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XII Commerce

Name: _______________________________

Std. _________________________________

2015-16

SUMMER HOLIDAYS

HOME WORK TRAVELLING AN EXTRA MILE.......

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Dear Children,

Holidays are always a welcome change. With summer

break round the corner each one of you must be excited

about meeting relatives, going places and having fun.

However, you all must remember that a judicious

balance must be maintained between academics and

entertainment. To spend your time constructively you all

need to be organized and follow some regular schedules

as per choice. Your teachers have made earnest efforts to

design some constructive assignments and projects to

keep you productively engaged during the vacations.

Give some quality time to your books and keep yourself

gainfully occupied.

Have Fun Filled Holidays!

With Love

PRINCIPAL

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UNIT: THE LAST LESSON

1. Answer the following questions in 30-40 words each a) What was the mood in the classroom when M. Hamel gave his last French lesson?

b) What was Hamel’s reaction to Franz not being able to answer a question on participles?

c) What does Hamel say about the importance of language to an ‘enslaved’ people?

d) What was Franz tempted to do instead of going to school and being reprimanded?

e) Who did M. Hamel blame for the neglect of learning on the part of boys like Franz?

f) “This is your last French lesson.” How did Franz react to this declaration of M. Hamel?

g) “What a thunderclap these words were to me!” Which were the words that shocked and surprised little Franz?

h) What had the narrator counted on to enter the school unnoticed?

2. Answer the following question in 125-150 words:

Q. What was the reaction of the people when they came to know about the ‘Last lesson’? Why?

UNIT: LOST SPRING

1. Answer the following questions in 30-40 words each-

a) What does garbage mean to the slum dwellers and what does it mean to the children?

b) What is the lament in every house in Firozabad?

c) Why is Mukesh’s family oblivious to the dangers of their trade?

d) Bring out the irony in Saheb’s name.

e) Who is Mukesh? Why is he different from other children?

f) Why had people of Bangladesh left their fields?

g) Why don’t bangle makers of Firozabad organize themselves?

2. Answer the following questions in 125 to 150 words

a) ‘Sahib and Mukesh are the victims of an insensitive and apathetic social set up’. Comment. b) Give a brief account of life and activities of the people like Sahib-e-Alam settled in Seemapuri.

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UNIT: DEEP WATER 1. Answer the following questions in 30-40 words each-

a) When did Douglas realize that he had an aversion to water?

b) What were his first thoughts as he went down the deep end of the pool?

c) What was the immediate effect of Douglas’ experience of almost drowning in the pool? What was the long term effect?

d) Describe in brief the efforts that Douglas made to overcome his fear of water.

e) How did the instructor make a swimmer of Douglas?

f) ‘The instructor was finished. But I was not finished’. What does he mean by this?

g) What sort of terror seized Douglas as he went down the pool with a yellow glow? How could

he feel that he was still alive?

h) Why was Douglas determined to get over his fear of water?

i) Why did Douglas go to Lake Wentworth in New Hampshire?

2. ‘The experience has a deep meaning for me’. What experience is being referred to? How did

this experience impact the life of William Douglas? (150 words)

UNIT: THE RATTRAP

Answer the following question in 30 -40 words:-

1. How did the peddler make his living?

2. Why did he think of the world as a rattrap?

3. What was the iron master’s attitude towards the peddler?

4. Why did the peddler refuse to go to the ironmaster’s house initially?

5. Why did peddler go to the ironmaster’s house?

6. How did the ironmaster wish to improve the peddler’s situation?

7. What did the peddler wish to convey to Edla through the note he left for her?

8. What brought about a transformation in the peddler? (150 words)

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UNIT: POEM -MY MOTHER AT SIXTY SIX Q. Read the extract given below and answer the questions that follow:

1. ………….and felt that old

Familiar ache, my childhood’s fear

But all I said was, see you soon, Amma,

All I did was smile and smile and smile…….

(a) What was the childhood fear that now troubled the poet?

(b) What do the poet’s parting words suggest?

(c) Why did the poet smile and smile?

2. …………Put that thought away, and

Looked out at young

Trees sprinting, the merry children spilling

Out of their homes,……….

(a) Which thought does the poet put away?

(b) What do the sprinting trees signify?

(c) What do the ‘merry children’ symbolize?

3. I looked again at her, wan, pale

As a late winter’s moon and felt that old

Familiar ache, my childhood’s fear

(a) How does the poet feel on looking at her?

(b) What does the poet mean by ‘wan’?

(c) What were the parting words of the poet?

