 Ans. (b) 18000 176. f(x) = ax + b 3< x < 3 f(3) = 1

∴ a.3 + b = 1 ⇒ 3a + b = 1

f(5) = 7

a.5 + b = 7 ⇒ 5a + b = 7

Ans. (a) a = 3,

Come together = 20160 2160 −

∴ a = 3, b = 8 −b = 8 −

303


ANSWERS

177. 3x

lt→

⎥⎦

⎤⎢⎣

⎡

−−

− )3x(x9

3xx =

3xlt→ )3x(x

)9x( 2

−−

= 3x

lt→

x

3x + App lt. ⇒ 3

33 + = 2

Ans. (c) =2

178. 2x

lim→ 2x

)x(f)2(f−− ⇒

2x)x4(0 2

−−− ⇒

2x4x2

−−

2x

lt→

(x+2) App lt.

= 2 +2 = 4 Ans. (d) 4

179. y = x1x1

+−

⇒ dxdy =

)x1(

x1dxdx1x1

dxdx1

+

+−−−+

⇒ )x1(

x121x1)1(

x121x1

++

−−−−−

+⇒

)x1.(x12

x1x12 +−

+−−−

⇒ 2x1)x1(

1

−+

−

Ans. (b) 2x1)x1(

1

−+

−

180. y = x

xlog10 x + ⇒ =dxdy

x

xdxd)xlog10()xlog10(

dxdx xx +−+

⇒ ( )

xx2

1xlog10x1elog10x x10x +−⎟⎠

⎞⎜⎝

⎛ +

x

x2xlog102x2.10log.10 xx −−+

⇒ xx2

xlog2)110logx2(10 x −+−

Ans. (a)

304


181. Here, considering x 2 as the first function as 2x as the second function and applying the method of integration by parts, we may write

∫ ∫−= dx2log

2.x22log

2.xdxx2xx2

2x

= ∫− dx2x2log

22log

x2 x2x

= ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−− ∫ dx

2log2

2log2.x

2log2

2logx2 xx2x

= ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−−

2logx2.

2log1

2log2.x

2log2

2logx2 x2x

= ( ) ( )

c2log

22log

2.x2x2

3

1x

2

1x2x++−

++

Ans. (a)

182. let log zx =

zxlog21 =

dzdxx1.

21 =

∴ I = ∫ ∫= dxx2

xlog32dx

x3xlog

= ∫ dzz32

= ( ) cxlog31

3z

2z

32 222

+==⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

Ans. (c)

183. ∫ ∫= dxx1.xlogdx

xxlog

22

Using Integrating by parts

(Note: here (log x) is to be taken as first function and ⎟⎠

⎞⎜⎝

⎛2x

1 as second function)

305


ANSWERS

∴ ∫ ∫ ⎟⎠

⎞⎜⎝

⎛−−⎟⎠

⎞⎜⎝

⎛−= dxx1

x1

x1xlogdx

x1.xlog 2

= ∫+− dxx1xlog

x1

2

= cx1xlog

x1 +−−

= ( ) cxlog1x1 ++−

Ans. (b)

184. ( ) ( )∫ ∫

⎥⎥⎦

⎤

⎢⎢⎣

⎡

++−=

++ dx

1x21xe.dx

1x1x.e 2

2x

2

2x

= ( ) ( )∫

⎥⎥⎦

⎤

⎢⎢⎣

⎡

++

+− dx

1x2

1x1xe 22

2x

= ( ) ( )∫⎥⎥⎦

⎤

⎢⎢⎣

⎡

++

+− dx

1x2

1x1xe 2

x

= [ ]∫ ′+ dx)x(f)x(fe x

Where f (x) = 1x1x

+−

= ( ) cxf.e x +

= c1x1xe x +⎟⎠

⎞⎜⎝

⎛

+−

Ans. (a)

185. Let I = ( )∫ +

dxx1

xe2

x

∴ I = ( )∫ +

−+ dxex1

1x1 x2

= ( )∫ ⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛

+−

+dxe

x11

x11 x

2

306


= ( )∫ ∫ +

−+

dxex1

1dxex1

1 x2

x

= ( ) ( ) ( ) ( ) ⎥⎦

⎤⎢⎣

⎡ +−−+ ∫

− dxe1X11ex1

1 X2x∫ +

dxe)x1(

1 x2

= ∫ ∫ +−

++

+dxe

)x1(1dxe

)x1(1

x1e x

2x

2

x

I = cx1

e x+

+

Ans : (a)

186. Given y = x

1x +

( )( )

( )⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −+= 2

xx2

110x

x21

dxdy

= xx2

1x2

1 −

= ⎥⎦

⎤⎢⎣

⎡ −x11

x21

dxdy = ⎥

⎦

⎤⎢⎣

⎡ −x

1xx2

1

∴ ( )⎥⎦

⎤⎢⎣

⎡ −= 1xxx2

1x2dxdyx2

= x

1x

x −

= x

1x −

1x1x

1x1x22

22

−−+

−++

Multiply Reciprocal of R.H.S. to R.H.S.

−

187. Given y =

307


ANSWERS

i.e. y = 1x1x

1x1x

1x1x

1x1x22

22

22

22

−−+

−++×−−+

−++

= ( ) ( )1x1x

1x1x22

222

−−+

⎟⎠⎞

⎜⎝⎛ −++

( )( )[ ]22 bababa −=−+∴

= ( ) ( )2

1x1x21x1x 2222 −++−++

= ⎥⎦⎤

⎢⎣⎡ −++ 1x1x2x2

21 222

= ( )( )1x1xx 222 −++

Differentiate on both sides.

( )( ) ( )( ) ( )( )[ ]x21xx21x1x1x2

1x2dxdy 22

22−++

−++=

= 2x + [ ]x2x2x2x21x2

1 334

−++−

= 2x + 1x2

x44

3

−

dxdy = 2x +

1x

x24

3

−

Ans. (b)

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎠

⎞⎜⎝

⎛

+− 4

3

x

2x2xe

( )( )( ) ( )( )

( ) ⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+−−+

⎟⎟⎠

⎞⎜⎜⎝

⎛

+−

⎟⎠

⎞⎜⎝

⎛

+−

=−

2

143

x

43

x2x

12x12x2x2x

43e

2x2xe

1dxdy

+ ⎥⎥⎥

⎦

⎤

⎟⎠

⎞⎜⎝

⎛

+− x4

3

e2x2x

188. Given y = log

308


= ( )

43

x

43

241

x

2x2xe

2x2x

2x2x2x

2x2x

43e

⎟⎠

⎞⎜⎝

⎛

+−

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎠

⎞⎜⎝

⎛

+−+⎟⎟

⎠

⎞⎜⎜

⎝

⎛

++−+

⎟⎠

⎞⎜⎝

⎛

+−

−

= ( )

43

43

241

2x2x

2x2x

2x4

2x2x

43

⎟⎠

⎞⎜⎝

⎛

+−

⎟⎠

⎞⎜⎝

⎛

+−+⎥

⎦

⎤⎢⎣

⎡

+⎟⎠

⎞⎜⎝

⎛

+− −

= ( )

12x2x

2x3 4

341

2 +⎥⎦

⎤⎢⎣

⎡

+−

+

−−

= ( )

12x2x

2x3 1

2 +⎟⎠

⎞⎜⎝

⎛

+−

+

−

= ( )

12x2x

2x3

2 +⎟⎠

⎞⎜⎝

⎛

−+

+

= 14x

32 +

−

= 4x1x

4x4x3

2

2

2

2

−−=

−−+

Ans. (a) xx

Taking log on both sides.

log y = log ( )xx

log y = x. log x Differenciate on both sides.

1.xlogx1.x

dxdy

y1 +=

[ ]xlog1ydxdy +=

189. Given y =

[∴ log e = 1]

309


ANSWERS

= y [log e + log x] [log m + log n = log (mn)] = y [log ex] = xx [log ex] Ans. (b)

2xex−

taking log on both sides

log y = log ( )2xex−

log y = 2xe − log x

( ) )x2(exlogx1e

dxdy

y1 22 xx −+⎟

⎠

⎞⎜⎝

⎛= −−

= ⎥⎦

⎤⎢⎣

⎡ −− xlogx2x1e

2x

⎥⎦

⎤⎢⎣

⎡ −= −

xxlogx21e.y

dxdy 2

x2

⎟⎟⎠

⎞⎜⎜⎝

⎛ −= −−

xxlogx21e.x

dxdy 2

xe 22x

Ans : (a)

191. Sn = ]d)1n(a2[2n −+

0 = ]d)1n(20[2n −+

)n1(

a2−

Sn = ]d)1m()nda(2[2m −++

⎥⎦

⎤⎢⎣

⎡

−−+

−+

n1a2)1m(

n1a2.n2a2

2m

Sm = ma ⎥⎦

⎤⎢⎣

⎡

−−++−

n11mn2n1

190. Given y =

differenciate on both sides

2a = (1 n)d ⇒ d = −

310


= ma n1

)nm(−+

Sm = )1n(

)nm(ma−

+−

Ans. (b) )1n(

)nm(ma−

+

192. a = m Tl = 2m

mn

m−

∴ N = mn

m−

+1+ mn

mmn−

−+

N = mn

n−

∴ s =2N [a + l] ⇒

mnn−

[m + 2m]

S = mn

mn3−

Ans. (a) mn

mn3−

Let n th term be 0

∴ n = 9.28 (not possible)

∴ 10th term will be positive

∴ Sum of remaining 31 terms.

S 31 = 231 ⎥

⎦

⎤⎢⎣

⎡−+⎟

⎠

⎞⎜⎝

⎛ ×+−×27)131(

279292

d = n m −

−

2m = m+(N 1)d −

⇒ 2m m = (N 1) (n m) ⇒ = N 1 − − − −

193. a = 29 −a + 4d = 15

0 = a+ (n 1) d

0 = 29 + (n 1) 7/2 ⇒ 58/7 = n 1

−

4d = 15 + 29 ⇒ d = 14/4 = 7/2 −

−− − −

311


ANSWERS

= ]1055[231 +

= 1705110231 =×

31S = 1705 (Sum of all positive nos.)

Ans. (b) 1705

∴n1

d)1n(am1 −+=

by solving eg. (i) and e.g. (ii)

a = mn1 , d =

mn1

∴ S mn = 2

mn ⎥⎦

⎤⎢⎣

⎡ −+×mn1)1mn(

mn12

= ⎥⎦

⎤⎢⎣

⎡ +×mn11

2mn ⇒

2mn ⎥

⎦

⎤⎢⎣

⎡ +mn

1mn

Smn = ⎥⎦

⎤⎢⎣

⎡ +2

1mn

Ans. (c) )1mn(21 +

195. ]d)1n(a2[2/n]D)1n(A12[2/n

nSS n

−+−+=

′

⎥⎦

⎤⎢⎣

⎡⎟⎠

⎞⎜⎝

⎛ −+

⎥⎦

⎤⎢⎣

⎡⎟⎠

⎞⎜⎝

⎛ −+=

++

d2

1na2

d2

1nA(2

2n31n7

Put n = 25

22531257

+×+× =

d12aD12A

++

194. Tn = a + (n 1) d −

= a + (m 1)d − ...(i)

...(ii)

312


∴ 7

1677

176tT

13

13 == ⇒ 16:7

Ans. (b) 16:7

196. A1 = 2

ba + a, G 1, G 2, b

∴ b = a(r) 3 ∴ r = 31

ab⎟⎠

⎞⎜⎝

⎛

∴ 33/1

32

31 a

baGG⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⇒+ +

33/2

aba

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

= 2

33

aba

ab.a ⎟

⎠

⎞⎜⎝

⎛+⎟⎠

⎞⎜⎝

⎛⇒ ⎥

⎦

⎤⎢⎣

⎡ +⎟⎠

⎞⎜⎝

⎛

ab1

aba 3

= ⎟⎠

⎞⎜⎝

⎛ +⎟⎠

⎞⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛=⎟⎠

⎞⎜⎝

⎛ +2

ba2.aba.

aba

ababa

3/23/12

= G1 . G 2 . 2A = 2A G 1 G 2 Ans. (b) 2A G1 G 2

197. mm

1m1m

babaab

++=

++⇒ 1m1m2/1m2/12/12/1m bab.ab.a ++++ +=+

1m2/1m2/12/12/1m1m bbab.aa ++++ −=−

⇒ [ ] [ ]2/12/12/1m2/12/12/1m babbaa −=− ++

∴ ba

2/1m

2/1m

+

+

198. Ans. (c)

199. Value of 1. 4

∴ 9x = 13.00 ∴ x = 13/9

Ans. (a) 13/9

= 1 ∴ m+1/2 = 0 ∴ m = 1/2 −

Ans. (a) 1/2 −

x = 1.444... 10x = 14.444...

313


ANSWERS

200. x = 0.35 6

∴ 990x = 353.0 ⇒ x = 990353

Ans. (c) 990353


151. 1T.2T q1P +=+

⇒ a + pd = 2a + 2qd

∴ Pd3d)q2P(

d)qP(d)q2P(Pd3a

d)qP(aT

T

1p3

1qp

+−++−=

+++=

+

++

= d)qP2(2

d)qP2(−− =

21⇒ 1:2

Ans. (a) 1:2

152. d = a ∴ TnTm =

d)1n(ad)1m(a

−+−+ =

d)1n(dd)1m(d

−+−+

= d)1n1(dd)1m1(d

−++−++ =

nm ⇒ m:n

Ans. (b) m:n

153. =n1 =

m1

∴ a = mn1 , d =

mn1

mnmn1

mn1

mnT = 1

Ans. (a) 1

∴ 10x = 3.565656...

1000x = 356.5656...

⇒ a + (P+ 1 1) d = 2 [a+qd] −

a = d (P 2q) −

a + (m 1)d & − a+ (n 1)d −

∴ T = a+ (mn 1)d ⇒ − +(mn 1) −

314


154. termsn.....11.81

8.51

5.21 ++

Tn = ])1n(5[])1n(2[

133 −+−+

=)2n3()1n3(

1+−

Tn = 31 ⎥

⎦

⎤⎢⎣

⎡

+−

− 2n31

1n31

∴ S n = )Tn(∑ ⇒ ⎥⎦

⎤⎢⎣

⎡

+−

2n31

21

31

⇒ ⎥⎦

⎤⎢⎣

⎡

+−+

)2n3(222n3

31

S n ⇒ 31

)2n3(2n3+

= )2n3(2

n+

Ans. ⇒ (a) )2n3(2

n+

∴ a = 0.004 r = 004.002.0 = 5

∴ 12.5 = 0.004 (5) ⇒ 004.0500.12 = (5)

3125 = (5) ⇒ 5 5 = 5

Ans. (c) 6

157. C I = 2000 ( )[ ]10125.01 10 −+

CI = 2000 ( )[ ]10125.1 10 − (Solved by taking log)

CI = Rs. 260.12

158. 9P = P 2

100r1 ⎟⎠

⎞⎜⎝

⎛ +

(3) 2 = 2

100r1 ⎟⎠

⎞⎜⎝

⎛ + ⇒ 3 = 1+ 100

r

∴ r = 200%

155. 0.004 + 0.02 + 0.1 + ... is 12.5

n 1− n 1−

n 1− n 1−

∴ n 1 = 5 ⇒ n = 6 −

315

Ans. (b) 200%


ANSWERS

159. 101.50 = P [(1+0.03) 2

P = 0609.0

50.101 = 1667

P = 1667

∴ S I = 1667 × 100

3 ×2 = 100 (Approx)

Ans. (a) Rs. 100

160. C I = P [ ]1)05.01( 2 −+

CI = 0.1025 P

S I = P × 2100

5 × = 0.1P

∴ 0.0025P = 1.50

∴ P = 600

Ans. (c) Rs. 600

161. Let average is x

∴ x = 17

85)3x(16 +−

x = 37 Ans. (a) 37

162. Time from A to B = 20d hrs

Time from B to A = 30d hrs.

⇒ Average speed = 600d50

d2

30d

20d

dd ×=+

+

Average speed = 24 km/4. Ans. (b) 24 km/4

− CI S I = 1.50

⇒ 17x = 16x 48 + 85 −

1] −

0.1025P 0.10P = 1.50 −

316


163. Average speed =

15d

30d

40d

ddd

++

++

Av. Speed = H/km24120d15d3 =×

Ans (b) 24 km/H

164. Time to cover 12 km = 3

12 = 4 hrs.

Time to cover 18 km = 18/9 = 2 hrs. Time to cover 24 km = 24/4 = 6 hrs.

∴ Av. speed = 1254

624241812 =

++++ = 4.5 km/H

Ans. (a) 4.5 km/H

165. Av. speed =

10d3

6d

10d

10d3

2d

5d

++

++ =

d17d × 30

∴ Av. speed = H/km1730

Ans. (b) H/km1730

166. x = nxΣ

Σx = 100 × 50 = 5000

∴ Corrected x = 1004990 = 49.90

Ans. (b) 49.90

167. x = 321

332211nnn

xnxnxn++++

12 = 532

x53332 3

+++×+×

120 = 15 + 5x3

Corrected Σx = (5000 50 + 40) = 4990 −

317


ANSWERS

∴ x3 = 5

105 =21

Mean of third group = 21 Ans. (b) 21 168. Made is most frequent value Ans. (c) Most Frequent Value.

169. AM = 2

ba +

10 = 2

ba + ⇒ a + b = 20 … (i)

am = ab

8 = ab ⇒ ab = 64

⇒ a 2

∴ a = 16, b = 4

Ans. (b) 16, 4 170. A frequency distribution can be presented graphically by a Histogram. Ans. (b) Histogram. 171. Ans. (c) Refer Properties 172. Ans. (a) Refer Properties. 173. Since x and y are connected by the linear relation: 2x + 3y = 4

There is perfect correlation between x and y i.e. r = ± 1

(1) ⇒ x increases, y decreases

Hence, there is perfect negative correlation between x and y

Ans. (c) 174. Ans. (d) Refer Properties 175. Ans. (b) Refer Properties 176. Ans. (a) Refer Properties

∴ a (20 a) = 64 −

20a + 64 = 0 −

−(a 16) (a 4) = 0 −

⇒ y = 2/3 x + 4/3 → (1) −

∴ r = 1. −

318


177. Ans. (a) Refer Properties 178. Ans. (b) Refer Properties 179. Ans. (a) Refer Properties 180. Ans. (a) Refer Properties 181. Let A be the number which is multiply 3 with in 1 to 20 A = {3, 6, 9, 12, 15, 18}

Probability of A =P(A) = 206 =

103

Let B be the number which is multiply 7 with in 1 to 20 B = {7, 14}

P(B) = 101

202 =

∴ Probability of number which is multiple of 3 or 7

P(AUB) = P (A) + P (B) = 3/10 + 1/10 = 4/10 = 2/5 Ans. (b) 182. Let A be the Card drawn King from the pack P(A) = 4/52 Let B be the card drawn heart from the pack P(B) = 13/52

P(King and Heart) = P (A ∩ B) = 1/5

∴

= 521

5213

524 −+

= 5216

= 134

∪ B)

13413 − =

139

Ans. (b)

−Here, A and B are non mutually exclusive

P (King or Heart) = P(A∪B) = P(A) + P(B) P(A ∩ B) −

But P (neither a king nor a heart) = 1 P (A

= 1 4/13 = −

−

319


ANSWERS

183. Total number of balls = 3 Red + 5 yellow + 4 green. Since 3 balls are drawn at Random, total number of possible outcomes = 12 C 3

Probability of balls drawn contain exactly two green balls.