(d) Explain “as a late winter’s moon”. Mention the figure of speech.

Q. Answer the following questions in 30-40 words each:

a) What does the poet think while looking at her mother?

b) How does the poet bring out contrast between what she watches inside and what she sees outside?

c) What does the poet do after the security check?

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UNIT: AN ELEMENTARY SCHOOL CLASSROOM IN A SLUM Q. Read the following extract & answer the question that follows: 1. And yet, for these

Children, these windows, not this map, their world,

Where all their future’s painted with fog,

A narrow street sealed in with a lead sky

Far far from rivers, capes & stars of words.

(a) What does the map on the wall signify?

(b) Who are ‘these’ children? What is their world like?

(c ) What kind of future does the poet foresee for them?

2. Unless, governor……………………….…………..they break the town.

(a) How is the tone of this stanza different?

(b) Who spells hope for these children?

(c) With the words ‘Break o break’ what does the poet seem to say?

(d) How does the word ‘catacombs’ assume significance?

3. For lives that………………..mended glass

(a) What does the poet mean by ‘cramped holes’?

(b) Mention the words that spell of physical ailments of children?

(c) Explain ‘from fog to endless night’.

Q. Answer the following questions in 30-40 words:

Q1. What does Stephen Spender want for children of slums?

Q2. Why are the maps and the pictures on the walls of the classroom meaningless in the context of the lives of the slum children?

Q3. What is the classroom in the elementary school in slum like?

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UNIT: THE TIGER KING

Q. Answer the following questions in 30-40 words each-

1. Describe how the prediction made by the astrologers at the birth of the tiger king came to pass?

2. How did the hundredth tiger take the revenge on the tiger king?

3. Why was it celebration time for all the tigers inhabiting Pratibandapuram?

4. What did the maharaja do to save his throne?

5. What efforts did the maharaja make to kill hundred tigers?

6. What difficulties did the maharaja face after killing 99 tigers?

7. “The tiger king is a story about crime and retribution. Comment (150 words)

8. When did the tiger king stand in danger of losing his kingdom? How was he able to avert the danger?

UNIT: THE ENEMY Q) Answer the following questions in 30-40 words each-

1) What were the reasons for Sadao being retained in Japan and not being sent overseas with the troops?

2) How did Sadao happen to meet his wife Hana and why did he not marry her in America?

3) How does the writer indicate that Sadao’s father was very traditional and conventional man?

4) In what way did Hana support her husband’s efforts to save the Americans life?

5) Why did the general consider Sadao critical in maintaining his own health?

6) What kind of a person was the general?

7) Why did the domestic servants in the house of Sadao show their resentment to the enemy’s stay?

8) Describe the difficulties faced by Dr. Sadao when he decided to help the enemy soldier?

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ALGEBRA OF MATRICES Ex. 1.1

1. Class the following matrices.

i) [3-4 3i] ii) 6

62

iii) 5 60 −6

iv) 0 48 0

−5 6 7 −2

v) −1 00 −3

vi) 0 1 11 0 11 0 0

vii) 3 0 00 0 00 2 0

viii) 3 0 00 3 00 0 3

2. If a matrix has 24 elements. What are the possible orders it can have? What if it has 11 elements?

3. If A =

1 4 5

0 −1 3

311

72

0

5−8

4. Construct a 2×2 matrix A= ( a i j ) whose elements are given by

i) aij = (𝑖+𝑗 )2

2 ii) aij =

(𝑖−𝑗 )2

2 iii) aij =

(𝑖−2𝑗 )2

2

iv) aij = (2𝑖+𝑗 )2

2 v) aij =

2𝑖−3𝑖

2 vi) aij =

−3𝑖+𝑗

2

5. A) Construct a 3×4 matrix whose element are:

i) aij = i + j ii) aij = i - j iii) aij = i - j iv) aij = 𝑖 𝑗

B) Construct a 2×3 marix whose elements are given by aij = 𝑖 + 𝑗

2

2

C) Construct a 2×4 marix whose elements are given by aij = 2i - j

6. If matrices 𝑎 + 𝑏 2

5 𝑎𝑏 =

6 25 8

find the value of ‘a’ and ‘b’