= 3

12C12

C8.C4

(Since out of Four green balls two green exactly taken 4C2 and the remaining one balls from total number of other two colours).

= 5512

22048

22086 ==×

Ans. (a) 184. Let A = event that Husband is selected. B = event that wife is selected

∴ P(A) = 3/5 and P(B) = 1/5

Now A B = The event that only Husband is selected.

A B = the event that only wife is selected.

∴ A B ∪ A B = the event that only one of them is selected.

Now A B and A B are mutually exclusive events.

∴ By Addition thereon P ( )BABA ∪ = P( BA ) + P( BA )

Also, the interviews of husband and wife are independent experiments.

∴ P( BA ) = P(A) . P( B ) = 3/5 × 4/5 = 12/25

and P( BA ) = P( A ) P(B) = 2/5 * 1/5 = 2/25

∴ P (only one is selected)

= P ( )BABA ∪

= P( BA ) + P( BA )

= 2514

252

2512 =+

Ans. (c)

−⇒ P( A ) = 1 P(A) = 1 3/5 = 2/5 −

− − P ( B ) = 1 P(B) = 1 1/5 = 4/5

320


185. Balls in first bag = 4 White + 2 Black Balls in Second bag = 3 White + 5 Black. The draws from bags are independent.

∴ Required probability = (w1B2 or B1W2)

= (PW 1). P(B 2) + P(B 1) P(W 2)

= 83.

62

85.

64 +

= 4826

= 2413

Ans. (b) 186. Ans. (b) … Refer Properties 187. Ans. (a) … Refer Properties 188. Ans. (c) … Refer Properties 189. Ans. (a) … Refer Properties 190. Ans. (b) … Refer Properties 192. Probability to get red ball case I

= ⎟⎠

⎞⎜⎝

⎛×⎟⎠

⎞⎜⎝

⎛

114

95 (Red ball from 1st bag and also from 2nd)

= 9920

Case II If Red ball from 1st bag no t drawn but from 2nd bag Red ball drawn

= 9912

113

94 =⎟

⎠

⎞⎜⎝

⎛×⎟⎠

⎞⎜⎝

⎛

∴ Total probability = 9932

9912

9920 =+

Ans. (a) 9932

196. Six boys & five girls may sit in such manner (B) G (B) G (B) G (B)G (B)G (B)

∴ Total No. of ways to sit the girls = 5 !

321


ANSWERS

Total No. of ways to sit the boys = 6P6 = 6 !

∴ Total No. of way that they sit

(No. 2 Girls and Boys sit together = 5! × 6! = 120 × 720 = 86400 Ans. (a) 86400 197. If sum of two dice throw is odd = { (1,2), (1,4) (1,6), (2,1), (2,3) (2,5), (3,2) (3,4) (4,1), (4,3), (4,5), (5,2), (5,4), (5,6) (6,1), (6,3), (6,5)}

∴ Probability to get sum as odd

P = 94

3616

)6(16

2 ==

∴ Probability to get sum as even nos.

= 95

94 =

Ans. (b) 95

198. If 0 not selected then total no.of expectation to select two digits

P(E) = ⎟⎠

⎞⎜⎝

⎛×⎟⎠

⎞⎜⎝

⎛

98

109

P(E) = 9072

∴ Probability to get one digit as 0 so product will be zero

9072

= 51

9018 =

Ans. (a) 51

−1 P(E) = 1 −

= 1 P(E) = 1− −

322


199. If !)1n(

Pn!n4

195x 33

n ++−=

!n

1!n4

195!)1n()1n(

!n4195xn −⇒

++−=

After solving we get 4 term will be positive Ans. (c) 4

200. zy

1,y2

1,yx

1++

in AP

∴2

zy1

yx1

y21 +

++=

2)zy()yx(

yx2yy2

1+++++=

⇒ xy + y2 +xz + yz = 2y2 + yz + xy

xz = y2

∴ yz

xy =

∴ x, y, z in GP

Ans. (b) G.P.

Model Test Paper – BOS/CPT – 3 / 2007 151. Let the two numbers are x and y

i.e. x + y = 7 → (1)

(1) + (2) ⇒ 2x = 8

x = 4

∴ (1) ⇒ 4+y = 7

∴ x : y = 4 : 3

Given x + y : x y = 7 : 1 −

x y = 1 → (2) −

y = 7 4 = 3 −

Ans. (b)

323


ANSWERS

152. Let the unit's digit of the num ber be x and the ten's digits by y. Then the number = 10y + x Reversing the order of digi ts of the given number Unit's digit becomes y and ten's digit becomes x

∴ New number = 10x + y

According to the given condition of the problem

( ) ( ) 54xy10yx10 =+−+

i.e. The differences of the digit is 6. Ans. (c) 153. Let the fraction be x/y According to the first condition of the problem, .................(i) According to the second condition of the problem,

⇒ 8x-y=17 .....................(ii)

subtraction 1 from 2, we get 7x = 21

x = 721 = 3

y = 3 + 4 = 7 Hence, the required fraction is 3/7 154. Let the present ages of father and his son be x and y years respectively. According to the

first condition of the problem, x = 6y

9 x 9y = 54 −

−x y = 6

x = y 4 −

x y = -4 −

y+1 = 8(x 2 ) − y+1 = 8x 16 −

⇒ 8x y=1+16 −

(i) ⇒ 3 y = 4 − −

324


..............(i) Four years hence Age of father = (x+4) years Age of son = (y+4) years According to the second condition of the problem x+4 = 4(y+4) x+4 = 4y+16 ................ (ii)

⇒ 2y = 12

y = 12/2 = 6

x = 36 Hence, present age of father = 36 years and present age of son = 6 years

∴Ans.(b)

155. Sum of n natural number = 2

)1n(n +

= 2

)1105(105 +

= 5565

156. log 7.0

03.0 = log ⎟⎠

⎞⎜⎝

⎛ ×7

10100

3

= log ⎟⎠

⎞⎜⎝

⎛

703

= = =

Ans. (c)

157. let x = 5173.04

= (0.5173) 1/4

x 6y = 0 −

x – 4y = 16 – 4 x – 4y = 12

(ii) – (i)

(i) ⇒ x – 6(6) = 0

log3 – log 70 log 3 – (log 7 + log 10) 0.48 – (0.84 + 1)

= –1.36

325


ANSWERS

Taking log on both sides log x = log [0.5173) 1/4 log x = 1/4 log (0.5173)

= 1/4 ( 1 .7138) (from the table) =

= =

= 1 .9284

∴ x = Anti log ( 1 .9284) = 0.8480

Ans. (a)

158. Let x = 8.69

37.207214.03 ×

Taking log on both sides

= 1/3 ( 1 .3232)

= 1/3 ( 3 +2.3232)

= 1 + 0.7744

= 1 .7744

∴ x = Antilog ( 1 .7744) = 0.5948

Ans. (b) 159. Here P(O) = 4000 i = 0.06 P(n) = 5353 and we are required to find n. Since p(n) = (1+i) n × P(0)

⇒ 5353 = (1+0.06) n × 4000

n)06.01(40005353 +=

(or) 1.3382 = (1.06) n

1/4 (– 1 + 0.7138) = 1/4 (–1–3+3+0.7138)

1/4 (–4 + 3.7138) –1 + 0.9284

log x = 1/3 (log 0.7214+log 20.37– log 69.8)

= 1/3 ( 1 .8581+1.3090–1.8439)

326


Taking log on both sides. log (1.3382) = n log (1.06) 0.1265 = n ( 0.0253)

n = 0253.01265.0 = 5

Hence, the required number of years is 5 Ans. (b)

160. Given 1523xlogxlogxlog 3282 =++

2log

1

x+

8log1

x+

32log1

x=

1523

2log

1

x+ 3

x 2log1 +

25log1

x=

1523

2log

1

x+

2log31

x+

2log51

x =

1523

⎟⎠

⎞⎜⎝

⎛ ++51

3112logx =

1523

⎥⎦

⎤⎢⎣

⎡ ++15

35152log

1

x =

1523

1523

1523

2log1

x=⎟

⎠

⎞⎜⎝

⎛

12log

1

x=

log 2x= 1

∴ The value of x = 2

Ans. (c)

(Because two books ta ken together as 1 book) Ans. (b) 162. No. of ways to arrange two books (each 3 copies) and 5 book (each 2 copies) = 7! = 5040

161. The no. of ways to arrange n different books if two are always together = (n–1) ! × 2!

(n–1)! ×2!

Ans. (a) 5040

327


ANSWERS

163. Total No. of words by letters

=!3!2

!8 = 3360

No. of words if all 'L comes together = !2!6 = 360

∴ Total words if 'L' does not come together

Ans. (b) 3000

164. Total no. of 4 digit by (1, 3, 3, 0) = !2!4 = 12

If 0 comes at thousandth place

then total Nos. = !2!3 = 3

(1, 3, 3, 0) each comes at Unit , tenth, hundredth place 2! times.

and 1, 3, 3, each comes at thousandth place 3 times

∴ Sumof digit = 1+3+3+0 = 7

∴ Total sum = 7 × 2 [10 0 + 10 1 + 10 2) + 7×3[103]

= 14×111+21×1000

Total sum = 22554

Ans. (a) 22554

166. Let I = ∫ + 43 x53x dx

Put 3 + 5x4 = t

20x 3 dx = dt

x3dx = 201 dt

∴I = ∫ ∫=+201.tdxxx53 34 dt

(P, A, R, A, L, L, E, L)

= 3360 – 360 = 3000

∴ Net 4 digit Nos. by (1, 3, 3, 0) = 12 – 3= 9

328


= ∫ =2/3

t201dtt

201 2/3

2/1 +c

= 2/3t301 +c

( ) 2/3443 x53301dyx53x +=+∫ +c

Ans.(c)

167. Let I = ∫ ++ dx

)1x(x1x2

= ∫ ++ dx

xx1x2

2

= c)xx(log 2 ++

Ans. (b)

168. Put x =t

∴x=t2

dx = 2t dt

∴ ∫∫ ∫ +=

+=

+ 1tdt2

ttdtt2

xxdx

2

= 2 log (t+1) + c

2 log ( )1x + +c

169. Let z = xlog

= log(x)1/2

z = 21 log x

dz = x1.

21 dx

∴ ∫ ∫=x2

xlog32dx

x3xlog dx

= ∫ dzz32

329


ANSWERS

= ⎥⎦

⎤⎢⎣

⎡

zz

32 2

+c

= 3z 2

+c

( )∫ =2

xlog31dx

x3xlog +c

Ans.(a)

170. Let I = ∫ dxex x22

Integrating by parts

I = ∫− x2x22

e2x2

2ex dx

I = ∫− dxxe2ex x2

x22

................... (i)

consider ∫ dxxe x2

Integrating by parts,

= ∫−2

e2

xe x2x2

dx

= 4

e2

xe x2x2

−

(i) becomes

I = ⎥⎦

⎤⎢⎣

⎡−−

4e

2xe

2ex x2x2x22

I = 4

e2

xe2ex x2x2x22

+− +c

Ans.(b)

330


171. I = dx)x5(x

x22

25

0 −+∫

I = dx)x()x5(

)x5(22

25

0 +−−

∫

2I = 50

5

0

]x[dx =∫

2I = 5 I = 5/2 Ans. (d) None of these

172. 1x11x1.

1x1)12(lt

x

0x ++++

−+−

→

( )1x1lt.x

)12(lt0x

x

0x++−

→→

App lt.

⇒ log 2 × 2 ⇒ 2 log 2

173. 0x

lt→ 1x

|1x|−−

RHL … +→0x

lt )1x()1x(

−− = 1

LHL −→0x

lt)1x()1x(

−−−

LHL ≠ RHL ∴ f(x) does not exist

(c) Does not exist

174. f(x) = x

|x|x−

RHL +→0x

lt x

xx − = 0

LHL −→0x

ltx

)x(x −− = xx2 = 2

f (0) = 2

... (i)

... (ii) [f(x) = f(a–x)]

Ans. (a) 2log 2

= –1

331


ANSWERS

⇒ RHL ≠ LHL ≠ f(0) ∴ f(x) is not continuous at x = 0

Ans. (b) No. 175. y = log 3 (log 3x)

)x(logdxd.tlog

dtd

dxdy

33=

= 3log.x

1.log.xlog

1

33 ⇒

2)3.(log3logxlog.x

1

= xlog.3log.x

1

Ans. (a) = xlog.3log.x

1

176. C I if calculated annually.

CI1 = P ⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎟

⎠

⎞⎜⎝

⎛ + 1100201

2

= 25

P11

CI if calculated semi annually.

CI2 = P P1000046411

100101

4

=⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎟

⎠

⎞⎜⎝

⎛ +

∴ 48225

P1110000

P4641 =− ⇒ 48210000

P241 =

∴ P = 20,000 Ans. (a) Rs. 20,000

177. Value of annuity (A) = P ( )⎥⎥⎦

⎤

⎢⎢⎣

⎡ −+i

1i1 n

= 3000 ( )( ) ⎥

⎥⎦

⎤

⎢⎢⎣

⎡ −+09.0

109.01 3

= 9833.33 Ans. (c) Rs. 9833.33

332


178. Present Value of Annuity = ( )1005.01

10000+

= Rs. 7724 Ans. (a) Rs. 7724

179. A = ( )[ ]1i1iP n −+ ⇒

06.045000 ( )[ ]106.01 10 −+

750000 ( )[ ]106.01 10 −+ {Solve by taking log}

A = 517500

= 17,500 Ans. (c) Rs. 17,500

P = A ⎥⎦

⎤⎢⎣

⎡ +− −

i)i1(1 n

⇒ 2000 ⎥⎦

⎤⎢⎣

⎡ +− −

)10.0()1.01(1 5

P = 20000 [ ]5)1.1(1 −−

P = 7294 which is less than the Purchase Price.

∴ leasing is preferable.

Ans. (a) leasing is preferable. 181. The sum of deviations of the given values from their Arithmetic Mean is 0. Ans. (a) Arithmetic Mean 182. The sum of squares of the deviations of the given values from their Arithmetic Mean is

minimum. Ans. (a) Arithmetic Mean

Ans. (a) Arithmetic Mean

Ans. (d) Both (b) and (c)

185. 2

ba + = 15 ⇒ a + b = 30 … (i)

2b = 34 ⇒ b = 17

∴ Surplus = 517500 – 5,00,000

180. Present value of P (rest) of the annuity.

183. Which is greatly affected by the extreme values – Arithmatic mean

184. Which is not amenable to further algebric treatment – Mode and Median

b – a = 4 – (ii) [By eq (i) & (ii)]

333


ANSWERS

∴ a = 13 lower limit = 13

Ans. (c) 13 186. Ans. (b) Refer Properties 187. Ans. (a) Refer Properties 188. Ans. (c) Refer Properties 189. Given, consumer price index in, (say), period I = 120 and consumer price index in (say),

period II = 215. The wages of the worker in period I and II are given to be Rs. 1,680 and Rs. 3000 respectively. The real wages of the worker in the current period II with respect to the period I as base, are given by:

Rs. 42.1674.Rs3000215120 =×

Since this wage (Rs. 1674.42) is less than the wages of the worker in the period I (Viz. Rs. 1680) the workers is not better off but wors

Ans. (a) 190. Purchasing power (P.P) of a rupee in 1994 with respect to the base period 1980 is given

by

P.P. of a rupee = 1980base.t.r.w1994forIndexicePrConsumer

100

250100

Ans. (a) 191. Let B1, B2 and B3 be the events of drawing a boy from the 1st , 2 nd and 3 rd group

respectively and G 1, G 2 and G3 be the events of drawing a girl from the 1st , 2 nd , and 3rd group respectively then P (B 1) = 1/4, P (B 2) = 2/4, P(B 3) = 3/4 and P(G 1 )=3/4, P(G 2) = 2/4, P(G 3) = 1/4.

The required event of getting 1 girl and 2 boys in a random selection of 3 children can materialize in the following mutually exclusive cases.

(i) Girl from the first group and boys from the 2nd and 3rd group i.e. the event G1 ∩ B2 ∩ B3

(ii) Girl from the 2nd group and boys from 1st and 3rd groups, i.e. the event B 1 ∩ G2 ∩ B3 happens.

(iii) Girl from the 3 rd group and boys from the 1st and 2 nd groups. i.e., the event B1 ∩ B2 ∩ G 3 happens.

Hence by the addition theorem of probability, required probability ρ is given by:

P = P(i) + P(ii) + P(iii)

e off R. 5.58 as compared to the period I.

= Rs. = Re. 0.40

334


= P (G1 ∩ B2 ∩ B3) + P (B 1 ∩ G2 ∩ B3) + P(B 1 ∩ B2 ∩ G3)

= P (G1) P(B 2) P(B 3) + P(B 1) P(G 2) P(B 3) + P(B 1) P(B 2) P(G 3)

= 41

42

41

43

42

41

43

42

43 ××+××+××

= 3213

6426

642618 ==++

192. Let P(A) = x

∴ P(B) = 23 P(A) =

23 x

and P(C) = 21 P(B) =

21

⎟⎠

⎞⎜⎝

⎛ x23 = x

43

The events A, B and C are exhaustive

∴ P (A or B or C) = 1

⇒ P(A) + P(B) + P(C) = 1 ( ∵ A, B, C are mutually exclusive)

1x43x

23x =++

14

364x =⎥⎦

⎤⎢⎣

⎡ ++

∴ x = 134

∴ P(A) = 134

Ans. (b) 193. There are 3+4+2+1 = 10 members in all and a Committee of 4 out of them can be formed

in 10C 4 ways. Hence exhaustive number of Cases is:

210!4

78910C10 4 =×××=

The probability 'p' that the Committee Consists of the doctor and at least one economist is given by

p = P [One doctor, One economist, 2 others] + P [One doctor, Two economist, 1 others] + P[One doctor, Three economist]

335


ANSWERS

4

31

4

121

4

211

C10C3C1

C10C6C3C1

C10C6C3C1p ×+××+××=

= ( ) ( )⎥⎦

⎤⎢⎣

⎡×+××+⎟

⎠

⎞⎜⎝

⎛ ××× 116312

5631210

1

= [ ]11845210

1 ++

= 3048.010532

21064 ==

Ans. (a) 194. Let A = event that the company executive travel by plane.

∴ P(A) = 2/3

Let B = event that the Company executive travel by train.

∴ P(B) = 1/5

Now the events A and B are mutually exclus ive, because he cannot travel by plane and train at the same time.

∴ The prob. of his traveling by plane or train

= P (A or B) = P(A) + P(B) = 2/3 + 1/5

= 1513

Ans. (b) 195. Let A and B denote the events that the contractor will get a 'plumbing' Contract and

'Electric' Contract respectively. Then we are given:

P(A) = 2/3, P( B ) = 5/9

= 4/5

⇒ )BA( ∩ = 4/5

)BA( ∩ = 4/5

∴ P(B) = 1 P( B ) = 4/9

Ans. (a)

and P (A∪B) = Probability that Contractor gets at least one contract.