7. For what value of ‘a’ and ‘b’ are the following matrices equal?

A= 𝑎 + 3 𝑏2 + 20 6

, B = 2𝑎 + 1 3𝑏

0 𝑏2 − 5𝑏

8. Find x, y, a and b if 2𝑥 − 3𝑦 𝑎 − 𝑏 3

1 𝑥 + 4 3𝑎 + 4𝑏 =

1 −2 31 6 29

a) Find the order of A

b) Find the elements a21, a31, a42, a22, a43, a33

c) If ai j 7

2 , find i, j

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Ex 1.2

1. Evaluate the following:

i) 𝑎 𝑏𝑐 𝑑

+ 𝑝 𝑞𝑟 𝑠

ii) 𝑎 𝑏

−𝑏 𝑎 +

𝑎 −𝑏𝑐 𝑎

iii) 𝑎2 + 𝑏2 𝑏2 + 𝑐2

𝑎2 + 𝑐2 𝑎2 + 𝑏2 + 2𝑎𝑏 2𝑏𝑐−2𝑎𝑐 −2𝑎𝑏

2. i) If A = 2 −14 2

, B = 4 3

−2 1 and C =

−2 −3−1 −2

Find a) A+B+C b) 2B+3C

ii) If A= 1 2 32 3 1

, B = 3 −1 3

−1 0 2 Find 2A - B.

3. Given the matrices A = 2 13 −10 2

, B = 1 −10 24 −5

C= 2 30 1

−2 5

i) Verify that (A+B)+C= A+(B+C) ii) Find 2A-3B+4C

4. a) Find X if Y = 3 21 4

and 2X + Y = 1 0

−3 2

b) Find matrix X and Y. X + Y = 5 20 9

and X – Y = 3 60 −1

5. If A= 2 34 5

, B = 1 −3

−5 7 , C =

−3 5−7 9

Find A + 2B - 3C.

6. If X - Y = 1 1 11 1 01 0 0

and X + Y = 3 5 7

−1 1 411 8 0

Find X and Y.

7. i. Find a matrix X such that 2A + B + X = 0 Where

A = 3 10 2

, B = −2 10 3

ii. Find a matrix X such that 2A - B + X = 0 Where

A = 3 10 2

, B = −2 10 3

8. If A= 1 −3 22 0 2

, B = 2 −1 −11 0 −1

Find the matrix C, (A+B+C) is a zero matrix

9. A) Find x, y, z if 2 𝑥 𝑧𝑦 𝑡 + 3

1 −10 2

= 3 4 54 6

B) Find the value of x and y from the following equations.

2 𝑥 57 𝑦 − 3

+ 3 −40 2

= 7 6

15 14

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Exercise 1.3

1. Complete the indicated products:

i) 𝑎 𝑏

−𝑏 𝑎

𝑎 −𝑏𝑏 𝑎

ii) 1 −22 3

1 2 32 3 1

iii) 2 3 5 123 iv)

123 2 3 4 5

2. Corporate are following products:

i. 2 3 43 4 54 5 6

1 −3 50 2 43 0 5

ii. 2 13 2

−1 1

1 0 1−1 2 1

3. Evaluate the following.

a) 1 3

−1 −4 +

3 −2−1 1

1 3 52 4 6

b) 1 2 34 + 1 2 3 4

−1010

4. Show that:

i) 5 −16 7

2 13 4

≠ 2 13 4

5 −16 7

ii) 1 2 30 1 01 1 0

−1 1 00 −1 12 3 4

≠ −1 1 00 −1 12 3 4

1 2 30 1 01 1 0

5. If A= 1 2 32 3 −1

−3 1 2 and B=

1 0 20 1 21 2 0

obtain the product AB and BA and show that AB ≠ BA.

6. If A = 1 2 13 4 21 3 2

and B = 10 −4 −1

−11 5 09 −5 1

Show that AB = BA

7. The matrix R(t) is defined by R(t) = cos 𝑡 sin 𝑡

− sin 𝑡 cos 𝑡 show that R(s). R(t) = R(s + t)

8. i) If A = 1 2 0

−1 0 1 , B =

1 0−1 20 3

and c= 1

−1 Verify (AB)C = A (BC)

ii) If A= 1 23 1

, B = 2 13 2

, C = 1 2 33 1 0

verify that (AB) C = A(BC)