P(A) + P(B) P

2/3 + 4/9 P

⇒ P (A∩B) = 2/3 + 4/9 4/5

336


= 45

362030 −+

= 4514

Hence, the probability that the Contractor will get both the contracts in 14/45 Ans. (a)

196. Standard deviation = σ

05.0)60x(P =>

∴ P (x < 60) = 0.95

∴ P ⎥⎦

⎤⎢⎣

⎡

σ−≤

σ− 506060x = 0.95

∴ P ⎟⎠

⎞⎜⎝

⎛

σ≤ 10 = 0.95 ⇒ ϕ ⎟

⎠

⎞⎜⎝

⎛

σ10 = ϕ (1.64)

⇒ σ = ⎟⎠

⎞⎜⎝

⎛

64.110 = 6.7 ⇒ S.D. = 6.7

Ans. (a) 6.7

197. P ⎟⎠

⎞⎜⎝

⎛ −≥20

10xZ = 0.10

∴ 20

x100 − = 1.28

x = 74.40 Ans. (c) 74.40

198. P ⎟⎠

⎞⎜⎝

⎛ −≤20100xx = 0.10

∴ 20100x − = 1.28

x = 25.6 + 100 = 125.6 Ans. (b) 125.6 200. P = P(x>70) =

⇒ 1 P (x < 60) = 0.05 −

100 x = 25.6 −

1 P (x < 70) −

337


ANSWERS

= ⎥⎦

⎤⎢⎣

⎡ −≤−5

657025

65x

=

P = 0.06 Ans. (c) 0.06


151. P = RT100A100

+⇒

124045.0100

21315100

×+

×

P = 21000 Ans. (a) Rs. 21000

152. I1 = 500 × 401100

8 =×

2 6043

1008 =×

3 4021

1008 =×

∴ Total Amount = 500 + 1000 + 1000+40 + 60 + 60

= 2640 Ans. Rs. 2640

153. 2000 = 1200 n4

100451 ⎟

⎠

⎞⎜⎝

⎛

×+

5 = 3 n4

8081

⎟⎠

⎞⎜⎝

⎛ After taking log both side and solved.

n = 10 years 3 months Ans. (a) 10 years 3 months

1 P −

1 P (z < 1) −

= 1 0 .041 −

I =1000 ×

I =1000 ×

log 5 = log 3 + 4n [log 81 log 80]

338


154. 26500 = 20000 4

100r1 ⎟⎠

⎞⎜⎝

⎛ +

After taking log and solving it r = 7.5% Ans. (c) 7.5%

155. C I = 7000 ⎥⎦

⎤⎢⎣

⎡−⎟

⎠

⎞⎜⎝

⎛ +⎟⎠

⎞⎜⎝

⎛ +⎟⎠

⎞⎜⎝

⎛ + 1100851

10081

10071

CI = 1776

157. I 1 = P × 100

3 ×2 = 100

P6

I2 = P × 100

8 × 3 = 100

P24

I3 = P × 10010 × 1 =

100P10

Total interest = 1520

∴ 100

P40 = 1520 ⇒ P = 40

1520100 ×

P = 3800 Ans. Rs. 3800 (a)

158. A = 7500 [ ]n)i1( + [I = 0.01 n = 2]

= 7500 [1+0.01) 2 ⇒ 7500 × (1.01)2

A = 7650.75 Ans. (a) Rs. 7650.75

159. 512.50 = P [ ]1)05.01( 2 −+

512.50 = P × 0.1025

∴ P = 5000

Ans. (b) Rs. 5000

160. 1331 = 1000 3

100r1 ⎥⎦

⎤⎢⎣

⎡ +

3

1011

⎟⎠

⎞⎜⎝

⎛ = 3

100r1 ⎟⎠

⎞⎜⎝

⎛ + ⇒ 1.1 = 1+ 100

r

339


ANSWERS

∴ 0.1 = r / 100 ⇒ r = 10%

Ans. (a) 10%

L … S = 20 → (i)

If each item is increased by 15 [from eg (i)] Ans. (a) 20

∴

Range = )SL(21

2S

2L −−=

−−

−

21−

Range = 10 (because it is difference between largest and smallest data) Ans. (b) 10 164. In grouped frequency distribution, if the class interval is unequal then quartile deviation is

more appropriate. Ans. (a) Q.D.

165. SD = nd2∑

⇒ (4) 2 = 10

d2∑⇒ ∑ 2d = 160

Corrected ∑ 2)'d( = 2)2(160−

=40

∴ Corrected S.D. = n

)'d( 2∑ = 1040 = 2

S.D. = 2 Ans. (a) 2

161. Range = L S −

Range = (L + 15) (S + 15) −Range = L S = 20 −

162. Range = L S −

L S 20 −

If each item is divided by 2 −

Range = ×20 = 10 [( ) sign ignored] −−

If each item divided by 2 −

340


166. x =25

125..............15105( +++

[ ]

652

13025

5)125(522

25

==−+×

Average = 65 Ans. (a) 65 167. a, b, c, d, e are five add integers.

average = 5

)8a()6a()4a()2a(a5

e d c b a ++++++++=++++

⇒ (a + 4)

Ans. (d) a+4

168. Av = 3

x258180 ++

230 = x4386903

x438 =−⇒+

∴ x = 252 he should score 252 runs.

Ans. (d) None of these

169. 100 = 2xx)2x(

180)2x(120.x60)2x(−+++

−+++

∴ 60x = 240

x = 4 Ans. (a) 4

170. 16 = 25

x∑ ⇒ ∑ x = 400

15 = 24

x1∑ ⇒ ∑ 1x

Ans. 40 Years 171. Ans. (b) Refer Properties 172. Ans. (b) Refer Properties 173. Given two regression lines are

−

300x = 360x 240 −

= 360 ∴Age of Teacher = 400 360 = 40

341


ANSWERS

26y2x3 =+ → (1)

31yx6 =+ → (2)

Since the two lines of regression intersect at the point ( )y,x , replacing x and y by and respectively in the given regression equation, we get.

(1) ⇒ 2 y x

y23 x → (3)

23 x = 31

312

x326x12 =−+

6226x9 =+

2662x9 −=

= 36 x = 4

23 (4)

∴ x = 4, y = 7

Ans. (a)

174. Let us assume that 3x + 24 = 26 → (1) represent the regression line of y on x and

6x + y = 31 →(2) represent the regression line of x on y.

(1) ⇒

23

23

(2) ⇒

631

61 y

61

−

= 26 3 −

= 13 −

(2) ⇒ 6 x + 13 −

∴ (3) ⇒ y = 13 −

= 13 6 = 7 −

2y = 26 3x

−

∴ byx = −

6x = 31 y −

y = 13 x −

x = −

∴ bxy = −

342


∴ 41

61

23bxybyxr2 =⎟

⎠

⎞⎜⎝

⎛−⎟⎠

⎞⎜⎝

⎛−=×=

r = 5.021

41 ±=±=

Ans. (b) We take the sign of n as negative since bot h the regression coefficients are negative). 175. Ans. (a) Refer Properties 176. Let E1, E 2, E 3 denote the events that the probability is solved by X,Y and Z respectively. Then we have

P(E 1) = 1/3 ⇒ )E(P 1 )E(P 1 = 2/3

P(E 2) = 1/4 ⇒ E(P 2 )2 = 3/4

P(E 3) = 1/5 ⇒ E(P 3 )3 = 4/5

Problem will be solved if at least one of the three is able to solve it. Hence, the required probability that the problem will be solved is given by 321 EEE(P ∪∪ )

= )EEE(P1 321 ∩∩−

= ( ) ( ) ( )[ ])EP.EP.EP1 321−

= [Since E 1, E 2, E 3 are independent] = Ans. (c)

177. Given P(A) = 21

P(B) = 31

P ( )41BA =∩

∴ P(A|B) = ( )43

13

41

3141

)B(PBAP =×==∩

Ans. (a)

− = 1

) = 1 P (E

) = 1 P (E

−

−

−

1 2/3 x 3/4 x 4/5 1 2/5 = 3/5

−

−

343


ANSWERS

178. Given P(A) = 21 , P(B) =

31 and ( )

41BAP =∩

∴ P ( )BA∩ ( )BA∩

= 121

1234

41

31 =−=−

Ans. (c)

179. Given P(A) 21 , P(B) =

31 , ( )

41BAP =∩

P ( )BA∩ ( )BAP ∪

( ){ }BA∩

= ( )BAP ∩

= 41

31

211 +−−

= 125

1234612 =+−−

Ans. (a)

180. P (A) = ½, P(B) = 31 , ( )

41BAP =∩

= ( ) ( )BAPBAP ∩∪ =

( )BA∩

= 1 ¼

= 43

414 =−

Ans. (b) 181. Given x1 = 1, x 2 =2, x 3 = 3

( ) ( ) 6/1xP,31xP,

21)x(P 321 ===

∴ E(x) = x1 P(x 1) + x2 P(x 2) + x3 P(x 3)

= ⎟⎠

⎞⎜⎝

⎛ ×+⎟⎠

⎞⎜⎝

⎛ ×+⎟⎠

⎞⎜⎝

⎛ ×613

312

211 =

21

32

21 ++

−

= P(B) P −

= 1 −

= 1 P (A) +P(B) −P−

1 P(A) P(B) + − −

= 1 P

−

344


= ....666.135

610

6343 ===++

= 1.67 Ans. (c)

182. Given 3x,2x,1x 321 ===

( )61xP,

31)x(P,

21)x(P 321 ===

2 2

E(x) = )x(Px)x(Px)x(Px 332211 ++

= ⎟⎠

⎞⎜⎝

⎛ ×+⎟⎠

⎞⎜⎝

⎛ ×+⎟⎠

⎞⎜⎝

⎛ ×613

312

211

E(x) = 21

32

21 ++

= 35

610

6343 ==++

( ) ( ) ( ) ( )32

322

212

12 xPxxPxxPxxE ++=

= ⎟⎠

⎞⎜⎝

⎛ ×+⎟⎠

⎞⎜⎝

⎛ ×+⎟⎠

⎞⎜⎝

⎛ ×619

314

211

= 23

34

21 ++

= 3

106

206

983 ==++

∴ V(x) = 2

35

310

⎟⎠

⎞⎜⎝

⎛−

= 9

253

10 −

V(x) = 5556.95

92530 ==−

Ans. (a) 183. Let x denote the number of defective lamps. X can assume the values 0, 1, 2, 3

∴ V(x) = E(x ) … [E(x) ]

345


ANSWERS

p(X=0) p:probably having 0 bad orange out of 4 bad orange and 3 good orange out of 8 good orange.

P(x=0) = 5556

C12C8C4

3

30 =×

P(x=1)= 5528

C12C8C4

3

21 =×

P(x=2)= 5512

C12C8C4

3

22 =×

P(x=3) = Probability having 3 bad orange out of 4 bad orange and 0 good orange out of 8 good orange.

= 551

C12C8C4

3

03 =×

= 5554

55155 =−

Ans. (a) 184. Given P(A) = 0.5, P (AB) < 0.3 By Addition thereon,

∴ [∴ P(A or B) < 1]

P(B) < 0.8 Ans. (a) 185. Let the given events be A, B and P(A) = 2/3 P(B) Let P(B) = x

∴ P(A) = 2/3 x

The events A and B are exhaustive

∴ P(A or B) = 1

P(A) + P(B) = 1

⇒ 2/3 x + x = 1

−Probability that at least one orange out of three oranges is good = 1 P (x=3) = 1 1/55 −

P(A or B) = P(A) + P(B) P (AB)

P(A) + P(B) P(AB) < 1

∴ P(B) < 1 P(A) + P (AB)

< 1 0.5 + 0.3

346


5/3 x = 1 x = 3/5

∴ P(B) = 3/5

P(A) = 2/3 x 3/5 = 2/5

P(B) = 3/5 ⇒ odds in favour of B are

3 : 5 Ans. (b) 186. Given person variates with parameter = 1

i.e. λ = 1

By the poison distribution

p(x) = 0x,!x.e x

>λλ−

∴ The required probability

P(3 < × <5) =

= !4.e 4λλ−

= !4

)1(e 41−

= 24

136783.0 ×

P(3 < x <5) = 0.015326 Ans. (a) 187. Given p = 2% = 2/100 = .02 n = 200

∴ λ = np = 200 × .02 = 4

The probability of at least 5 defective means. P(x > 5)

= ⎭⎬⎫

⎩⎨⎧

++++−−−−−−

!4)4(e

!3)4(e

!2)4(e

!1)4(e

!0)4(e1

4434241404

− 3 = 3: 2

P(x = 4)

= 1 P (x < 5) = 1 {P(x=0) + P(x=1) + P(x=2) + p(x=3) + P(x=4)}

−

−

347


ANSWERS

= ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

++++− −

!44

!34

!2441e1

4324

= ⎭⎬⎫

⎩⎨⎧ ++++− −

24256

664

21641e1 4

= }667.106667.1085{)183.0(1 +++−

= )3334.34()83.0(1−

P (x > 5) = 0.3717 Ans. (a)

Now, 3 more cards can be dealt to the same man out of the 48 cards in 48C3 ways, which determines the exhaustive number of ways.

pade cards, then the 3 additional cards must be 3 ways.

The probability that none of the three additional cards dealt to the man is a spade card =

3

3C48C39

Hence, the required probability, 'P' that at cards is given by:

3

3C48C391p −=

= 464748

!3!3

3738391××

×××−

= 2347163719131

××××−

= 1729691361−

p = 0.4718 Ans. (c) 190. Given P (x = 1) = P (x = 2) Given x is a poison variable.

−188. After a man is dealt 4 spade cards from an ordinary pack of 52 cards, there are 52 4 =

If none of these 3 additional cards is a s

48 cards left in the pack, out of which 9 are spade cards and 39 are no spade cards.

drawn out of the 39 non-spade cards, which can be done in 39C

least one of the additional cards is a spade

= 10.5282

= 1 0 6283 .

348


∴ !2

)(e!1

)(e )2()1( λ=λ λ−λ−

2

2λ=λ

2=λ = variance

Ans. (b)

50065

50065

Q = 500435

n = 500

SE of Proportion of defectives = nQP

= 500

1500435

50065 ××

SE = 0.015 Ans. (a) 0.015

192. Standard Error of Mean (SE) = 10075.0

n=σ

SE = 0.075 95% Confidence Limit for population m 1.96 SE

= 5.6 ± 1.96 × 0.75 = 5.6 ± 0.147 The Confidence level are 5.453 and 5.747 Ans. (a) 5.453 and 5.747

193. Standard Error (SE) = 353.01284

n==σ

96% confidence limit for population mean are

⇒ x + 2.05 × SE

= 28 ± 2.05 × 0.353 ⇒ 28 ± 0.72

The confidence level are 27.272 and 28.728 Ans. (b) 27.272 and 28.728

191. P = Q = 1 P = 1 − −

ean are given by : x ±

349


ANSWERS

194. P = 50065

50065 ⇒ Q =

500435

SE of proportion of defectives = nQP

= 500

1500435

50065 ××

SE = 0.015 Confidence limits for the population are = P ± 3 × SE

= 015.0350065 ×± ⇒ 0.13 ± 0.045

Levels are 0.085 and 0.175 or Levels are 8.5% and 17.5% Ans. (a) 8.5% and 17.5 196. Variance = 4

σ = 4 = ± 2

Statement is true Ans. (a) True 197. n = 10 P = 0.3

∴ σ = npq

∴ Variance = npq = 10×0.3×0.7

Variance = 2.1 Ans. (a) 2.1 198. When the cost of living increases, the standard of living improves. Ans. (b) false

199. The 95% confidence limit for the sample mean ( )x is x ± 1.96 ⎟⎟⎠

⎞⎜⎜⎝

⎛ σn

which is not given

Ans. (b) False

, Q = 1 P = 1 − −

−∴ Q = (1 P) = 1 0.3 = 0.7 −

350


200. Mean and variance never be equal

∴ Statement is false

Ans. (b) False

Model Test Paper – BOS/CPT – 5 / 2007 151. Let the fraction be x/y. Then accordi

1118

3yx3 =

−

.................... (i)

and 52

y28x =+

⇒ 5x + 40 = 4y

.....................(ii)

.....................(iii)

.... ................(iv)

7x= 84

x = 84/7 = 12

6y = 150

y =150/6 = 25

Hence, the required fraction is 12/25

152. Let the two numbers are x and y Given x + y = 150 % of y

33x = 18y 54 33x 18y+54 = 0

11x 6y+18 = 0

5x 4y+40 = 0

−

−

−

−

(i) × 2 ⇒ 22x 12y+36 = 0

(ii) × 3 ⇒ 15x 12y+120 = 0

−

−

(iii) (iv),w e get −

7x 84 = 0 −

(i) ⇒ (11) (12) 6y + 18 = 0 −

132 6y + 18 = 0 −

∴Ans. (c)

ng to the given condition of the problem,

351


ANSWERS

= y100150 ×

x + y = 1.5y x = 0.5 y

x = 21 y

Ans. (a) 153. Let three consecutive even numbers are x, x + 2, x + 4.

Given condition is x + (x+2) + (x+4) = 154360 −×

3x = 24

x = 3

24 = 8

Ans. (b)

Five years ago According to the first condition of the problem,

.................(i)

Ten years later my age = (x+10) years According to the second condition of the problem, x+10 = 2(y+10) x+10 = 2y+20

154. Suppose my present age is x years and my sons present age is y years

my age = (x 5) years

−

−

∴ The middle number = x + 2 = 8 + 2 = 10

3x + 6 = 30

my son's age = (y 5) years

x 5= 3(y 5) x 5 = 3y 15

⇒ x 3y = 15 + 5

⇒ x 3y = 10

−−

−

−

−−

my son's age = (y+10) years

x-2y = 20 10 −

352


..................(i i)

(i) (ii)⇒ y = 20

Hence, my presence age = 50 years and my son•s present age = 20 years

∴Ans.(a)

155. The compound ratio of 4:3, 9:13, 26:5 and 2:15 is

= 15513322694

××××××

= 2516

Ans. (b)

156. We know nPr = !)4n(

!n−

∴ 6rP56

+=

!)}6r(56{!56+−

= )!r50(

!56−

3rP54 + = )}!3r(54{

!54+−

= )!r51(

!54−

Thus, !54

)!r51()!r50(

!56P54P56

3r

3r −×−

=+

+

= !54

)!r50()r51()!r50(

!545556 −−×−

××

= 1

)r51(5556 −××

But we are given the ratio as 30800 : 1

∴ 1

)r51(5556 −×× = 1

30800

x 2y = 10 −−

(i) ⇒ x – 60 = –10

x = 60 –10 = 50

353


ANSWERS

5556

30800×

= 10 ∴ r = 41

Ans. (b) 157. He can arrange his schedule in 8P6 = 8 × 7 × 6 × 5 × 4 × 3 = 20160 ways. Ans. (b) 158. The two Indians can stand together in P 2 = 2! = 2 ways. So is the case with the two Americans and the two Russians. Now these 3 groups of 2 each can stand in a row in 3P 3 = 3×2 = 6 ways. Hence by the

generalized fundamental principle, the total num ber of ways in which they can stand for a photograph under given conditions is

6 × 2× 2× 2 = 48 Ans. (c) 159. This is the number of combination of 52 cards taken five at a time. Now applying the formula.

52C 5 = )!552(!5

!52−

= !47!5

!52

= !4712345

!474849505152×××××

×××××

= 2598960 Ans. (a) 160. Let the unit's digit of the number be x and the ten's digit by y. Then

x + y = 9 → (1)

and the number = 10y + x Reversing the order of digi ts of the given number, Unit's digits becomes y and ten's digits becomes x

∴ Now number = 10x + y

According to the given condition of the problem,

(or) (51 – r)! =

2

354


Adding (1) and (2), 23 get

x = 2

12 = 6

(1) ⇒ 6 + y = 9

∴ The given number is 36

Ans. (b)

161. 0x

lt→

xx

xx

2439

−− ⇒

0xlt→

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−−−

−−−

x)12()14(

x)13()19(

xx

xx

0x

lt→

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −−⎟⎟⎠

⎞

⎜⎜

⎝

⎛ −

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −−⎟⎟⎠

⎞

⎜⎜

⎝

⎛ −

x12

x14

x13

x19

xx

xx

⇒ 2log4log3log9log

−−

⇒ 2log3log

2log2log23log3log2 =

−−

Ans. (a) 2log3log

162. 0x

lt→ )x1(log

15.25)x1(log

)15( xx22x

++−=

+−

⇒ 0x

lt→

)x1(log

)15.225( xx

++−

⇒ 0x

lt→

x)x1log(

x152

x125 xx

+

⎟⎟⎠

⎞⎜⎜⎝

⎛ −−⎟⎟⎠

⎞⎜⎜⎝

⎛ −

App lt.

(10x + y) – (x+10y) = 27 10x + y – x – 10y = 27 9x – 9y = 27

x – y = 3 → (2)

y = 9 – 6 = 3

2 × = 12

355


ANSWERS

⇒

15log.225log − =

125log25log − = 0


163. 1x

lt→

f(x) ⇒ 1x

lt→

(x+1)

App lt.

⇒ 1 + 1 = 2

Ans. (a) 2

164. LHL 2x

lt→

App lt.

2xlt→

App. lt.

∴ LHL = RHL = f(2)

∴ f(x) Continuous at x = 2

Ans. (a) Continuous x = 2

165. f(x) = 2x3x7x2x3

2

2

+−++ =

)1x()2x(7x2x3 2

−−++

∴ x ≠ 2 & x ≠ 1

∴ Points of discontinuity = 1, 2

Ans. (a) 1, 2 166. Let z = log x

dz = dxx1

dx = x dz

∴ I = ∫ ∫= xdzz.x

1dxxlogx

1

= ∫ dzz1

(x – 1)

⇒ 2 – 1 = 1 ∴ LHL = 1

RHL (2x – 3)

LHL 2.2 – 3 = 1

f(2) = 2.2 – 3 = 1

To be continuous (x – 2) ≠ 0 & (x – 1) ≠ 0

356


= log z = log (log x) + c

167. Let I = ∫ dxlog x10

= ∫ dxlog.log e10

xe

= ∫ dx1.xlogloge10

= ⎥⎦

⎤⎢⎣

⎡ − ∫ x1x.xlogloge

10

I = [ ] cxxlogxloge10 +−

168. Let I = ∫ −

−

−+ dx

e4e9e6e4

xx

xx

∴ I = ∫ −+ dx

4e96e4

x2

x2

Let t = x2e

∴ dt = 2 x2e dx

= 2t dx

∴ I = ∫ ∫ −+=

−+ dt

)4t9(t3t2

t2dt

4t96t4

= ( )( )∫ ⎥

⎦

⎤⎢⎣

⎡

−++

−+ dt

4t99/439/42

)40(t30

= ( )∫ ⎥⎦

⎤⎢⎣

⎡

−+− dt

4t9435

t43

= ( ) c9

4t9log.4

35tlog43 +−+−

( ) c4e9log3635elog

43 x2x2 +−+

Ans. (a)

169. Let x = 2 Sin 2θ +Cos 2 θ

× dx

= −

dx = [4 Sin θ Cos θ + 10 Cos θ ( – Sin θ)] dθ

357

Ans. (b)


ANSWERS

∴ I = ( )∫ θθ−−θ+θ

θ+θ dxCosSin6)2Cos5Sin2()Cos5Sin2(*5

22

22

= ( )∫ θθ−θ−+θ

θ+θ dxCosSin6)Sin1(2Cos5

)Sin2Cos1(522

22

∫ θθθθθ dCosSin.

Cos3Sin3

2

2

∫ θθθθθ dCosSin.

CosSin

∫ θθ d2

∫ ⎥⎦

⎤⎢⎣

⎡ θ−2

2Cos1 dθ

= ⎥⎦

⎤⎢⎣

⎡ θ−θ22Sin

= 3 Sinθ Cos θ … 3θ

= θ−θθ 3Cos3.Sin3

I = c3

2xCos32x.x5 1 +−−−− −

Ans. (c)

170. Put t100x6x2 =+−

∴ 2x2 t1006x =+−

∫ ∫ −+−=+−− dx)3x(100x6xdx100x6x)3x( 22

= ∫ tdt.t

= ∫ dtt2

dx = – 6 Sinθ Cos θ dθ

= – 6

= – 6

= – 6 Sin

= – 6

3 –

(2x – 6) dx = 2t dt (x – 3) dx = t dt

358


= ∫ + c3t3

= c)1006x(31 2/3x2 ++−

Ans. (c) 171. No. of ways in which one or more friends may invited

= 654321 CCCCCC 666666 +++++

= 126 − = 63 ways. Ans. (a) 63 ways. 172. No. of ways of failure of candidate.

= 4321 CCCC 4444 +++

= 124 − = 15 ways. Ans. (c) 15 173. A voter can vote in following ways

254 = 1n7654321 CCCCCCCC n....nnnnnnn

−++++++

∴ 254 = )11(2)1n(2 nC

nn

+−=+−

∴ 256 = 2 n

∴ 2 8 = 2 n ⇒ ∴ n = 8 Total candidate = 8 Ans. (a) 8 174. No. of words of 3 consonants and 2 vowels among 17 consonants and 5 vowels are

= !551723 CC ××

= 816000 Ans. (b) 81,6000 176. The present value of annual profit V = A.P. (ni) = 34000 × 3.7079

the

s

Ans. (a) Machine should not be purchased. V = 128886 which is less than initial cost of machine. achine must not be purchased M

359


ANSWERS

177. 40 = 2000 × 4100

r ×

∴ r = -0.5%

Ans. (b) 0.5%

178. I1 = 2000 × 1100

4 × = 80

I2 = 3000 × 10014 × 1 = 420

Total Interest = 500

∴ rate of interest = 15000

100500×

× = 10%

r = 10% Ans. (a) r = 10%

1 2100R 3

100R × =30

6R = 30

∴ R = 5%

Ans. (c) 5%

180. 40 = 2000 × 100

2 × n

n = 1 yr. Ans. (a) = 1 yr.

181. 202

ba =+ ⇒ a + b = 40 → (1)

SD = 5 → 52

ba =−

∴ a … b = 10 → (2)

⇒ 2a = 50 ⇒ a = 25

∴ b = 15

Ans. (a) 25, 15

179. I – I = 30 ⇒ 1200 × ×3 – 1000

⇒ 36R – 30R = 30

360


182. Mean = n

x∑

4.4 = 5

ba621 ++++

∴ a + b = 13 → (1)

σ2 = 22

xN

x−∑

8.24 = 22

)4.4(5

x−∑

∑ 2x = 138

138ba941 22 =++++

∴ a 2 + b 2 = 138 ⇒ a 2 2

2 a = 9, 4

∴ Nos → 9, 4

183. For individual series, the rank of the median is = th

21N⎟⎠

⎞⎜⎝

⎛ + term

Ans. (b) th

21N⎟⎠

⎞⎜⎝

⎛ + term

184. Rank of the median of the series 2, 3, 4, 5, 6, 7

= th

21N⎟⎠

⎞⎜⎝

⎛ + term = th

216⎟⎠

⎞⎜⎝

⎛ + term

= 3.5 th term Ans. (a) 3.5

If y = 50

None of these Ans. (d) None of these.

+ (13 – a) = 138

⇒ a – 13a – 36 = 0

185. Regression Eq. 2x + 3y – 10 = 0

∴ 2x = +10 – 3 × 50 = – 140

x = – 70

361


ANSWERS

186. Ans. (c) Refer Properties 187. Ans. (c) Refer Properties

188. Given r (x, y) = 0.4 → (1)

We know that r (a X, cY) = )y,x(r.|c||a|

→ (2)

Using (2) in (1), we get

= )y,x(r.|1||2| −×

= 12

4.02××−

Ans. (b) 189. Computation of Correlation Coefficient

x y xy x2 y2

69 85

70 87

4830 7395

4761 7225

4900 7569

Total 154 157 12225 11986 12469

5.782

157y,772

154x ====

Cov (x,y) = n

yx ii∑ yx = 2

12225

= 68

Sx = 22

2i )77(

211986x

nx

−=−∑

= 8

Sy = 5.8)5.78(2

12469yny 22

2i =−=−∑

∴ n = ( ) 16868

5.8868

SySxy,xCov ==

×=

2 × (−1)

a c××

r (2x, – y) = r (2x, – 1y)

r (2x, – y) = – 0.4

– – (77) (78.5)

Ans. (a)

362


x y xy x2 y2

102 109

50 48

5100 5232

10404 11881

2500 2304

Total 211 98 10332 22285 4804

49

298y,5.105

2211x ====

Cov (x, y) = ( ) ( )495.105

210332yx

nyixi

−=−∑

=

( ) 5.35.105

222285x

nxi

Sx 222

=−=−= ∑

Sy = ( ) 1492

4804ynyi

Sx 222

=−=−= ∑

∴ n = ( )

( ) ( ) 115.3

5.3SySx

y,xCov −=×

−=

Ans. (b) 191. Ans. (a) … Refer Properties 192. Ans. (a) … Refer Properties 193. Ans. (b) … Refer Properties

194. Given X ~ N ( μ, σ2), where μ = 2 and σ2 = 9 σ = 3 We want x so that

P(2 < × < x) = 0.4115 → (1)

When X = 2, Z = 03

22x =−=σ

μ−

When x = x, Z =

32x − = Z1 (Say) → (2)

From (1), we get P (0 < Z < Z1) = 0.4115 ⇒ Z1 = 1.35 (from Normal Table)

5166 – 5169.5 = – 3.5

190. Computation of correlation Co – efficient.

363


ANSWERS

Substituting in (2), we get

3

2x − = 1.35

∴ x = 2+3 (1.35)

x = 6.05 Ans. (b)

195. Mean = First moment about origin = 35 (given) → (1)

Second moment about 35 = 10 (given)

⇒ Second moment about mean = 10

μ2 = 0 → (2)

Since the given distribution is normal,

β1 = 0 and β2 = 3

∴β1 = 3

2

2μ3μ = 0 ⇒ μ3 = 0

β2 = 24

2μμ = 3 ⇒ μ4 = 3 2

2μ = 3×10 2 = 300

∴ μ1=0 (always), μ2 = 10, μ3 = 0, μ4 = 300

Ans. (c)

196. The most commonly used confidence limit is → 95%

Ans. (c) 95% 197. Sample mean is statistic Ans. (b) Statistic

Ans. (b) Non random sampling

200. Random Sampling is also called lottery sampling Ans. True

198. Deliberate sampling is – Non \random sampling

199. Stratified random sampling issued for Non – Homogeneous population. Ans. (b) Non – homogeneous

364


Model Test Paper – BOS/CPT – 6 / 2007 151. Let iven number is x

Then the condition 15x21

31

51 =⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛

1530x =

x = 450 152. Let the number be = x.

Then given the condition = 60x51

43 =⎟

⎠

⎞⎜⎝

⎛

6020

x3 =

4003

2060x =×=

Ans. (b) 153. Let the number be x.

Given ( ) 24x83

54 =⎥

⎦

⎤⎢⎣

⎡

24x103 =

803

1024x =×=

∴ 250% of x = 250% of 80 = 20080100250 =×

Ans. (d) 154. Let the number be x

Given condition 821xx 2 =+

0182xx2 =−+

( ) ( ) 013x14x =−+

13x,14x =−=

g

∴ x = 13 (negative reflected)

Ans. (a)

365


ANSWERS

155. Let the unit's digit of the number be x and ten's digit by y

Then x + y = 12 → (1)

and the number = 10y + x Reversing the order of digits of the given number, Unit's digit becomes y and ten's digits becomes x

∴ New number = 10 x + y

Adding (1) and (2) ⇒ 2x = 10

x = 5

∴ ⇒y = 7

∴ The number is 75

Ans. (a) 156. Let the number of coins is x

Given 430x4

18x2

14x10 =++

4304

x18x28x40 =++

4304

x86 =

x = 2086

4430 =×

∴ The one Rupee coins = 10x = 10×20 = 200

The 50 paise coins = 14x = 14×20 = 280 The 25 paise coins = 18x = 18×20 = 360 Ans. (a) 157. First Vessels Contain Milk Ratio 5 First Vessels Contain Water Ratio 2

According to the given condition of the problem (10x + y) – (x + 10y) = 18 9x – 9y = –18

x – y = – 2→ (2)

366


Second Vessels Contain Milk Ratio 6 Second Vessels Contain Water Ratio 1 Both the Vessels Milk = 5 + 6 = 11 Both the Vessels Water = 2 + 1 = 3

∴ The new Ratio = 11:3

Ans. (b) 158. Let the two numbers are x and y

Given 8x = 5y → (1)

and x + 27 = y → (2)

3y = 216

y = 723

216 =

∴

∴ Sum of two number = x + y = 72 + 45 = 117

Ans. (c) 159. Let their monthly incomes be Rs. 9x and Rs. 7x respectively. Let their monthly expenditures be Rs. 4 y and Rs. 3 y respectively. According ot the given condition of the problem,

Multiply (1) by 3, we get Multiply (2) by 4, we get Subtracting (3) from (4), we get x = 200 Hence their monthly income are Rs. (9×200=1800) and Rs. (7 × 200 = 1400). Ans. (a)

(2) ⇒ x = y – 27

(1) ⇒ 8 (y – 27) = 5y

8y – 216 = 5y

x = 72 – 27 = 45

9x – 4y = 200 → (1)

7x – 3y = 200 → (2)

27x – 12y = 600

28x – 12y = 800

367


ANSWERS

160. Let x be the distributed amount of A, B and C Given

∴ 5x + 11x + 3x = 950

19x = 950

x = 5019950 =

∴ The amount of A = 5x = 5 × 50 = 250

The amount of B = 11x = 11 × 50 = 550

∴ The difference of A and B = 300

Ans. (a)

161. 1x

lt→

1xee 1x

−− −−

⇒ 1x

lt→

)1x(e1e x1

−−−

let 1 + h → x where h → 0

∴ 0x

lt→

)h(e1e h

−− =

e1−

162. 0x

lt→

x

1)x1( n −+

= 0x

lt→

x

1......)!2

x)1n(nnx1(2

−+−++

= 0x

lt→

x

......!3

x)2n)(1n(n!2

)1n(nnx2x

⎥⎥⎦

⎤

⎢⎢⎣

⎡ −−+−+

App Lt. n + 0 = n Ans. (c) n

163. 0x

lt→

ax

)2a()2x( 3/53/5

−+−+

0x

lt→

)]2a()2x[()2a()2x( 3/53/5

+−++−+

App lt.

Ans. (b) –1/e

368


⇒ 35 .(a+2) =

35 (a+2) 2/3

Ans. (a) 35 (a+2) 2/3

165. 0x

lt→

x

32 xx − ⇒ 0x

lt→

x

)13()12( xx −−−

0x

lt→

x

12 x −0x

lt→

x

13 x − ⎥⎥⎦

⎤

⎢⎢⎣

⎡=−

→

ax

0xelog

x1alt

⇒ log ⎟⎠

⎞⎜⎝

⎛

32

Ans. (b)

166. ( ) 2x3xf 2 +=′

( ) ( )∫ ∫ +=′ dx2x3dxxf 2

( ) cx23x3cxf

3++=+

When f (0) = 0 ⇒ c = 0

∴ f(x) = x2x3 +

∴ f(2) = 32 + 2 (2)

= 8 + 4 = 12 Ans. (c)

167. Let I = ∫ +++

4x6x3x

2

Put x2+6x+4 = t

∴(2x+6)dx = dt

(x+3)dx = 2dt

∴ ∫ ∫=++

+t2

dtdx4x6x

3x2

= ∫ dtt1

21

5/3 – 1

–

⇒ log 2 – log 3

369


ANSWERS

21 log(t)

∴ ∫ =++

+21dx

4x6x3x

2 log(x2+6x+4) + c

168. ∫∫ +−+=

+− dxe

)1x(21xdx

)1x(1xe x

33x

= ∫ ⎥⎦

⎤⎢⎣

⎡

+−

+ 32x

)1x(2

)1x(1e dx

= { }∫ + )x('f)x(fe x dx

= e x f(x) where f(x) = 2)1x(1+

∫ +=

+−

2

x

3x

)1x(edx

)1x()1x(e +c

Ans.(a)

169. ( ) ( )( ) ( )∫ +

++=+

+c

3145x3dx5x3

144

= ( ) c15

5x3 5++

Ans. (b)

170. ∫ + dx5x7

= ( )∫ + dx5x7 21

= ( )( )

c71

21

5x7 121

+⎟⎠

⎞⎜⎝

⎛ +

+ +

= ( )( )

c7

23

5x7 23

+⎟⎠

⎞⎜⎝

⎛

+

370


( ) c21

5x72 23

++

171. Voter has option

(i) Two candidates from gentlemen = 332c =

(ii) Two candidates from ladies = 332c =

(iii) One from each ladies & gentlemen = 11 Cc 33 × = 9

Total options = 3 + 3 + 9 = 15 Ans. (c) 15

172. Total hand shakes in the party = 2c40 = 780

Ans. (a) 780

173. Total triangle formed by m sides = 3Cm

⇒ !3)!3m(

)!3m)(2m)(1m(m−

−−−

⇒ 6

)2m)(1m(m −−

Ans. (a) 6

)2m)(1m(m −−

174. Cricket team of 11 among 14 players out of which one wicket keeper

= 10C12 ×

1C2 = 66 ×2

⇒ 132

Ans. (b) 132

175. No. of ways in which a particular child goes to circus = 2C7 ×1 = 21

Ans. (c) 21 176. ax = b y = c z = k (let )

∴ log a k = x, log bk = y, log ck = z

∴ log ka = 1/x, log kb = 1/y, log kc = 1/z

x, y, z in GP

∴ y2 = xz

(log bk)2 = (log ak).(log ck)

371


ANSWERS

∴ klogklog

klogklog

b

c

a

b = ⇒ clogblog

klogalog

k

k

k

k =

∴ log a , log b and log c in GP

Ans. (b) G.P.