9. Without using concept of inverse of a matrix find the matrix.

𝑥 𝑦𝑧 𝑢

Such that 5 −7

−2 3

𝑥 𝑦2 𝑢

= −16 −6

7 2

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Exercise: 1.4

1. If A = 0 11 1

and B = 0 −11 0

Prove that (A + B) (A - B) ≠ A2

- B2

2. a) If A = 0 11 1

and B = 0 −𝑖𝑖 0

whose i2

= 1 Verify that (A + B)2 = A

2 + B

2

b) If A = 3 45 7

and B = 2 45 3

verify that (A+B)2 ≠ A

2 + 2AB + B

2

3. a) If A = 1 22 1

. Show that A2 - 3I = 2A

b) If A= 0 3

−7 5 , I

1 00 1

, find K such that KA2= 5A – 21 I

4. If A = 3 1

−1 2 , show that A

2 - 5A + 7I. Find f (A) where t (x) = x

2 - 5x + 7

5. a) If A= 4 2

−1 1 , find (A - 2I) (A - 3I)

b) If A = 2 −1

−1 2 show that A

2 - 4A + 32 = 0

6. a) if A = −1 3 5−1 −3 −5−1 3 5

verify that A2 = A

b) A = 0 04 0

find A16

.

7. if A = 1 0

−1 7 aws =

1 00 1

, then find k so that A2

= 8A + KI

8. If A= −1 1 13 −3 35 −5 5

, B= 0 4 31 −3 −3

−1 4 4 complete A

2 B

2.

9. a) Let t(x) = x2 - 5x + 6, find f (A) if A=

2 0 12 1 31 −1 0

b) If A= 3 2 01 4 00 0 5

show that A2

- 7A + 10 I3x3 = 0

c) A= 2 3

−1 2 find t(A) where t(x) = x

3 + 3x

2 - 4x.

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10. If I = 1 00 1

C= 0 10 0

Show that (aI + bc)3

= a3I + 3a

2bc

11. If A = 1 10 1

then prove by induction that An =

1 𝑛0 1

∀ n ∈ N

12. Let a) A = 𝑐𝑜𝑠 𝜃 𝑠𝑖𝑛 𝜃−𝑠𝑖𝑛 𝜃 𝑐𝑜𝑠 𝜃

show by mathematical induction that

An =

cos 𝑛𝜃 𝑠𝑖𝑛 𝑛𝜃−𝑠𝑖𝑛 𝑛𝜃 𝑐𝑜𝑠 𝑛𝜃

∀ all positive x integer n.

b) If A = cos α sin α−sin α cos α

show that A2 =

𝑐𝑜𝑠 2𝛼 𝑠𝑖𝑛 2𝛼−𝑠𝑖𝑛 2𝛼 𝑐𝑜𝑠 2𝛼

13. a) If A = 2 −2

−3 4 find –A

2 + 6A b) If A =

2 −3−2 4

find –A2

+ 6A

14. a) If A = 1 0 20 2 12 0 3

verify that A3

- 6A2

+ 7A + 2I = 0

b) If A = 1 2 33 −2 14 2 1

show that A3

- 23A - 40I = 0 whose I is unit

15. a) Prove that the product of matrix (in any order)

𝑐𝑜𝑠2𝜃 𝑐𝑜𝑠𝜃 𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜃 𝑠𝑖𝑛𝜃 𝑠𝑖𝑛2𝜃

and 𝑐𝑜𝑠2𝜑 𝑐𝑜𝑠𝜑 𝑠𝑖𝑛𝜑

𝑐𝑜𝑠𝜑 𝑠𝑖𝑛𝜑 𝑠𝑖𝑛2𝜑

Is a null matrix 𝜃 and 𝜑 differ by an odd multiple of 𝜋

2.

b) Give an example of two square matrices of order 2×2 each so that (A+B)2 = A

2 + 2AB + B

2

16. A store has in stock 20 dozen shirts, 15 dozen trousers and 25 dozen pairs of socks of the selling

prices are K 50 per shirt, 90 per trouser and 12 per pair of socks, then find the total amount the

store owner will get after selling all the items in the stock.

17. AA trust fund has K 50,000 that is to be invested into two types of bonds. The first bond pay

5% interest for year and the second bond pays 6% interest per year. Using matrix multiplication

determines how to divide by K 50,000 among the two types of bonds so as to obtain an annual

total interest of K 2780.

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18. A fruit seller has in stock 20 dozen mangoes, 16 dozen apples and 32 dozen bananas, suppose

the selling prices are K 0.35, K 0.75 and K 0.80 for mango, apple and banana respectively. Find

the total amount the fruit seller will get by selling his whole stock.

19. In a development plant of a city, a contractor has taken a contract to construct certain houses for

which he need building materials like stones, sand etc. There are three firms A, B, C that can

deeply him these materials.

At one time these firms A, B, C supplies him 40, 35 and 25 truckloads of stones and 10, 5 and 8

truck loads sand respectively. If the cost of one truck load of stone and sand is K 1,200 and K500

respectively then find the total amount paid by the contractor to each of these firms A, B, C

respectively.

20. A firm has in stock 12 dozen blankets. 10 dozen coats and 5 dozen gowns. The selling prices are

K 200, K 160 and K 120 each respectively. Find the total amount the firm will receive from

selling all the items.

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Exercise- 1.5

1. Let B = 1 3

−2 5 and C =

−2 53 4

find (BC)│

2. Taking A = 4 2

−2 3 and B =

0 21 5

verify that

a) (3A) │=3A│ b) (A+B)1 = A│+B│

c) (AB) │ = B│A│

3. a) If A = −245

, B = 1 3 −6 , verify that (AB) │ = B│A│

b) If A = 31

−2 , B = 1 −5 7 , verify that (AB) │ = B│A│

4. For two materials A and B

a) A= 0 −1 23 0 1

, B= 5 −12 03 −4

, verify that (AB) │ = B│A│

b) If A = 1 −32 4

, B = 1 42 5

verify that (AB) │ = B│A│

5. If A is symmetric, An is symmetric for all positive integral value of n.

6. If A, B be square matrices of same orders. They prove that A, B are symmetric, A+B is also

symmetric.

7. If A, B are skew symmetric, A+B is also skew symmetric.

8. Prove that (ABC) │= C│B│A│

9. If A is a skew-symmetric matrix of order n and P any square matrix of order n, prove P│AP is also

skew symmetric.

10. If A = 2 35 −7

, Then verify that (A2) │ = (A

1) │

11. If A = −1 1 00 −1 12 3 4

verify that 3

2 A│ = (

3

2 A) │

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12. Find 1

2 (A+A│) and

1

2 (A-A│) whose A=

0 𝑎 𝑏−𝑎 0 𝑐−𝑏 −𝑐 0

13. Let A be a square matrix. Show that 1

2 (A + A│) is a symmetric matrix and

1

2 (A - A│) is a skew

symmetric matrix.

14. a) Express −1 7 12 3 45 0 5

as the sum of a symmetric and a skew symmetric matrix.

b) Express the matrix A = 3 −41 −1

as the sum of a symmetric and a skew symmetric matrix.

15. Find the integer value of x, given 𝑥 4 −1 2 1 −11 0 02 2 4

𝑥 4 −1 = 0

16. Show that positive odd integer power of a skew symmetric matrix are skew symmetric and

positive even integral power of a skew symmetric matrix are symmetric.

17. If A and B symmetric matrix prove that AB - BA is a skew symmetric matrix.

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DETERMINANTS Exercise 2.1 Q1. Evaluate the following determinants:

1. 𝑠𝑖𝑛 10 −𝑐𝑜𝑠 10𝑠𝑖𝑛 80 𝑐𝑜𝑠 80

2. 𝑙𝑜𝑔𝑎𝑏 −1

1 𝑙𝑜𝑔𝑏𝑎 3.

𝑐𝑜𝑠 25 𝑠𝑖𝑛 25𝑠𝑖𝑛 65 𝑐𝑜𝑠 65

4. 2 0 05 9 31 6 7

5. 6 −3 −22 −1 2

−10 5 2 6. 𝑥

2 − 𝑥 + 1 𝑥 − 1𝑥 + 1 𝑥 + 1

7. 2 + 3𝑖 4

1 2 − 3𝑖 8.

𝑎 + 𝑖𝑏 𝑐 + 𝑖𝑑−𝑐 + 𝑖𝑑 𝑎 − 𝑖𝑏

9. 𝑠𝑖𝑛 10 −𝑐𝑜𝑠 10𝑠𝑖𝑛 80 𝑐𝑜𝑠 80

Q2. Find all the minors of the elements in the determinants:

1. A = 𝑎 𝑏𝑐 𝑑

2. A = 1 69 8

Q3. Find all co-factors of the elements in the determinants:

1. A = 𝑎 𝑏𝑐 𝑑

2. A = 7 3

−1 8

Q4. Write the co-factors of the second column of the determinants:

1. A = 5 2 13 0 28 1 2

and hence evaluate it.

Q5. Find co-factors of all elements of A = 1 𝑎 𝑏 + 𝑐1 𝑏 𝑐 + 𝑎1 𝑐 𝑎 + 𝑏

hence find det A.

Q6. 3 𝑚4 5

=3write the value of m.

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Exercise 2.2

Q1. Without expanding. Show that the value of the following determinants is zero.