177. 1n

21.8

10241 −

⎟⎠

⎞⎜⎝

⎛= ⇒ 13

21⎟⎠

⎞⎜⎝

⎛ = 1n

21 −

⎟⎠

⎞⎜⎝

⎛

∴ n = 14

321

21.8

21.8T

819

9 =⎟⎠

⎞⎜⎝

⎛=⎟⎠

⎞⎜⎝

⎛=−

Ans. (c) 1/32 178. Product of 2nd term from start & last 2nd term from end = (ar) × a(r) n…2 = a 2 r(n…1)

Product of first & last term = 1n21n raara −− =×

Hence proved the statement. It is true statement Ans. (a) True

179. a, b, c in GP ∴ b 2 = ac

a, x, b in AP ⇒ x = 2

ba +

b, y, c in AP ⇒ y =2

cb +

∴ cb

c2ba

a2yc

xa

++

+=+ ⇒

bcacbab]bcacacab[2

2 ++++++

⇒ bcacacab

]bcacacab[2++++++ }acb{ 2 =

= 2 Ans. (c) 2

180. y1

x1 + =

xyyx +⇒

4)cb()ba(

2cb

2ba

++

+++

⇒ )bcacbab(

)cb2a(22 +++

++ =bcbbab)cb2a(2

22 +++++

6th team from end = (14 – 6+1) from beginning = 9th term

372


= )cb2a(b)cb2a(2

++++ =

b2

Ans. (b) b2

181. The number of times a particular item occurs in a given data is called its frequency. Ans. (b) Frequency 182. Lower class (s) = 10.6 Width = 2.5 (Class interval) Upper Class (L) of Ligh est Class = S = 10 × C.I. = 10.6 + 10 x 2.5 = 35.6 Ans. (a) 35.6

183. 2

ClassUpperClassLower + = Mid Value

m2Class.UL =+

184. Mean = 2/x).1n(n

nx.n....x3.3x2.2x.1+

+++

= 2/x).1n(n

x)n......321( 2222

++++

= 2/x).1n(n

x)n......321( 2232

++++

= x)1n(n

2x)1n2)(1n(6

n−+

×++ = 3

)1n2( +

Mean = 3

)1n2( +

Ans. (c) 3

1n2 +

t

∴ Upper class = (2m – L)

Ans. (c) (2m – L)

373


ANSWERS

185. x = 10, n = 4

Σx = n. x = 4 × 10 = 40

Corrected Σx = (40 + 4a)

Corrected x = 4

a440 +

13 = 4

a440 +

4a = 12 a = 3 Ans. (c) 3 186. From the given data, we observe that 20 + 5 = 25 21 + 4 = 25 and 22 + 3 = 25

Thus, x and y are connected by the linear relation: x + y = 25 → (1)

⇒ There is perfect correlation between x and y

⇒ r = ± 1 → (2)

∴ As x increases, y decreases (by the same amount)

⇒ x and y are negatively correlated → (3)

From (2) and (3), we conclude that Ans. (c) 187. Ans. (b) Refer Properties 188. Ans. (b) Refer Properties 189. Ans. (b) Refer Properties 190. Ans. (b) Refer Properties 191. Lt X … B (n=6, p). When X denotes the number of successes. Then, by binomial

probability law, the probability of r successes is givenby

p(r) = P(x=r) = 6C r P rq → (1)

Put r = 3 and 4 in (1)

From (1) / We get y = 25 – x

r = r (x, y) = –1

6 – r

r = 0, 1, 2, ........... 6

374


(1) ⇒ p(3) = 6C 3p3q3 = 20p3 q3 = 0.2457 (given)

p(4) = 6C 4 p 4 q 2 = 15 p 4q2 = 0.0819 (given)

31

2457.00819.0

qp20qp15

)3(p)4(p

33

24===

⇒ 31

qp.

43 =

∴

∴ 13p = 4

p = 4/13

∴

192. Ans. (a) 193. Ans. (b) 194. Ans. (a) 195. Ans. (b) Refer Properties

196. Which measure of dispersion has some desirable mathematical properties → Standard Deviation.

Ans. (a) Standard Deviation.

197. 0x1yy1x =+++

⇒ xyyx +−=+ 11

Eg. Both side

)x1(y)y1(x 22 +=+

yxxy)y 2222 −=−

)yx(xy)yx()yx( −−=−+

∴ x + y +xy = 0 ⇒ y = x1

x+−

∴ 22 )x1(xx1

)x1()1()x()1()x1(

dxdy

++−−=

+−−−+=

∴ 1dxdy)x1(

)x1(1

dxdy 2

2 −=+⇒

+−=

9p = 4q = 4 (1 – p)

q = 1 – p = 1 – 4/13 = 9/13

– Refer Properties – Refer Properties – Refer Properties –

x(

Ans. (c) (–1)

375


ANSWERS

198. y = x 1x2 + + log ⎟⎠⎞

⎜⎝⎛ ++ 1xx 2

dxdy = x.

1x2

12 +

.2x + 1x2 + .1 + 1xx

12 ++

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

++ x2.

1x2

112

= 1x

1

1xx

x1x1x1x

x22

22

2

2

+⎟⎠⎞⎜

⎝⎛ ++

++++++

= 22

2

2

22

x121x

)1x(2

1x

11xx +=+

+=+

+++

Ans. (c) 2 2x1+

199. y = mxmx beae −+

∴ mxmx bmeamedxdy −−=

( )mxmx2

2

bmeamedxd

dxyd −−==

= mx2mx2 ebmeam −+

= ( )mxmx2 beaem −+

2

2

dxyd = ym2

Ans. (c) ym2

200. x345 CCCC 141212.212 =++

( )45 CC 1212 + + ( )

34 CC 1212 +xC14=

45 CC 1313 + =

xC14

[ ]r1n

1rn

rn CCC +

− =+

5C14 =

xC14

x = 5 but value 9C14 =

5C14

∴ xC14 =

9C14

∴ x = 9

376


x = 5 or 9 Ans. (c) 5 or 9.

Model Test Paper – BOS/CPT – 7 / 2007 151. Let the number be x. Then according to the given condition of the problem,

14

1x3x ++=

⇒ 4

1x3x +− =1

⇒ 12

)1x(3x4 +− =1

⇒ 12

3x − =1

Hence the required number is 15 152. Let the fraction = x And Correct answer = y

∴ Given yx1716 = → (1)

and 34033y

1716x +=

i.e. 34033yx

1617 += → (2)

(1) ⇒ x = y1617

Substitute x the value of x in equation (2)

34033yy

1617

1617 +=×

34033yy

256289 +=

⇒ x – 3 = 12

⇒ x = 3 + 12 = 15

377


ANSWERS

34033yy

256289 =−

34033y

256256289 =⎟

⎠

⎞⎜⎝

⎛ −

34033y

25633 =

y = 33

25634033 ×

y = 8564

Ans. (a) 153. Let the number be x

Given ( ) ( )⎥⎦

⎤⎢⎣

⎡+=⎥⎦

⎤⎢⎣

⎡ x94

528x

154

75

x4588x

214 +=

8x458x

214 =−

8x945

168180 =⎟⎠

⎞⎜⎝

⎛ −

8x94512 =

x = 8 × 12945

x = 708.75 Ans. (d) 154. Let two numbers are x and y

Given condition x + y = 14 → (1)

Adding (1) and (2) ⇒ 2x = 24

x = 12

(1) ⇒ 12 + y = 14

y – x = 1 0 → (2)

378


y = 2

∴ Product of two numbers = x × y = 12 × 2 = 24

Ans. (a) 155. Let two numbers are x and y.

Given

And 95

yx =+

i.e. x + y = 45 → (2)

Adding (1) and (2) ⇒ 2x = 56

X = 28

y = 17

∴ The two numbers are 28, 17.

Ans. (d)

156. Sub duplicate Ratio of 16:49 = 49:16

= 4 : 7 Ans. (a)

157. Duplicate Ratio of 4 : 5 = 22 5:4

= 16 : 25 Ans. (a)

158. Triplicate Ratio of 3 : 5 = 33 5:3

= 27 : 125 Ans. (a)

33 125:8

= 2 : 5 Ans. (b)

160. 4 th Proportion of 6, 8 and 15 is x

1586 =

6x = 15 × 8

x – y = 11 → (1)

(1) ⇒ 28 – y = 11

– y = 11 – 28 = –17

159. The sub – triplicate Ratio of 8 : 125 =

379


ANSWERS

x = 6

815 ×

= 20 Ans. (c) 161. Let the two numbers be x and y. According to the First condition of the problem,

14

yx =

⇒ x = 4y → (1)

According to the second condition of the problem,

13

5y5x =

++

x + 5 = 3 (y + 5) x + 5 = 3y + 15

Put x = 4y from (1) in (2), we get y = 10

(1) ⇒ x = 4 (10) = 40

Hence the required numbers are 40 and 10. Ans. (b) 162. Let A having money = 3x B having money = 4x C having money = 5x Given 3x = 300 x = 1 00

∴ C = 5x = 5 × 100 = 500

Ans. (c) 163. Let the two numbers be x and y. According to the first condition of the problem.

65

yx =

6x = 5y

→ (1)

x – 3y = 15 – 5 = 10 → (2)

4y – 3y = 10

6x – 5y = 0

380


According to the second condition of the problem

54

5y5x =

−−

→ (2)

Subtracting (3) from (4), we get y = 30

6x = 150

x = 6

150 = 25

Ans. (c)

ing to the given conditions of the problem.

21

1y1x =

++

⇒ 2x + 2 = y + 1

and 115

5y5x =

−−

→ (2)

∴ → (3)

→ (4)

y = 71

2x = 70

5(x – 5) = 4 (y – 5) 5x – 25 = 4y – 20

5x – 4y = 5

(1) × 5 ⇒ 30x – 25y = 0 →(3)

(2) × 5 ⇒ 30x – 24y = 30

(1) ⇒ 6 x – 5 (30) = 0

164. Let the given numbers be x and y. Then accord

Hence the required numbers are 25 and 30

2x – y = –1 → (1)

11x – 55 = 5y – 25

11x – 5y = 30

(1) × 11 ⇒ 22x – 11y = –11

(2) × 2 ⇒ 22x 10y = 60 –

(3) – (4) ⇒ – y = – 71

(1) ⇒2x – 71 = – 1

381


ANSWERS

x = 35 Hence, the required numbers are 35 and 71 Ans. (b) 165. Let the number to be subtracted be x. Then according to the problem

157

x43x27 =

−−

⇒

⇒

8x = 104

x = 8

104 = 13

Hence the required number is 13 Ans. (a)

and ten digits = y

∴ x+y = 3 → (1)

and the number = 10y + x Reversing the order of digits Units digit = y and ten's digit = x

∴ Number = 10x + y

According to the given condition of the problem 7(10y + x) = 4(10x+y) 70y + 7x = 40x + 4y

→ 92)

Adding (1) and (2) we get 3y = 3 y = 1

15 (27– x) = 7 (43 – x)

405 – 15x = 301 – 7x

15x – 7x = 405 – 301

166. Let the unit digit = x

70x – 40x + 70y – 4y = 0 – 33x + 66y = 0

– x+2y = 0

382


(1) ⇒ x + 1 = 3

Hence, the required number is 12 167. The committee of six must include atleast 2 ladies. i.e. two or more ladies. As there are only 3 ladies, the following possibilities arise: The committee of 6 consists of (i) 4 men and 2 ladies, (ii) 3 men and 3 ladies. The number of ways for (i) = 7C4 + 3C2 = 35 × 3 = 105 The number of ways for (ii) = 7C3 × 3C3 = 35 × 1 = 35 Hence the total number of ways of forming a committee so as to include atleast two

ladies = 105 + 35 = 140 Ans. (a)

168. We have nCr = )!4n(!r

!n−

Now substituting for n and r, we get

28C2r = )!r228()!r2(

!28−

24C = { }!)4r2(24)!4r2(!24

−−−

= )!r228()!4r2(

!24−−

Given r2C28 :

4r2C24−

= 225:11

⇒ 4r2

r2

C

C

2428

−

= )!r228()!r2(

!28−

÷!24

)!r228()!4r2( −−

= )!r228()!4r2)(3r2)(2r2)(1r2(r2

!2425262728−−−−−

×××× × !24

)!r228()!4r2( −−

=)3r2)(2r2)(1r2(r2

25262728−−−

××× = 11

225

x = 3 –1 = 2

2r – 4

383


ANSWERS

⇒ 225

2526272811 ××××

= 11 × 28 × 3 × 26 = 11 × 7 × 4 × 3 × 13 × 2 = 11 × 12 × 13 × 14 = 14 × 13 × 12 × 11

∴ 2r = 14

r = 7 Ans. (b) 169. Let in the number unit's digit = x and ten's digit = y

∴ Number = 10y + x

According to the given conditions of the problem, 8 (x+y) + 1 = 10y + x (or) 8x + 8y + 1 = 10y + x

⇒

⇒

⇒ → (2)

→ (3)

y = 4 Put y = 4 in (1), we get 7x = 7 x = 1 Hence, the required number is 41 Ans. (b)

2r (2r – 1) (2r – 2) (2r – 3) =

8x – x + 8y – 10y + 1 = 0

7x – 2y + 1 = 0 → (1)

and 13 (y – x) + 2 = 10y + x 13y – 13x + 2 = 10y + x

x + 13x + 10y – 13y – 2 = 0

14x – 3y – 2 = 0

(1) × 2 ⇒ 14x – 4y + 2 = 0

(2) – (3) ⇒ y – 4 = 0

7x – 8 + 1 = 0

384


170. We want to find out the number of combination of 12 things taken 3 at a time and this is by:

3C12 =

)!312(!3!12−

= !9!3

!9101112!9!3

!12 ×××=

= 23

101112×

××

= 220 Ans. (c)

172. 9x

lt→ 9x

3x−− =

9xlt→ 3x

13x3x

+−−

App lt = 61

331 =+

Ans. (a) 61

173. 9x

lt→ 0x

a20x−−+ ⇒

9xlt→ 0x

a2ax−−+ × ( )

( )a2axa2ax

++−+

⇒ 9x

lt→ ( )a2ax)ax(

a2ax++−

−+ = ax

lt→ ( )a2ax)ax(

)ax(++−

−

App lt

( )a2aa1++

= a22

1

Ans. (b) a22

1

174. ∞→x

lt 2

2

x15x4x56

++ ⇒

∞→xlt x2

⎟⎠

⎞⎜⎝

⎛ +

⎟⎠

⎞⎜⎝

⎛ +

x415x

x65

2

2

App lt.

⇒ 01505

++ =

31

Ans. (c) 31

385


ANSWERS

175. ∞→x

lt 2xbxa − ⇒

∞→xlt ⎟

⎠

⎞⎜⎝

⎛ −xb

xa2

App lt.

⇒ (0 … 0) = 0

Ans.(a) 0

xx

xx

eeee

−

−

+− ⇒

dxdy = 2xx

xxxxxxxx

)ee(

)ee(dxd).ee()ee(

dxd)ee(

−

−−−−

+

+−−−+

= 2xx

xxxxxxxx

)ee()ee)(ee()ee)(ee(

−

−−−−

+−−−++

= 2xx

x2x2x2x2

)ee(2ee2ee

−

−−

++−−++ = 2xx )ee(

4−+

Ans. (b) 2xx )ee(4

−+

177. y = 2)x1(x

+⇒

dxdy = 4

22

)x1(

)x1(dxdxx

dxd)x1(

+

+−+

⇒ 4

2

)x1()x1(2.x1.)x1(

++−+ = 4

22

)x1(x2x2x2x1

+−−++

= 4

2

)x1(x1

+− = 3)x1(

x1+−

Ans. (b) 3)x1(x1

+−

178. y = xx +

)xx(dxd.t

dtd

dxdy 2/1 +=

= ⎟⎟⎠

⎞⎜⎜⎝

⎛ +⎟⎠⎞⎜

⎝⎛ + x2

11.xx2

1

176. y =

386


= xxx4

1x2

+

+

Ans. (a) xxx4

1x2

+

+

179. y = x2x27 +

)x2x(dxd.7

dtd

dxdy 2t +=

= x2x27 + .log 7. (2x+2)

7log.7).1x(2dxdy 2x2 ++=

Ans. (b) 7log.7).1x(2 2x2 ++

180. y = log ⎟⎠⎞

⎜⎝⎛ ++ 22 axx

⎟⎠⎞

⎜⎝⎛ ++= 22 axx

dxd.tlog

dtd

dxdy

= ⎥⎥⎦

⎤

⎢⎢⎣

⎡

++

++x2.

ax2

11.axx

12222

= ⎟⎠⎞

⎜⎝⎛ +++

⎟⎠⎞

⎜⎝⎛ ++

2222

22

axxax

xax

22 ax

1dxdy

+=

Ans. (a) 22 ax

1

+

181. Given ( ) aeyx yxx

=− −


387


ANSWERS

( )( ) ( )

( )0

dxdy1e

yxdxdy1.x1yx

e.yx yxx

2yx

x

=⎟⎠

⎞⎜⎝

⎛ −+

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−

⎟⎠

⎞⎜⎝

⎛ −−−− −−

( ) 0dxdy1

yxdxdyxxyx

e yxx

=⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−+−

+−−−

( ) 0dxdy1

yxdxdyxy

=−+−

+−

0dxdy1

dxdy

yxx

yxy =−+

−+

−−

1yx

y1yx

xdxdy −

−=⎥

⎦

⎤⎢⎣

⎡−

−

yx

yxyyx

yxxdxdy

−+−=⎥

⎦

⎤⎢⎣

⎡

−+−

yxxy2

yxy

dxdy

−−=⎥

⎦

⎤⎢⎣

⎡

−

y

xy2dxdy −=

∴ xy

xy2yxdxdyy +⎥

⎦

⎤⎢⎣

⎡ −=+

=

y2xdxdyy =+

Ans. (c)

182. Given demand law x = 2p10 −

x = 2/12 )p10( −

)p2()p10(21

dpdx 2

12 −−=

2y – x + x

−1

388


2p102

)p2(1

−

−

2p10

pdpdx

−

−=

dpdx.

xped =

= 22/1

p102

p.)p10(

p

−

−−

when p = 2

62.

62ed −=

32ed =

Ans. (a) Alternate

183. ∫ +∴ dx

1xx3

= dx1x

11xx3∫ ⎟

⎠

⎞⎜⎝

⎛

+−+−

= 2x

3x 23

−

184. dxe

eex3

x2x4

∫ ⎟⎟⎠

⎞⎜⎜⎝

⎛ +

= dxee

ee

x3

x2

x3

x4

∫ ⎟⎟⎠

⎞⎜⎜⎝

⎛+

= ∫ ∫−+ dxedxe xx

x

ed = – 2/3

+x – log(x+1) + c

= e – e + c –x

Ans. (b)

Ans. (c)

389


ANSWERS

185. dx1x

21xdx1x1x

22

2

4

∫∫ ⎟⎠

⎞⎜⎝

⎛

++−=

++

= ∫ ∫ ∫ ++−

1x12dxdxx 2

2 dx

3x3

x + c

186. Let I = ∫ + dx)1x(log

∴ I = ∫ + dx1).1x(log

Integrating by parts [Here log (x+1) is to be taken as first function and unity as second function) [d/dx (log (x+1)] + integral of '1']

∫ +dxx.

1x1

= ∫ +−+ dx1x

11x

∫ ⎟⎠

⎞⎜⎝

⎛

+− dx

1x11

=

187. Consider )x1(xx1x

x1x1

+−+−=

++

= xx1 −+

∴ I = ∫ ++ x1xdx

= ∫∫ −+ dxxdxx1

1 2

I1 = ∫ + dxx1

= – x + 2 tan –1

Ans. (c)

I = [log (x+1] integral of '1' – integral of

= log (x+1).x –

x log (x+1) –

= x log(x+1) –

I = x log (x+1) – x + log (x+1) +c x log (x+1) – [x – log (x+1)]

I = I – I

390


dz = dx

∴ I1 = ∫∫ dzz

= 2/3z32

= 2/3)x1(32 +

∴ I = 2/3 (1+x) 3/2

2/3x 2/3

+ c

I = 2/3 ( ){ } cxx1 2/32/3 +−+

188. Consider )2xx(xx2xx 223 −+=−+

= )2xx2x(x 2 −−+

=

∴ We may write )2x()1x(x

2xxx2xx

2xx 2

23

2

+−+−=

−++−

Let 2x

C1x

BxA

)2x()1x(x2xx2

++

−+=

+−+−

(or) x2

Substituting x = 1, We find 2 = 3B B = 2/3 i.e. C = 4/3

∴ I = ∫ ∫ ∫ ∫ ++

−+−=

−++−

2xdx

34

1xdx

32

xdxdx

x2xx2xx

23

2

Ans. (c)

–

x (x – 1) (x + 2) = x {x(x+2) – (x+2)}

Substituting x = – 2, We find 8 = 6c

Substituting x = 0, We find 2 = – 2A A = – 1

I = – log x + 2/3 log (x – 1) + 4/3 log (x+2) + log c

1+ x dx =

Let z = 1 + x

− x + 2 = A(x −1) (x + 2) + Bx(x + 2) + Cx(x −1)

391


ANSWERS

189. Let I = ∫ −+dx

10x13x31

2

= ∫−+

dx

310

3x13x

131

2

= ∫−⎟

⎠

⎞⎜⎝

⎛−⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠

⎞⎜⎝

⎛++

dx

310

613

613x

613.2x

131

222

= ( )∫

−+dx

362896/13x

131

2

Let t = x+13/6

∴ dt = dx

∴ I = 1/3 ∫ −dt

)6/17(t1

22

= ( ) ⎥⎦

⎤⎢⎣

⎡

+−

6/17t6/17tlog

6/1721.

31

= ⎥⎦

⎤⎢⎣

⎡

+−

17t617t6log

171

=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

+⎟⎠

⎞⎜⎝

⎛ +

−+

176

13x6

17)6/13x(6log171

= c15x32x3log

171 +⎥

⎦

⎤⎢⎣

⎡

+−

Ans. (b)

190. ( ){ }∫ ′+ dx)x(fxfe x

By the method of integration by parts, we may write

( ) ( )∫ ∫ ∫ ∫ ⎭⎬⎫

⎩⎨⎧−= dxdxex)x(f

dxddxexfdxxfe xx

= ( ) ∫ ′− dx)x(fexfe xx

392


Transposing ( )∫ ∫ =′+ xfedx)x(fedx)x(fe xxx

(or) { } ( )∫ =′+ xfedx)x(f)x(fe xx

191. ∫b

a

dxx

xlog Let log x = t x = a, t = log a

dxdt

x1 = x = b, t = log b

∫alog

blog.dt.t ⇒

blog

alog

2

2t⎥⎥⎦

⎤

⎢⎢⎣

⎡

⇒ 21 ( ) ( )[ ]22 alogblog − ⇒

21 ⎥

⎦

⎤⎢⎣

⎡⎟⎠

⎞⎜⎝

⎛

ablog).ablog(

Ans. (a) 21 ⎥

⎦

⎤⎢⎣

⎡⎟⎠

⎞⎜⎝

⎛

ablog).ablog(

192. [ ] [ ] dx)x(g)x(g)x(f)x(f −−−+∫

⇒ [ ]dx)x(g)x(g.0∫ −− ⇒ 0

Ans. (a) 0

193. ∫ −+

b

a3/2)xba(

dx Let x = a, t = b

dxdt x = b, t = a

∫−

a

b

3/2 dtt ⇒ ∫−

b

a

3/2t dt

⇒ [ ]ba

3/1t3 ⇒ [ ]3/13/1 ab3 −

Ans. (a) [ ]3/13/1 ab.3 −

194. I = ∫ −+

2

0

dxx2x

x

I = ∫ +−−2

0 xx2x2

a + b – x = t

– 1 =

⇒ –

... (i)

... (ii) [f(x) = f(a − x)]

393


ANSWERS

2I = 2]x[dx 20

2

0

==∫

∴ I = 1221 =×

Ans. (a) 1

195. I = ∫ ⎟⎠

⎞⎜⎝

⎛ −1

0

dx1x1log ⇒ ∫ ⎟

⎠

⎞⎜⎝

⎛ −1

0 xx1log

I = ∫ ⎟⎠

⎞⎜⎝

⎛

−+−1

0

dxx1

x11log )]xa(f)x(f[ −=

I = ∫ −

1

0 x1xlog dx

xx1log

1

0∫ ⎟

⎠

⎞⎜⎝

⎛ −

2I = 0 ∴ I = 0

Ans. (c) 0 196. No. of ways in which 7 dept distributed among 3 minister

= ( ) !3x47()147 2CCCC 333××+××

= (120 + 330) × 6 = 1980 Ans. (d) None of these 197. No. of selections of letters

(i) 2 like and 1 different = 6232311 CC =×=×

(ii) 3 different = 3C5 = 10

∴ Total no. of ways of selection letters = 16

∴ Total words = 16×3! = 96 words.

Ans. (b) 96 198. No. of ways to form three digit nos. Ans. (b) 42

199. 1n2nn S.2SS −− −+ = ]d)1n(a2[2n −+ +

22n −

21n −

dx ... (i)

... (ii) ⇒ −

by using (1, 2, 3, 4, 3, 2) are – 42.

[2a+(n – 2 – 1)d]

…2. [2a + (n – 1 – 1)d]

394


2n

22n⎟⎠

⎞⎜⎝

⎛ −

= an + )1n(a2d2

)2n()3n()2n(ad2

n)1n( −−−−+−+− d)2n()1n( −−

= d ⎥⎦

⎤⎢⎣

⎡ −−−−−+− )2n()1n(2

)2n)(3n(n2

)1n(

d⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ +−−+−+−2

n64n26n5nnn 2222

= d2d2 =

Ans. (a) d

200. 31

)1n(A3A =−

31

d)1n(ad3a =

−++

∴ d = 10n

6−

∴ 10n

6−

28 = (n+1) 10n

6−

∴ n = 13

Ans. (c) 13

Model Test Paper – BOS/CPT – 8 / 2007 151. The first no. divide by 8 between 100 and 200 is 104 The last no. divide by 8 between 100 and 200 is 200

∴ The total number divide by 104 and 200 is 13.

All number divide by 8 also divide by 2 is 13 Ans. (b) 152. Sum of 1st n odd number

= [2a+(n – 1)d] + [2a + (n − 3)d] – (n −1)[2a + (n − 2)d]

⇒ (3+3 d) 3 = 3 + (n – 1)d

7n = a + (N…1) d ⇒ 31 = 3+ (n + 2 – 1)

395

−


ANSWERS

S =

Since S = [ ]d)1n(a22n −+

= n(n) S = n2

Ans. (a) 153. Let the number be x. According to the given condition of the problem is 36x = x + 1050 36x = 1050

x = 35

1050

x = 30 Ans. (b)

154. The formula is 2

3333

2)1n(nn........321⎭⎬⎫

⎩⎨⎧ +=++++

∴ 2

3333

2)112(1212........321⎭⎬⎫

⎩⎨⎧ +=++++

= [ ] 2)13(6

= [ ] 608478 2 =

Ans. (c) 155. Let S = 1+9+24+46+75+........+t n shifting 1 places to the right in the RHS S = 1+9+24+46+75+...........t n-1+tn subtracting term by term, 0=1+8+15+22+29+............+(t n-tn-1 ) - tn Transposing tn = 1+8+15+22+29+ ............ to nth term

1+3+5+ ... + (2n – 1)

S = n/2 [2.1 + (n – 1)2] = n (1+n – 1)

396


2n

= n25n

27 2 −

Now Sn = ∑∑∑ −= n25n

27tn 2

= 2

)1n(n25

6)1n2)(1n(n

27 +−++

= ⎭⎬⎫

⎩⎨⎧ −++

25)1n2(

67

2)1n(n

= ⎟⎠

⎞⎜⎝

⎛ −+34n

37

2)1n(n

Sn = 6

)4n7)(1n(n −+

156. Let the number to be added be x then according to the problem.

31

x263x83 =

++ '

3(83+x) = 263 + x 249 + 3x = 263 + x 2x = 14

x = 2

14 = 7

Hence the required number is 7 Ans. (c) 157. Initially, let the number of employees be 9 and wages per head be Rs. 14. Then, total

wages bill = Rs. (9×14) = Rs. 126 Further, the number of employees becomes 8 and the wages per head becomes Rs. 15.

∴ Now total wages bill = Rs. (8×15) = Rs. 120

∴ Ratio of the wages bill = 126:120

= 21:20 Thus the wages bill is decreased in the ratio 21:20 Ans. (c)

= {2.1+(n – 1)7}

3x – x = 263 – 249

397


ANSWERS

158. Let C gets Rs. = x Given B = ¼ of C = ¼ (x)

and A = 32 of B = 2/3 (¼x) =

61 x

Also, given 680xx41x

61 =++

68012

x12x3x2 =++

68012

x17 =

x = 48017

12680 =×

Ans. (c) 159. Let us assume that when x is added to each of the four given numbers, they become in

proportion.

⇒ 10 + x : 18 + x = 22 + x : 38 + x

∴ Product of the means = Product of the extremes.

∴ (10+x) (38+x) = (18+x) (22+x)

⇒ 380+48x + x 2 =396 + 40x + x2

8x = 16 x = 2 Required number = 2 Ans. (a) 160. Let the required numbers be x and y. Since the mean proportional between a and c is

given by the relation acb =

∴ Mean proportional = xy


xy = 24

xy = 576 → (1)

Again suppose that the third proportional to x and y is z. Then x : y = y : z

398


⇒ x : z = y : y

xz = y2

⇒ z = x

y2


x

y2 = 192

⇒ y2 =192 x → (2)

From equation (2), 192yx

2

=

Putting this value of x in equation (1)

192y2

.y = 576

y3 = 576×192 = 24 × 24 × 24 × 8 = 24 × 24 × 24 × 2 × 2 × 2 y = (24 × 24 × 24 × 2 × 2 × 2 × 2) 1/3

= 24 × 2 y = 48

(1) ⇒ xy = 576

x (48) = 576

x = 48

576 = 8

Hence the required number are 12 and 48.

161. 0x

lt→

x

2ee xx −+ − ⇒

⎥⎥⎦

⎤

⎢⎢⎣

⎡ −+−−

x1e(

xe x1x

⇒ 0x

lt→

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ −+⎟⎟⎠

⎞⎜⎜⎝

⎛ − −

x1e

x1e xx

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

=−→

1x

1eltx

0x

Ans. (b) 0

1 – 1 = 0

399


ANSWERS

162. 0x

lt→

1e1e

1

1

x

x

+

−−

−

⇒ 0x

lt→

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+−

1e1e

x/1

x/1

RHL +→0x

lt ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+−

1e1e

x/1

x/1 App lt. =

∞∞

→ RHL does not exist

LHL −→0x

lt⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+−

1e1e

x/1

x/1 App lt.

∞∞

LHL does not exist.

→ lt does not exist in f(x)

Ans. (c) does not exist

163. 0x

lt→

|x|5x7

|x|x3−−

RHL +→0x

ltx5x7

xx3−− =

x2x2 = 1

LHL −→0x

lt)x(5x7

)x(x3−−−− =

31

x12x4 =

LHL ≠ RHS

∴ f(x) does not exist at x = 0

Ans. (c) does not exist

164. 0x

lt→ x

ee bxax −⇒

0xlt→

( ) ( )⎥⎥⎦

⎤

⎢⎢⎣

⎡ −−−bx

1ebax

1e.abxax

⇒ ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

=−→

1x

1eltx

0x

Ans. (a) a … b

165. 0x

lt→ )x1(log

1e x

+− ⇒

0xlt→

⎥⎥⎦

⎤

⎢⎢⎣

⎡

+⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −)x1(log

x.x

1e x

⇒ 0x

lt→

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −x

1e x .

0xlt→

x)x1(log

1+

⇒ 1.1 = 1

a.1 – b.1 ⇒ a – b

Ans. (b) 1

400


166. Given y = x1x1

+−

( ) ( ) ( ) ( )

( )2x1

x1dxdx1x1

dxdx1

dxdy

+

+−−−+=

= ( ) ( ) ( ) ( )

)x1(

x121x1)1(x1

21x1 1

211

21

+

⎥⎦

⎤⎢⎣

⎡ +−−⎥⎦

⎤⎢⎣

−−+ −−

= )x1(

x1x1

21

x1x1

21

++−−

−+−

= ⎥⎦

⎤⎢⎣

⎡ ++−−++−

1)x1(.

x1x1)x1()x1(

21

( ) ( )x1x11

1x1.

x1x12

21

dxdy

2/3 −+−=⎥

⎦

⎤⎢⎣

⎡ ++−

−=

Ans. (b)

2x1

x

+

( ) ( )

22

22

x1

x2x12

1.x1x1

dxdy

⎟⎠⎞

⎜⎝⎛ +

+−+

=

= ( )2

2

22

x1x1

xx1

++

−+

= ( )( ) ⎟

⎠⎞

⎜⎝⎛ ++

−+22

22

x1x1

xx1

( ) 2

32x1

1dxdy

+=

167. Given y =

⎡

401


ANSWERS

∴ ( )

3

223

2

33

x1

x

x1

xdxdyx

⎥⎥⎦

⎤

⎢⎢⎣

⎡

+=

+=

[ ]33 ydxdyx =

Ans. (c)

168. Given 4xy ex −=


log ( )yx = log ( )yxe −

y (1 + log x) = x

y = xlog1

x+

Differentiate on both sides

( )2xlog1

x1x1).xlog1(

dxdy

+

⎟⎠

⎞⎜⎝

⎛−+=

= ( ) ( )22 xlog1

xlogxlog1

1log1+

=+

−+

Ans. (a)

169. Given ( )853 yxxy += → (1)


( ) ( ) ⎥⎦

⎤⎢⎣

⎡ ++=+dxdy1yx8

dxdyy3.xx5y 72543

( ) ( )dxdyyx8yx8

dxdyyx3xy5 772543 +++=+

( )[ ] ( ) 437725 xy5yx88yx3dxdy −+=−

y log x = (x – y) log e y log x = x – y

x + y

402


( )( )725

437

yx8yx3xy5yx8

dxdy

+−−+= =

( ) ( )

( ) ( )78

87

yx8yxy3

xyx5yx8

+−+

+−+ Using equation (1)

= ( ) ( )

( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−++

⎥⎦

⎤⎢⎣

⎡ +−+

8yxy3yx

yxx58yx

7

7

= ( )[ ]( )[ ]y8yx3x

yx5x8y−++− = [ ]

[ ]y8y3x3xy5x5x8y

−+−−

= [ ][ ] x

yy5x3xy5x3y =

−−

Ans. (a)

170. Given y = ∞.....xxx

i.e. yxy =


log y = log ( )yx

log y = y log x Differentiate on both sides

dxdy.xlog

x1.y

dxdy

y1 +=

xyxlog

y1

dxdy =⎥

⎦

⎤⎢⎣

⎡−

xy

yxlogy1

dxdy =⎥

⎦

⎤⎢⎣

⎡ −

( )xlogy1xy

dxdy 2

−=

∴ x. xlogy1

ydxdy 2

−=

Ans. (b)

403


ANSWERS

171. ∫−

−1

1

xx dx)ee( = ∫−1

1dx)0(

= 0 Ans. (b) 0

172. ∫+e

1 xxlog1 dx

Let 1 + log x = t x = 0, t = 1

dxdt

x1 = x = e, t = 2

= ∫ ⎥⎦

⎤⎢⎣

⎡=+

2

1

2

1

2

2tdt

23

21 =

Ans. (a) 23

173. ∫ +

3log

0x dx

e1ex If 1 + e x = t x = 0, t = 2

xe = dxdt x = log3, t = 4

∫ −

4

2

dtt

1 = 42]t[log

= log 2 Ans. (b) log 2

174. ∫++

1

02x11

x let (1 + x 2) = t2 x = 0, t = 1

2t1x ==

2x = 2t dxdt ⇒ dx =

xt dx

∫ ∫ ⎟⎠

⎞⎜⎝

⎛

+−=

+

2

1

2

1

dtt1

11t1

dtt

= 2 –

⇒ log 4 – log 2

404


= ( )[ ] 21t1logt +−

= ( ) ( )[ ]1log21log12 −+−−

= ( ) ( ) 021log12 ++−−

= ( ) ( )21log12 +−−


175. ∫ ++

1

0 )x2()x1(dx

⇒ ∫ ⎟⎠

⎞⎜⎝

⎛

+−

+

1

0

dxx2

1x1

1

⇒ ( ) ( )[ ]10x2logx1log +−+ ⇒ 1

0x2x1log ⎥⎦

⎤⎢⎣

⎡

++

⇒ log 32

Ans. (a) log 32

176. a + ar = 15

a = ar + ar 2 + ar 3

r1ar−

∴ a = 3

215 × = 10

2/11

10r1

a−

=−

= 20

Ans. (a) 20

177. a = x1

1−

⇒ =a1

b = y1

1−

⇒ b1

∴ y1x1b1

a1 −+−=+

Ans. (c) 1

– ∞

a = ⇒ 1– r = r ⇒ r = 1/2

⇒ a (1+ r) = 15

∴ Sum of Series =

1 – x

= 1 – y

⇒ 2 – (x+y) = 2.1 = 1

405


ANSWERS

178. 90 = 2000 × 43

100R ×

∴ R = 6%

Ans. (b) 6%

179. 216 = 5400 × n100

6 ×

n = 4/6 yrs. = 8 months Ans. (b) 8 months

180. I1 = 10000 R2002100R =×

I2 = 6000 × R18003100R =×

I1 + I2 = 1900 ⇒ 200R + 180R = 1900

∴ 380R = 1900 ∴ R = 5%

Ans. (b) 5% 181.If all the observation are equal. Then standard deviation = 0 Ans. (a) 0 182. If every item is increased by 5 then mean ( x ) also increased by 5, but the value of

∑ − 2)xx( remain same.

∴ Standard deviation will remain same,

Standard deviation = 10

183. S.D. = N

d2∑ = 10360 = 6

Coefficient of variation = 100 AmSDx

= 1540

6100 =×

Ans. (a) 15

Ans. (c) – 10

406


184. Coefficient of M.D. = 100Am

D.M ×

44 = AM

10077.5 ×

A.M. = 13.11 Ans. 13.11 185. The S.D. of two values is equal to half their difference.

S.D. = 2

ba −

The Statement is correct Ans. (a) True 186. Computation of Correlation Coefficient

x y xy x2 y2

50 50

40 40

2000 2000

2500 2500

1600 1600

Total 100 80 4000 5000 3200

402

80y,502

100x ====

Cov (x, y) = 2

4000

∴ r = 0

Ans. (c)

187. Given ∑ == 55di,32r 2

R

∴ ( )1nn

dib1r 2

2

R −−= ∑

( )( )1nn

556132

2 −−=

( )1nn3301

32

2 −−=−

( )1nn330

31

2 −−=−

– (50) (40) = 0

407


ANSWERS

( )1nn 2 − = 990 = 10 ( )110 2 −

∴ n = 10 as n must a positive

Ans. (a)

188. Let us assume that 4x + 3y + 7 = 0 → (1)

represent the regression line of x on y and 3x + 4y + 8 = 0 → (2) represent the regression line of y on x.

(1)

47

43 y

∴ bxy = 43

(2)

43

∴ byx = 43

∴ 2r = byx. bxy = 169

43

43 =⎟

⎠

⎞⎜⎝

⎛−⎟⎠

⎞⎜⎝

⎛−

∴ r = 75.043

43

169 −=−=±=

(We take the sign of n as negative since both the regression coefficient are negative). Ans. (c) 189. Ans. (d) Refer Properties

190. Given byx = 1.2 → (1)

2100xU −=

⇒ x = 100 + 2U

⇒ x = 100 + 2 U

and v = 3200y −

⇒ y = 200 + 3 v

⇒ y = 200 + 3 v

4x = –7 – 3y

x = – –

–

4y = – 8 – 3x

y = –2 x–

–

408


2)xx(E

)yy()xx(byx

−

−−= ∑

( ) ( )[ ]

[ ]∑∑

−

−−= 2)UU(2

vv3.UU2

= ( ) ( )∑

∑−

−−×2)UU(

VVUU4

32

= 3/2 bvu

⇒ bvu = 2/3 byx = 2/3 × 1.2 = 0.8

Ans. (b) 191. Let A, is First bag is selected A2 is second bag is selected. B: In a draw of 2 balls, one is red and the other is black. The required probability

P = P(A1 ∩ B) + P (A 2 ∩ B)

= P(A1) P (B/A 1) + P (A 2). P(B/A 2) Since there are two bags, the selection of each being equally likely.