1. 1 𝑎 𝑏 + 𝑐1 𝑏 𝑐 + 𝑎1 𝑐 𝑎 + 𝑏

2. 𝑎 − 𝑏 𝑏 − 𝑐 𝑐 + 𝑎𝑏 − 𝑐 𝑐 − 𝑎 𝑎 − 𝑏𝑐 − 𝑎 𝑎 − 𝑏 𝑏 − 𝑐

3.

1 𝑏𝑐 𝑎(𝑏 + 𝑐)1 𝑐𝑎 𝑏(𝑐 + 𝑎)1 𝑎𝑏 𝑐(𝑎 + 𝑏)

4.

1𝑎 𝑏 − 𝑐 𝑏𝑐

1𝑏 𝑐 − 𝑎 𝑐𝑎

1𝑐 𝑎 − 𝑏 𝑎𝑏

5. 8 2 7

12 3 516 4 3

6. 9 9 121 −3 −41 9 12

7. 5 15 −257 21 308 24 25

8. 42 1 628 7 414 3 2

9. 1 𝑎 𝑎𝑏𝑐1 𝑏 𝑎𝑏𝑐1 𝑐 𝑎𝑏𝑐

10. 1 𝑎 𝑎2 − 𝑏𝑐1 𝑏 𝑏2 − 𝑐𝑎1 𝑐 𝑐2 − 𝑎𝑏

11. 0 𝑐 𝑏−𝑐 0 𝑎−𝑏 −𝑎 0

12. 1 3 52 6 103 11 38

13. 4 15 14

−5 5 108 −8 16

Q2. Without expanding the determinants, show that:

i) a + b + c is a factor of the determinants 𝑎 𝑏 𝑐𝑏 𝑐 𝑎𝑐 𝑎 𝑏

ii) x + y + z is a factor of the determinants

𝑥 − 𝑦 − 𝑧 2𝑥 2𝑥2𝑦 𝑦 − 𝑧 − 𝑥 2𝑦2𝑧 2𝑧 𝑧 − 𝑥 − 𝑦

Q3. Without expanding the prove that:

𝑎 𝑏 𝑐𝑥 𝑦 𝑧𝑝 𝑞 𝑟

= 𝑦 𝑏 𝑞𝑥 𝑎 𝑝𝑧 𝑐 𝑟

Q4. Without expanding the prove that:

𝑎 𝑏 𝑐𝑥 𝑦 𝑧𝑝 𝑞 𝑟

= 𝑥 𝑦 𝑧𝑝 𝑞 𝑟𝑎 𝑏 𝑐

= 𝑦 𝑏 𝑞𝑥 𝑎 𝑝𝑧 𝑐 𝑟

18

Q5. Without expanding the determinants show that 1 +1

𝑎+

1

𝑏+

1

𝑐 is a factor of the following

determinants: 1 + 𝑎 1 1

1 1 + 𝑏 11 1 1 + 𝑐

Q6. Prove that without: 𝑏 + 𝑐 𝑐 + 𝑎 𝑎 + 𝑏𝑞 + 𝑟 𝑟 + 𝑞 𝑝 + 𝑞𝑦 + 𝑧 𝑧 + 𝑥 𝑥 + 𝑦

= 2 𝑎 𝑏 𝑐𝑝 𝑞 𝑟𝑥 𝑦 𝑧

Q7. Without expanding the determinants given below prove that:

𝑎2 𝑏2 𝑐2

(𝑎 + 1)2 (𝑏 + 1)2 (𝑐 + 1)2

(𝑎 − 1)2 (𝑏 − 1)2 (𝑐 − 1)2

= 4 𝑎2 𝑏2 𝑐2

𝑎 𝑏 𝑐1 1 1

Q8. Using the properties of determinants prove that:

𝑎 + 𝑏 + 𝑐 −𝑐 −𝑏

−𝑐 𝑎 + 𝑏 + 𝑐 −𝑎−𝑏 −𝑎 𝑎 + 𝑏 + 𝑐

= 2 (a + b) (b + c) (c + a)

Q9. Prove that: 𝑎 + 𝑙 𝑚 𝑛

𝑙 𝑎 + 𝑚 𝑛𝑙 𝑚 𝑎 + 𝑛

= a2 (a + c + m + n)

Q10.

𝑥 + 𝑦 𝑥 𝑥5𝑥 + 4𝑦 4𝑥 2𝑥

10𝑥 + 8𝑦 8𝑥 3𝑥 = x

3

Q11. 1 𝑎 + 𝑏 + 𝑛𝑐 𝑛𝑎 − 𝑎 𝑛𝑏 − 𝑏

𝑛𝑐 − 𝑐 𝑏 + 𝑐 + 𝑛𝑎 𝑛𝑏 − 𝑏𝑛𝑐 − 𝑐 𝑛𝑎 − 𝑎 𝑐 + 𝑎 + 𝑛𝑏

= n (a + b + c)3

Q12. Prove that A= 𝑥 1 1𝛼 𝑥 1𝛼 𝛽 1

= ( x – α ) ( x – β )

Q13. Prove that 1 1 1𝛼 𝛽 𝛾𝛾𝛽 𝛾𝛼 𝑟𝛽

= (α – β ) ( β - 𝛾 ) ( 𝛾 - α )

Q14. Prove that

1 𝛼 𝛼2 + 𝛽𝛾

1 𝛽 𝛽2 + 𝛾𝛼

1 𝛾 𝛾2 + 𝛼𝛽

= 2 𝛼 − 𝛽 𝛽 − 𝛾 (𝛾 − 𝛼)

𝑅2 − 𝑅3 𝑅3 = 𝑅3 − 𝑅1 − 2𝑅2

Hint

19

Q15. Prove that 1 1 1𝑎 𝑏 𝑐𝑎3 𝑏3 𝑐3

or 1 𝑎 𝑎3

1 𝑏 𝑏3

1 𝑐 𝑐3

= 𝑎 − 𝑏 𝑏 − 𝑐 𝑐 − 𝑎 (𝑎 + 𝑏 + 𝑐)

Q16. Prove that 𝑎2 + 𝑏2 𝑐2 𝑐2

𝑎2 𝑏2 + 𝑐2 𝑎2

𝑏2 𝑏2 𝑐2 + 𝑎2

= 4 𝑎2 𝑏2 𝑐2

Q17. Prove that

𝑎2+𝑏2

𝑐𝑐 𝑐

𝑎𝑏2+𝑐2

𝑎𝑎

𝑏 𝑏𝑐2+𝑎2

𝑏2

= 4 𝑎𝑏𝑐

Q18. Prove that 𝑎 𝑏 𝑐𝑏 𝑐 𝑎𝑐 𝑎 𝑏

= 𝑎 + 𝑏 + 𝑐 𝑎𝑏 + 𝑏𝑐 + 𝑐𝑎 − 𝑎2 − 𝑏2−𝑐2

Q19. Without expanding the determinants given below, prove that:

𝑎2 𝑏2 𝑐2(𝑎 + 1)2 (𝑏 + 1)2 (𝑐 + 1)2

(𝑎 − 1)2 (𝑏 − 1)2 (𝑐 − 1)2 = 4

𝑎2 𝑏2 𝑐2

𝑎 𝑏 𝑐1 1 1

Q20. Prove that 𝑥 + 4 2𝑥 2𝑥

2𝑥 𝑥 + 4 2𝑥2𝑥 2𝑥 𝑥 + 4

= (5𝑥 + 4) (4 − 𝑥)2

Q21. Prove that:

𝑥 𝑦 𝑧

𝑥2 𝑦2 𝑧2

𝑦𝑧 𝑧𝑥 𝑥𝑦 = (𝑦 − 𝑧)(𝑧 − 𝑥)(𝑥 − 𝑦)(𝑥𝑦 + 𝑦𝑧 + 𝑧𝑥)

ii.

𝑥 𝑦 𝑧

𝑥2 𝑦2 𝑧2

𝑥3 𝑦3 𝑧3 = 𝑥𝑦𝑧(𝑥 − 𝑦)(𝑦 − 𝑧)(𝑧 − 𝑥)

Q22. Show that: 1 + 𝑎2 − 𝑏2 2𝑎𝑏 −2𝑏

2𝑎𝑏 1 − 𝑎2 + 𝑏2 2𝑎2𝑏 −2𝑎 1 − 𝑎2 − 𝑏2

= (1 + 𝑎2 + 𝑏2 + 𝑐2)3

20

Q23. Show that:

𝑎2 𝑎2 − (𝑏 − 𝑐)2 𝑏𝑐

𝑏2 𝑏2 − (𝑐 − 𝑎)2 𝑐𝑎

𝑐2 𝑐2 − (𝑎 − 𝑏)2 𝑎𝑏

= 𝑎 − 𝑏 𝑏 − 𝑐 𝑐 − 𝑎 𝑎 + 𝑏 + 𝑐 + (𝑎2 + 𝑏2 + 𝑐2)