∴ P(A 1) = P(A 2) = 1/2

P(B/A 1) = Probability of drawing one red and one black ball in a draw of 2 balls from the 1st bag

= 2815

C8C3C5

2

11 =×

P(B/A 2) = Probability of drawing one red and one black ball in a draw of 2 balls from the 2nd bags.

= 95

C9C5C4

2

11 =×

(1) ⇒ p = 1/2 × 95

21

2815 ×+

p. = 504275

504140135

185

5615 =+=+

Ans. (a)

409


ANSWERS

192. Let A1 is first purse is selected. A2 is second purse is selected. Let B: In a draw of one coin, one coin must be silver The required probabilities.

P = P ( )BA1 ∩ + P ( )BA2 ∩

= )A/B(P).A(P)A/B(P.)A(P 2211 + → (1)

Since there are two purse, the selection of each being equally likely

∴ 21)A(P,

21)A(P 21 ==

)A/B(P 1 = Probability of drawing one silver coin from the first purse.

= 7/3C7C3

1

1 =

)A/B(P 2 = Probability of drawing one silver coin from the second purse.

= 74

C7C4

1

1 =

Substituting (1) ⇒ p=1/2 ⎟⎠

⎞⎜⎝

⎛+⎟⎠

⎞⎜⎝

⎛

74

21

73

= 21

147

144

143 ==+

Ans. (a) 193. When two tosses of unbiased dice the total sample space. S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6) (2,1), (2,2), (2,3), (2,4), (2,5), (2,6) (3,1), (3,2), (3,3), (3,4), (3,5), (3,6) (4,1), (4,2), (4,3), (4,4), (4,5), (4,6) (5,1), (5,2), (5,3), (5,4), (5,5), (5,6) (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)} n(s) = 36 In the above sample space, let x be the number of sines getting from the experiment. Let x = 0, means no sin. = number of times = 25 x = 1, means no sin. = number of times = 10

410


x = 2, means no sin. = number of times = 01 36

∴ Expected table is:

x 0 1 2 p(x) 25 10 1

∴ The required probability = Mean = Expected Value

= ∑ )s(n)x(px

= 36

12101250 ×+×+×

= 31

3612 =

Ans. (a) 194. The experiment of throwing three dice is theoretically same as that of throwing a die

thrice. Let E be the event of throwing six in a throw of die. ∴ P(E) = 1/6 and P ( E

Let x denotes the random variable "number of Sixes". ∴ The possible values of x are 0, 1, 2, 3 ∴ P(x=2) = P(E 1E2 E 3 or E 1 E 2E3 or E 1E2E3)

= P(E 1) . P(E 2) P( E 3) + P(E 1) P( E 2) P(E 3)+ P( E 1)+ P(E 2) P(E 3)

= 61.

61.

65

61.

65.

61

65.

61.

61 ++

P(x=2) = 21615

Ans. (c) 195. let A and B denote the events that the Chartered Accountant is selected in firms X and Y

respectively. Then in the usual notations, we are given. P(A) = 0.7

P(

P( B ) = 0.5

) = 1 – P(E)

= 1–1/6 = 5/6

A ) = 1– P(A) = 1=0.7=0.3

411


ANSWERS

∴

and P ( )BA∪ = 0.6

( )BA∩ = BA∪

∴ P ( )BA∪ = 1 P ( )BA∩

= 1 P ( )BA∪

= 1 0.6 = 0.4 The probability that the Chartered Accountant will be selected in one of the two firms X or

Y is given by:

( )BA∩

= = 0.8 Ans. (a)

196. ∫⎥⎥⎦

⎤

⎢⎢⎣

⎡+ dx

)x(log1)x(loglog 2

I = log (log x) [ ]∫∫ ⎥⎦

⎤⎢⎣

⎡− dxx.)x(loglogdxddx + ∫ 2)x(log

1 = dx

∫ )x(log1 .dx + ∫ 2)x(log

1 dx

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+∫ dx

xx.

)x(log1dx

)x(log1

2 + ( )∫ = dx

xlog1

2

xlog

x∫ 2)x(log

1 + ∫ dx)x(log

12

⇒ x. log (log x) cxlog

x +

Ans. (a) x. log (log x) cxlog

x +−

∴ This is Equivalence Relation.

P(B) = 1 – P(B) = 1 – 0.5 = 0.5

By De – Morgan's law

–

–

–

P (AUB) = P(A) + P(B) – P

0.7 + 0.5 – 0.4

= log (log x).x –

x. log (log x) –

⇒ x log (log x) – –

−

Ans. (d) Equivalence Relation.

412

197. 'is equal to' Satisfies Reflexive, Symmetric and transitive Relation


198. f(x) = x2+2

∴ 2)x()x(f 2 +−=−

= 2x2 +

∴ f(x) is even function

Ans. (b) even function.

199. f(x) = x112 + = 12.12 x 0 < x < 9 Range = 12×12°, 12×12 1 9

∴ Range = 12 < f(x) < 12 10

Ans. (a) 1012)x(f12 ≤≤

200. 'Is greater than' over the set of real number is not satisfied Reflexive and Symmetric

Ans. (a) Transitive relation.


151. Given 2317

yxx =+

⇒ 23x = 17x + 17y

6x = 17y

y6

17x =

Now, yy

617

yy6

17

yxyx

−

+=

−+

= y6y17

66

y6y17−

×+

f(– x) = f(x)

.....12×12

relation it only satisfied transitive Relat ion

23x – 17x = 17y

413


ANSWERS

= 1123

y11y23 =

∴ 1123

yxyx =

−+

152. Given 12x1

144251 +=+

Squaring on both sides:

2

12x1

144251 ⎟

⎠

⎞⎜⎝

⎛ +=+

12

x2144x1

14425144 2

++=+

144

x24x144144169 2 ++=

∴ 025x24x2 =−+

( ) ( ) 01x25x =−+

1x,25x =−=

x = 1 ( ∴ negative neglected)

Ans. (a)

153. Given ( ) ( ) n83 224 =×

i.e. ( ) n

8

21

32 2)2()2( =⎟⎟

⎠

⎞

⎜⎜

⎝

⎛×

n46 222 =×

n10 22 =

∴ n = 10

Ans. (a) 154. Let total number of men went to a hotel = x Given, A man Spent Rupees = Total number of men = x

∴ Given Data = x + x = 15625

414


2x = 15625

12515625x ==

Ans. (b)

155. Given A + B + C = 1000 → (1)

A + C = 400 → (2)

B + C = 700 → (3)

(2) ⇒

(3) ⇒

(1) ⇒

C = 100 Ans. (a)

156. Given log ⎟⎠

⎞⎜⎝

⎛ −2

ba = 1/2 (log a + log b)

∴ 2 log 2

ba − = log a + log b

log 2

2ba⎟⎠

⎞⎜⎝

⎛ − = log ab

⇒ 2

2ba⎟⎠

⎞⎜⎝

⎛ − = ab

2

4ba⎟⎠

⎞⎜⎝

⎛ − = ab

2

ab4ab2ba 22 =−+

ab6ba 22 =+

Ans. (a)

157. Given xlog10 = 4

∴ x = 10 4

Ans. (c) x = 10000 158. log 225 = log (9×25) = log 9 + log 25

A = 400 – C

B = 700 – C

400 – C + 700 – C + C = 1000

(a – b) = 4ab

415


ANSWERS

= log 32 + log 5 2 = 2log 3 + 2 log 5 = 2log 3 + 2 log 10/2 = = log 225 = 2.352

159. Let 2100 = x Taking log on both sides. log 2100 = log x 100 log 2 = log x log x = 100 × 0.3010 log x = 30.1000

∴ the no. of digits in 2 100 is 31

Ans. (b)

160. Given nP3 = 60!)3n(

!n =−

∴ n = 5

Ans. (c)

161. 0x

lt→

x

2ba xx −+ ⇒ 0x

lt→

x

)1b()1a( xx −+−

⇒ 0x

lt→

x

1a x − + 0x

lt→

x

1b x − ⎥⎥⎦

⎤

⎢⎢⎣

⎡=−

→

ae

x

0xlog

x1alt

App lt. = log a + log b = log (ab) Ans. (a) log (ab)

162. 0x

lt→

x

12510 xxx +−−

⇒ 0x

lt→

⎥⎥⎦

⎤

⎢⎢⎣

⎡ −−−−−x

)12(x

)15(x

)110( xxx

⎭⎬⎫

⎩⎨⎧

=−→

ae

x

0xlog

x1alt

2log 3 + 2 log 10 – 2 log 2 2 × 0.477 + 2 – 2 (0.301)

Ans. (a)

∴ n(n – 1) (n – 2) = 60 = 5 × 4 × 3

416


App lt. =

= log ⎟⎠

⎞⎜⎝

⎛

×2510 = log 1 ⇒ 0

Ans. (b) 0

163. 0x

lt→

2

xxx

x12510 −−− ⇒

0xlt→

2

xxxx

x]12525[ −−−× = 2

xxx

x)12(1)12(5 −−−

0x

lt→

2

xx

x)15)(12( −− ⇒

0xlt→

x

)12( x − × 0x

lt→

x

)15( x −

⇒ log 2 × log 5

Ans. (a) log 5 × log 2

164. 0x

lt→

x

1eee x2x3x5 +−−

⇒ 0x

lt→

⎥⎥⎦

⎤

⎢⎢⎣

⎡ −−−−−x

x2

x

x3x5

2)1e(2

3)1e(.3

x5)1e(5

App lt.

= ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

=−→

1x

1eltx

0x

Ans. (b) 0

165. 0x

lt→

2

x2x3x5

x1eee −−− =

0xlt→

2

x2x3x2x3

x)1eee.e( −−−

0x

lt→

[ ]2

x2x2x3

x)1e(1)1e(e −−−

⇒ 0x

lt→

[ ]2

x2x3

x)1e()1e( −−

0x

lt→

⎟⎟⎠

⎞⎜⎜⎝

⎛ −x

1e x3

× 0x

lt→

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −x

1e x2

App lt. 3 × 2 = 6 Ans. (a) 6

log 10 – log 5 – log 2

5.1 – 3.1 – 2.1

5 – 3 – 2 = 0

417


ANSWERS

166. Given ∫+

dxax

122

Let xzax 22 −=+

∴ z = x + 22 ax +

( ) dxx2ax2

11dxdz

22 ++=

= 2222

22

ax

z

ax

xax

+=

+

++

∴ 22 ax

dxz

dz

+=

∴ ∫ ∫ +==+

czlogz

dz

ax

dx22

= caxxlog 22 +⎟⎠⎞

⎜⎝⎛ ++

167. ∫−

dxax

122

Let xzax 22 −=−

∴ z = x + 22 ax −

dxdz = 1 + ( )x2

ax2

122 −

= 1 + 22 ax

x

−

= 22

22

ax

xax

−

+− = 22 ax

z

−

z

dz = 22 ax

dx

−

∴ ∫ ∫ +=−

cdz21dx

ax

122

= log (z) = log caxx 22 +⎟⎠⎞

⎜⎝⎛ −+

Ans. (c)

418


168. Let t = 3x

∴ dt = 3 dx

∴ I = ∫ ∫ −=

−dt

1t1

31

3dt

1t1

222

= c1t1tlog1

31 +⎟

⎠

⎞⎜⎝

⎛

+−

= c1x31x3log

61 +⎟

⎠

⎞⎜⎝

⎛

+−

Ans. (b)

169. Let I = ∫+

− dx1x

1x2

∴ I = ∫⎥⎥⎦

⎤

⎢⎢⎣

⎡

+−

+dx

1x

1

1x

x22

= ∫ ∫+

−+

dx1x

1dx1x

x22

1 2

I1 = ∫+

dx1x

x2

Let t = x 2 + 1

∴ dt = 2x dx

∴ I1 = ∫ 2dt

t1

= ∫− dtt

21 2/1

= 1xt2/1

t21 2

2/1+==

I2 = ∫+

dx1x

12

= log ⎟⎠⎞

⎜⎝⎛ ++ 1xx 2

2 +1

I = I – I (say)

419


ANSWERS

∴ 1 2

I = c1xxlog1x 22 +⎟⎠⎞

⎜⎝⎛ ++−+

Ans. (a)

170. Let I = ( )∫ − dxxlogx1 2

∴ I = ∫ − dx)x1(xlog 2

[Here (log x) i s to be take 2) as second function] Integrating by parts:

I = log x ∫ ⎟⎟⎠

⎞⎜⎜⎝

⎛−−⎟

⎟⎠

⎞⎜⎜⎝

⎛− dx

3xx

x1

3xx

33

= ∫ ⎟⎟⎠

⎞⎜⎜⎝

⎛−−⎟

⎟⎠

⎞⎜⎜⎝

⎛− dx

3xxxlogx

3xx

22

= ∫ +⎟⎟⎠

⎞⎜⎜⎝

⎛−−⎟

⎟⎠

⎞⎜⎜⎝

⎛− c

3*3xxxlogx

3x1

32

I = c9

xxxlogx3

x132

+⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−−

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−

Ans. (c) 171. Among 4 doctors, 4 officers and 1 doctor who is also an officer committee of 3 can be

form in such manner.

(i) 1 doctor, 1 officer, 1 doctor who is also officer = 14411 cC ×× = 16

(ii) 142C × =6

(iii) 4C2×1= 6

(iv) 2 doctor and 1 officer = 244412 CC =×

(v) 1 doctor and 2 officer = 244421 CC =×

Total no. of ways = 16 + 6 + 6 + 24 + 24 = 76 Ans. (a) 76 172. Elector can vote for one or more vacancies in such manner …

(i) 1053C =

I = I – I

n as first function and (1 – x

2 doctor and doctor – officer =

2 officer and doctor – officer =

For 3 vacancies –

420


(ii) 1052C =

(iii) 51C =

∴ Total ways = 10 + 10 + 5 = 25

Ans. (c) 25 173. No. of ways in which 12 different thing distributed in 4 groups.

= 4)!3(!12 = 15400

Ans. (a) 15,400 174. Factor of 420 is = {2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 30, 28, 35, 42, 60, 84, 105, 210, 140, 420} No. of factor of 420 = 22 Ans. (b) 22. 175. Five balls are kept in 3 boxes as no box will empty

= ( ) !3345311 ccC ×××

= (5 × 4 × 1) × 6 = 120 ways. Ans. (b) 120 ways.

3 5.1 + 3 4.4 + 3 3 2

∴ a = 35 r =4/3

Sn = ⎟⎠

⎞⎜⎝

⎛ −

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎟

⎠

⎞⎜⎝

⎛

134

134.3

n5

= 35.3 ⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎟

⎠

⎞⎜⎝

⎛ 134 n

= ⎥⎥⎦

⎤

⎢⎢⎣

⎡−1

343 n

n6

Ans. (a) ⎥⎥⎦

⎤

⎢⎢⎣

⎡−1

343 n

n6

177. S8 =5.S 4 ⇒ [ ]1r

1ra 8

−− = [ ]

1r1ra.5 4

−−

⇒ ( )1r 4 + = 5

For 2 vacancies –

For 1 vacancy – 5

176. 243 + 324 + 432 + – n terms .4 + – n terms

421


ANSWERS

r4 = 4 = ( )42

∴ r = ± 2

Ans. (c) ± 2

= ]termsn.....999999[94 +++

= 94

= 94

⎥⎥⎦

⎤

⎢⎢⎣

⎡−

−− n110

)110(10 n ⇒

94

⎥⎥⎦

⎤

⎢⎢⎣

⎡−− n

9)110(10 n

Ans. (a) ⎥⎥⎦

⎤

⎢⎢⎣

⎡−− n

9)110(10

94 n

179. 152

ba =+ and ab = 9 ∴ ab = 81

2

∴ Nos are 27, 3

Ans. (a) 27, 3 180. Product of n Gm between two No. is equal to n th Power of single Gm between two nos.

This statement is correct. Ans. (a) True 181. The weighted arithmetic mean of first a natural numbers whose weights are equal to the

corresponding number is equal to

3

1n2 +

Ans. (a) 3

1n2 +

182. x = )xxx(

xwxwxw

321

332211++++

110 = 15

5w51255100 3 ×+×=×

178. 4+44+444 ... n terms

[(10 – 1)+(100 – 1) + (1000 – 1) + ... n terms)

a = (30 – b) & (30 – b)b = 01

∴ b – 30b + 81 = – 0 ∴ b = 27, 3 and a = 3, 27

422


3

w3 = 5

525 = 105 kg.

Ans. (b) 105 Kgs.

183. ∑ =×− 505.2nx

∑ =− 50n5.2x → (i)

∑ −=− 50n5.3x → (ii)

1.0n = 100

∴ n = 100 ∴ Σx = 300

∴ mean = nxΣ =

100300 = 3

Ans. (a) 100, 3 184. The most reliable value is mean. Ans. (a) Mean

Ans. (c) Median 186. There are 365 days in a normal year (without leap year) No. 365 = 7 × 52 + 1

∴ In a year will contain at least 52 Tuesday

The possible remaining one Tuesday Let A be the event of getting 53 Tuesday in the year.

∴ P (A) = 1/7

Ans. (b) 187. Given two unbiased dice are thrown, then the simple space are: S = { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

1650 = 500 + 625 + 5.w

[Eg. (i) – Eg. (ii)]

185. In which Central Value arranging is required – Median

423


ANSWERS

∴ n(S) = 36

Sample space of sum of the faces is not less than 10 A = {(4,6), (5,5), (5,6), (6,4), (6,5), (6,6)} n(A) = 6

∴ Required probability = 61

366

)S(n)A(n =

Ans. (a) 188. Let A be the person travels by a plane

∴ P(A) = 51

Let B be the person travels by a train

32

∴

P(AB) = P(A). P(B) (Since A and B are mutually exclusive conditional probability)

= 152

32

51 =⎟

⎠

⎞⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛

Ans. (b) 189. Let A denote the event of drawing a diamond and B denote the event of drawing a King

from a pack of Cards. Then we have P(A) = 41

5213 =

and P(B) = 524 =

131

∩ B)

= BA(P131

41

∩−+ ) → (1)

There is only one case favourable to the event A ∩ B vize, king of diamond.

Hence, P (A ∩ B) = 521

∴ (1) ⇒ P(AUB) = 52

1413521

131

41 −+=−+ =

134

5216 =

Ans. (c)

=

∴ P (B) =

Probability of his travelling neither by plane nor by train.

P(AUB) = P(A) + P(B) – P(A

424


190. Let us define the events: E 1 : A solves the problem E 2 : B solves the problem

P(E 1) = 52

156

966 ==+

and P (E2) = 1210

10+

= 115

Assuming that A and B try to solve the problem independently. E 1 and E 2 are independent.

∴ P )EE( 21 ∩ = P(E 1).P(E 2) = 112

115

52 =×

The problem will be solved if at least one of the students A and B solves the problem. Hence, the probability of the problem being solved is given by )EE(P)E(P)E(P)EE(P 212121 ∩∪ −+=

= 112

115

52 −+

= 673.05537

55102522 ==−+

Ans. (a)

192. Given Mean of Binomial distribution = μ = np = 3 → (1)

and Variance of Binomial distribution = σ2 = npq =.2 → (2)

32

npnpq

)1()2( =⇒

∴q = 2/3

∴p + q = 1

31

32 =

(1) ⇒ n(1/3) = 3

= n = 9

∴ p=1/3, q = 2/3, n=9

By the Binomial distribution p(x) = nC x p x q . The probability that the variate takes values less than or equal to 2

then we are given

p = 1– q = 1 −

n – x

425


ANSWERS

i.e. p (x < 2) = p(x = 0) + P (x = 1) + P (x = 2). = 9C 0 (1/3) 0 (2/3) + 9C 1 (1/3) 1 (2/3) + 9C 2 (1/3) 2 (2/3) = 9C 0 (1) (2/3) 9 + 9C 1 (1/3) 1 (2/3) 8 + 9C 2 (1/3) 2 (2/3) 7 = (2/3) 9 + 3 (2/3) 8 + 4 (2/3) 7 P(x < 2) = 0.3767 Ans. (a)

193. Exhaustive cases: 2 digits can be selected out of 9 digits 1 through 9 in 2C9 ways.

∴ Exhaustive number of cases = 2C9 = 362189 =

××

Even digits are: 2, 4, 6 and 8 i.e. 4 in all Odd digits are 1, 3, 5, 7 and 9 i.e. 5 in all. The sum of the two digits drawn will be even if (i) Either both the selected digits are even (or) (ii) both the selected digits are odd.

Two even digits can be selected out of the 4 even digits in 2C4 ways and two odd digits can be selected out of the 5 odd digits in 2C5 ways.

Hence, the favourable number of cases that the sum of the two selected digits in even.

= 22 C5C4 +

= 2145

2134

××+

××

= 6+10 = 16

∴ P (sum of the two selected digits is even)

= casesofnumberExhaustivecasesfavourableofNumber

= 94

3616 =

and P(Both selected digits are odd) = 185

3610

C9C5

2

2 ==

9 – 0

9 – 1

9 – 2

Favoarable number of cases. Among the digits 1 through 9.

Ans. (e)

426


194. Let S be the sample space of the experiment

Let A = event of getting sum 6 and B = event of getting 4 at least once.

∴ A = {(1,5), (2,4), (3,3), (4,2), (5,1)}

and B = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4), (5,4), (6,4)}

∴ P(A) = 5/36 and P(B) = 3611

Also, AB = {(4,2), (2,4)}

∴ P(AB) = 362

∴ The required probability

= Probability of getting 4 on at l east one die given that sum is 6

= P(B|A) = )A(P)AB(P

)A(P)BA(P =

= 52

36/536/2 =

Ans. (b)

196. Standard Error of mean = n

σ

= 6

6.1236

6.12 =

Standard Error of mean = 2.1 Ans. (a) 2.1 197. Standard Error of Mean without replacement

= 1NnN

n −−σ

= 65.01.21101

3610136

6.12 ×=−

−

SE = 2.1 × 0.806 = 1.69 Ans. (b) 1.69

∴ S = {(1,1), (1,2), ... (6,5), (6,6)}

427


ANSWERS

198. P = 51

255 =

Q = 54

511 =−

n = 5

nQP

= 032.051

54

51 =××

SE = 0.1088 Ans. (b) 0.1088 199. n = 2, N = 4 Total number of possible sample of size of with replacement = 4 2 = 16 Ans. (a) 16 200. n = 2, N = 4

Total number of possible sample of size without replacement = nCN =

2C4 = 6

Ans. (b) 6


151. The value of 3333 11.....543 ++++

= [ ]332

212

)111(11 +−⎥⎦

⎤⎢⎣

⎡ +

= ( ) ( )81611 2 +−×

= ( ) ( )966 2 −

= Ans. (c) 152. Let the two numbers are x and y

Given x + y = 75 → (1)

4356 – 9 = 4347

x – y = 20 → (2)

S.E. of proportion of defectives =

428


(1)+(2) ⇒ 2x = 95

x = 2

95

2

95

= 2

55

∴ The difference of their squares = 22 yx −

= 22

255

295

⎟⎠

⎞⎜⎝

⎛−⎟⎠

⎞⎜⎝

⎛

= 4

30254

9025 −

= 15004

6000 =

Ans. (a) 153. Let the two numbers are x and y

Given x + y = 13 → (1)

and 22 yx + = 85 → (2)

(1) ⇒

85)x13(x 22 =−+

085x26x169x 22 =−−++

084x26x2 2 =+−

042x13x2 =+−

06x7x =−−

x =7, x = 6

When x = 7 (1)

When x = 6 (1)

∴ The number (7, 6)

Ans. (a)

∴ (1) ⇒ = 75 –

y = 13 – x

Substitute y = 13 – x in (2)

⇒ y = 13 – 7 = 6

⇒ y = 13 – 6 = 7

( ) ( )

429


ANSWERS

Given 37)1x(x 22 =−−

37)x21x(x 22 =−+−

37x21xx 22 =+−−

2x = 38 x = 19

Ans. (a) 155. Let the number be x.

Given condition (1) 3x

x+

→ (1)

Given condition (2) ⇒ 23x

7x−+

+ = 2

x + 7 = 2 (x+1) = 2x + 2 x = 5

∴ (1) ⇒ 35

5+

= 85

156. Given 613logx =

3x 61

=

( )63x =

= ( ) ( ) ( )222333

=3×3×3 x = 27 Ans. (b)

157. Let y = xlogaa


log y = log [ ]xloga

154. Let the two consecutive members are x and x – 1

∴ x – 1 = 19 – 1 = 18

a

430


= logax. log a

log y = log x [ ∵ ablog . b

clog = aclog By properties]

Taking Exponent on both sides. xlogylog ee = xlogelog xy =

y = x Ans. (a)

158. Let y = 6log2 33 −

= 6log2 33.3 −

= [ ])2x3(log 33.9 −

= [ ]2log3log 333.9 +−

= [ ]2log1 33.9 +−

= 2log1 33.3.9 −−

= )2/1(log33.3

= 3.(1/2) [∵ a log ax = x properties]

∴ y = 3/2

Ans. (b)

= log 2 + log 3 + log 5 =

= 1.4771 Ans. (c) 160. log 10 124.5 + log 10379 = log 10

+ log10

= log1012.45 + log 1010 + log10 3.79 + log 10100

= 1.0952 + 0.5786 +2

∴ log 10124.5 + log 10379 = 4.6738

Ans. (b)

0.3010 + 0.4771 + 0.6990

159. log 30 = log (2×3×5)

(3.79 × 100) ×(12.45 10)

431


ANSWERS

161. n:n35 PP ⇒

12

!)3n(!n

)!5n(!n =

−÷

−

⇒ !)5n(!)3n(

−−

12=

Ans. (b) 5 162. No. of ways to enter into room = 10 No. of ways to came out from a different door = 9

∴ Total Ways = 10.9 = 90 ways

Ans. (a) 90 163. Five digit Nos. by using digit (1, 2, 3, 4, 6) = 5! = 120 Four digit nos. by using digit (1, 2, 3, 4, 6) = 5 P 4 = 120

∴ Total Nos. greater than 1000 = 120 + 120

= 240 Ans. (c) 240 164. Total Nos. of 6 digit (greater than 1 lakh)

by using (1, 1, 1, 2, 2, 3) are = !2!3

!6

= 60 Ans. (a) 60 165. No. of ways in which 17 billiard can be arranged. If 7 are black, 6 red and 4 white are

= !4!6!7

!17 = 4084080

Ans. (b) 4084080

166. Let I = ( )∫ +

dx1x

xe2

x

= ( )( )∫ +

−+ dx1x

e11x2

x

= 2 :1

⇒ (n – 3) (n – 4) = 2.1

∴ n – 3 = 2 ⇒ n = 5

432


= ( )( ) ( )∫ ∫ +

−++ dx

1xedx

1xe1x

2

x

2

x

= ( ) ( )∫ ∫ +−

+dx

1xedx

1xe

2

xx

= I1–I2

I = ∫ − )1x(dxe x

Integrating by parts.

I1 = ∫ ⎟⎟⎠

⎞⎜⎜⎝

⎛

+−−

+dxe

)1x(1e

x11 x

2x

∴ I = ∫ ∫ +−

++

+dx

)1x(edxe

)1x(1e

)x1(1

2

xx

2x

I = xe)x1(

1+

Ans. (b)

167. ∫ ∫ +−+=

+− dxe

)1x(21xdx

)1x()1x(e x

33x

= ∫ ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

+−

+dx

)1x(2

)1x(1e 32

x

= ( ) ( ){ }∫ ′+ dxxfxfe x

Where f(x) = 2)1x(1+

= c)x(fe x +

( )∫ +

+=

+− c

1xexdx

)1x()1x(e

23

x

Ans. (c)

168. Let t = 1x +

t2 = x + 1 2t dt = dx

433


ANSWERS

∴ I = ∫ +−dx

1x)4x(1

2

= [ ]∫ −− 4)1t(tdtt2

22

= ∫ −− 222 2)1t(dt2

= ∫ −−+− )21t()21t(dt2 22

= ∫ −+ )3t()1t(dt2 22

We resolve )3t()1t(

122 −+

into partial fractions

Let z = t 2

)3z()1z(

1)3t()1t(

122 −+

=−+

Let 3z

B)1z(

A)3z()1z(

1−

++

=−+

1 =

∴ B = 1/4

3z

4/11z4/1

)3z()1z(1

−+

+−=

−+

= )3t(4

1)1t(4

122 −

++

−

∴ I = 2 ∫ ⎥⎦

⎤⎢⎣

⎡

+−

−dt

)1t(41

)3t(41

22

We put z = –1, 3 A (z – 3) + B (z + 1)

Multiplying by (z + 1) (z – 3), we get

Z = –1, 1 = A (–4) + B (0)

∴ A = –1/4

z = 3, 1 = A (0) + B (4)

434


= ⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−

+− − )t(tan

3t3tlog

321

42 1

= c1xtan21

31x31xlog

341 1 ++−

⎥⎥⎦

⎤

⎢⎢⎣

⎡

++−+ −

169. ∫ − 22 axdx = ( ) ( )∫ +− axax

dx

dxax

1ax

1a21

∫ ⎟⎠

⎞⎜⎝

⎛

+−

−

= ⎥⎦

⎤⎢⎣

⎡

+−

−∫ ∫ axdx

axdx

a21

= ( ) ( )[ ]axlogaxloga21 +−−

∫ ⎥⎦

⎤⎢⎣

⎡

+−=

− axaxlog

a21

axdy

22

170. ( ) ( )∫ ∫ −+=

− xaxadxdx

xa1

22

= ∫ ⎥⎦

⎤⎢⎣

⎡

−−

+⎟⎠

⎞⎜⎝

⎛ − dxxa

1xa

1a21

= ⎥⎦

⎤⎢⎣

⎡

−−

+− ∫ ∫ dx

xa1dx

xa1

a21

= ( ) ( )[ ]xalogxaloga21 −−+−

= ⎥⎦

⎤⎢⎣

⎡

−+−

xaxalog

a21

171. 0xyxyloge yx =++−

d.wr.t.u.

01.ydxdyx1.y

dxdyx

xy1

dxdy1e yx =⎥

⎦

⎤⎢⎣

⎡ ++⎥⎦

⎤⎢⎣

⎡ ++⎟⎠

⎞⎜⎝

⎛ −−

0ydxdyx

x1

dxdy

y1

dxdy.ee yxyx =++++− −−

435


ANSWERS

dxdyx

y1e yx

⎟⎟⎠

⎞⎜⎜⎝

⎛++− − = y

x1e yx −−− −

dxdy)e.y1xy(

y1 y.x−+ = )xy1e.x(

x1 yx ++− −

∴ ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−+++−= −

−

yx

yx

e.yxy1xy1e.x.

xy

dxdy


172. y = )x(loglogx log y = log (log x) . log x

dxdy.

y1 = log (log x).

x1 + (log x).

)x(log1 .

x1

∴ xy

dxdy = [log (log x) + 1]

Ans. (a) xy [log (log x) + 1]

173. y = x +

x1x

1

+

y = 1xx2x

1xxxx

2

3

2

3

++=

+++

( )( ) ( )( )( )22

322

1x

x2x2x2x31xdxdy

+

+−++=

= ( )22

24224

1x

x4x22x2x3x3

+

−−+++

22

24

)1x(2xx

dxdy

+++=

Ans. (a) 22

24

)1x(2xx

+++

436


174. xy +

yx = 6

xy

xy + = 6 ⇒ x+y = 6 xy

∴ 1+ ⎟⎠

⎞⎜⎝

⎛ += 1.ydxdyx

xy26

dxdy

1xy3

dxdy

yx31 −=⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−

dxdy =

yx31

1xy3

−

− ⇒

( )( ) xx3y

yxy3−−

x3

6yx

6yxy3

x3xyxyy3

dxdy

−⎟⎠

⎞⎜⎝

⎛ +

⎟⎠

⎞⎜⎝

⎛ +−=

−−

=

x17yxy17

dxdy

−−= =

yx17y17x

−−

Ans. (c) yx17y17x

−−

175. 447 C + ∑

=

3

0iC3

⇒ 33334 CCCCC 4748495047 ++++

⇒ 178365 + 19600 + 18424 + 17296 + 16215

⇒ 249900

Ans. (a) 249900 176. a = 100 S 6 = 5. S

]d)16()d6a(2[26.5]d)16(a2[

26 −++=−+

3 [200 + 5d] = 15 [200+12d + 5d]

6

50 − i

437


ANSWERS

200+5d = 1000 + 85d

177. S n = 3n 2 + n

∴ S 1 = 4 ∴ a 1 = 4

S 2 = 14 2 ∴ d = 6 S 3 = 30 3

=

178. S m n

]d)1m(a2[2m −+ = ]d)1n(a2[

2n −+

d)mm(d)nn( 22 −−−

2 2

S m+n = 2

nm +

2

nm +

S m+n = 0 Ans. (a) 0

179. 0.....47,2,

49 −−−

49

49 =

41

41

49 ⇒

41)1n(

49 −=

Ans. (b) 10th term

80d = – 800 ⇒ d = –10

Ans. (a) – 10

a = 30 – 14=16

4 + (p – 1) 6 Tp = (6p – 2)

= S

2ma – 2na =

∴ Tp = a + (p – 1) d

a = 14 – 4 = 10

Ans. (b) (6p – 2)

– n – m – m)d 2a (m – n) = (n2a (m – n) = –(m – n) (m+n – 1)d

∴ 2a = –(m+n – 1)d

[2a + (m+n – 1)d]

[(–m+n – 1)d + (m+n – 1)d]

a = –

0 = – + (n −1)

d = –2 +

⇒ 9 = n – 1 ⇒ n=10

438


180. 6.T 6 = 15.T 15

∴ 6 (a+5d) = 15 (a+14d)

2a + 10d = 5a + 70d

T21 = a + 20d T21 = 0 Ans. (c) 0 181. The average of n numbers is x. If any no.is multiplied to each of datas.

∴ New average = (n + 1) x Ans. (c) (n + 1) x.

182. Av = n

x∑⇒ 1.5 =

δ∑x

= ∑ x = 12 kg. (increased weight)

∴ Weight of New person = 65 + 12 = 77 kg.

Ans. (c) 77 Kg. 183. If passes students = x

∴ 35 = 120

)n120(15x39 −+

2400 = 24x

∴ x = 100

Passed Students = 100 Ans. (a) 100

184. 4517

x=∑

∑ x = 765

Total of first 9 numbers = 9 × 51 = 459 Total of last 9 numbers = 9 × 36 = 324

∴ a = –20d 3a = –60d

= –20 d + 20d

Then average will also multiplied by such no.

4200 = 39x + 1800 – 15x

∴ Value of 9th number = (459 + 324) – 765

439


ANSWERS

= 18 Ans. (c) 18

185. ∑ x = 11 × 30 = 330

Total of last five numbers = 5 × 28 = 140

∴ Value of 6th number = (125 + 140) ~ 330 = 65

Ans. (b) 65 186. Ans. (a) Refer properties 187. Ans. (b) Refer Properties. 188. Let A be the hearts playing cards in a part.

∴ P(A) = 5213

P(B) = 5213

Here A and B are mutually exclusive.

∴ P ( )21

5226

5213

5213)B(P)A(PBA ==+=+=∪

189. Total number of balls in the bag = 6 + 4 = 10 Since three balls are drawn out of 10 balls in 10C3 ways

∴ Exhaustive number of Cases = 10 C 3 = 120

The number of favourable cases two balls are blue and balls is red = 6C 2 x 4C 1

= 60

∴ Probability of 2 balls are blue and 1 is red = 3

12c10

c4c6 ×

= ½12060 =

Ans. (c) 190. There are 366 days in a leap year. Now 366 = 7 x 52 + 2

∴ The leap year will contain at least 52 Mondays. The possible combination for the remaining two days are:

Total of first five numbers = 5 × 25 = 125

Let B be the club playing cards in a part.

440


(i) Sunday and Monday (ii) Monday and Tuesday (iii) Tuesday and Wednesday (iv) Wednesday and Thursday (v) Thursday and Friday (vi) Friday and Saturday (vii) Saturday and Sunday Let A be the event of getting 53 Mondays in the leap year. Therefore, only those

combinations will be favourable to the event A which contain "Monday"

∴ The combination (i) and (ii) are favourable to the happening of A

∴ P(A) = 2/7

Ans. (a) 191. Given P(A) = 1/3 P(B) = 3/4 and A and B are independent events

( ) ( )1BAP1BAP ∩∪ −=

= [ ]11

[ ] [ ])B(P1− [A and B are independent]

⎥⎦

⎤

⎣

⎡⎟⎠

⎞⎜⎝

⎛ −⎟⎠

⎞⎜⎝

⎛ −431

311

⎭⎬⎫

⎩⎨⎧

⎟⎠

⎞⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛

41

32

P ( )65

611BAP =⎥⎦

⎤⎢⎣

⎡−=∪

Ans. (b)

vowel. P(A) = 2/4 Let B be the second letter is vowel P(B) = 1/3 Here A and B are independent

1 − P(A ).P(B )

}{ = 1– 1−P(A)

⎢ = 1 –

= 1 –

are vowel (O,E). Let A be the first letter is 192. Out of given 4 letters, there are two letters

441


ANSWERS

P(AB) = P(A).P(B)

= 31.

42 = 1/6

Ans. (a) 193. Out of given 4 letters, there ar Let A be the first letter is vowel. i.e. P(A) = 2/4 Let B be the second letters is vowel. P(B) = 1/3 Here A and B are Mutually executive

∴ ( )BAP ∪ = P(A) + P (B)

= 65

1210

1246

31

42 ==+=+

Ans. (a)

∴

= 21

42

41

41 ==+

Ans. (b) 195. By addition thereon P(A or B) = P(A) + P(B) 0.65 =

& a 1, a 2, a 3 are in AP

∴ f(a1), f(a 2), f(a 3) also in AP

e two letters are vowel (O, E)

194. Let A be the first letter selected M from the 'HOME'. B be the second letter selected M from the 'HOME' P(A) = 1/4, P(B) = 1/4

[1 – P('not A)] + p

P(AUB) = P(A) + P(B)

A and B are Mutually exclusive

= [1 – 0.65] + p

∴ p = 0.65 – 0.35

p = 0.30 Ans. (c) 197. Since f(x) is a Polynomial.

442


∴ (af ),(af ),(af 321 ′′′

Ans. (a) AP

198. A = P ( )⎥⎥⎦

⎤

⎢⎢⎣

⎡−+ 1

ii1 n

20,000 = P ( )⎥⎥⎦

⎤

⎢⎢⎣

⎡−1

04.0

10

After solving we get P = 2470 (Approx) Ans. (a) 2470

Ans. (b) false.

greater than 2 Ans. (b) false.

) also in AP

This is wrong because bxy and byx have same sign.

1.04

199. byx = 1.2 & bxy = – 0.5

200. The mean of poison distribution is 1.6 and variance is 2. This is wrong because P – d will

443


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