Q24. Prove that: 1 𝑏 + 𝑐 𝑏2 + 𝑐2

1 𝑐 + 𝑎 𝑐2 + 𝑎2

1 𝑎 + 𝑏 𝑎2 + 𝑏2

= (𝑎 − 𝑏)(𝑏 − 𝑐)(𝑐 − 𝑎)

Q25. Prove that:

−𝑎(𝑏2 + 𝑐2 + 𝑎2) 2𝑏3 2𝑐3

2𝑎3 −𝑏(𝑐2 + 𝑎2 − 𝑏2) 2𝑐3

2𝑎3 2𝑏3 −𝑐(𝑎2 + 𝑏2 + 𝑐2)

= 𝑎𝑏𝑐(𝑎2 + 𝑏2 + 𝑐2)

Q26. Prove that: 1 𝑏𝑐 + 𝑎𝑑 𝑏2𝑐2 + 𝑎2𝑑2

1 𝑐𝑎 + 𝑏𝑑 𝑐2𝑎2 + 𝑏2𝑑2

1 𝑎𝑏 + 𝑐𝑑 𝑎2𝑏2 + 𝑐2𝑑2

Q27. If a, b, c are all different and: 𝑎 𝑎3 𝑎4 − 1𝑏 𝑏3 𝑏4 − 1𝑐 𝑐3 𝑐4 − 1

= 0

show that abc (ab + bc + ca)= a + b + c

Q28. If p + q + r = 0, prove that

𝑝𝑎 𝑞𝑏 𝑟𝑐𝑎𝑐 𝑟𝑎 𝑝𝑏𝑟𝑏 𝑝𝑐 𝑞𝑎

= 𝑎 𝑏 𝑐𝑐 𝑎 𝑏𝑏 𝑐 𝑎

Q29. Prove that

𝑎3 3𝑎2 3𝑎𝑎2 𝑎2 + 2𝑎 2𝑎 + 1𝑎1

2𝑎 + 13

𝑎 + 23

1 1 1 1

= (a -1)6

Q30. Without expending prove that

1 cos(𝛽 − 𝛼) cos(𝛾 − 𝛼)cos(𝛼 − 𝛽) 1 cos(𝛾 − 𝛽)cos(𝛼 − 𝛾) cos(𝛽 − 𝛾) 1

= 0

Q31. Show that A= 𝑎 − 𝑏 𝑏 − 𝑐 𝑐 − 𝑎𝑏 + 𝑐 𝑐 + 𝑎 𝑎 + 𝑏

𝑎 𝑏 𝑐 = 𝑎3 + 𝑏3 + 𝑐3 − 3𝑎𝑏𝑐

21

Exercise 2.3

1. Using determinants, Find the area of the triangle with vertices

i) (2, 7) (1, 3) (10, 8) ii) (2, 7) (1, 1) (10, 8)

iii) (-3, 5) (3, 6) (7, 2) iv) (-2, 4) (2, -6) (5, 4)

v) (1,-1) (2, 4) (3, 5)

2. Find the area of triangle with vertices of the points A(at12, 2at1) B(at2, 2at2) and C(at3, 2at3)

3. Show by using determinants, that the three point

a) (-1, -1) (5, 7) and (8, 11) are collinear.

b) (3,8) (-4,2) and (10,14) are collinear.

4. Using determinants, Find the value of K so that the points (K, 2-2K), (-K+1, 2K) and

(-4-K, 6-2K) may be collinear.

5. If the points (a, b) (a1, b

1) and (a - a

1, b - b

1) one collinear. Show that ab

1 = a

1b.

6. Points (a, o) (o, b) and (x, y) are collinear if 𝑥

𝑎 +

𝑦

𝑏 = 1

7. If the points (a, o) (o, b) and (1, 1) are collinear, prove that a + b = ab.

22

1. Solve the following system of equations:

2

𝑥 +

3

𝑦 +

10

𝑧 = 4

4

𝑥 -

6

𝑦 +

5

𝑧 = 1

6

𝑥 +

9

𝑦 -

20

𝑧 = 2

2. Find a, b, c when t (x)= ax2

+ bx + c f (0)=2, f (2)=11, f (-3)=6, Determine the Quadratic

function (x) and find its value when x =1.

3. find A-1

, where A = −1 2 52 −3 1

−1 1 1 , hence solve.

The equations -x + 2y + 5z = 2

2x + 3y + z =15

-x + y + z = -3

4. If A = 1 −2 02 1 30 −2 1

, find A-1

, using A-1

, solve the following system of linear equations

x - 2y = 10

2x + y + 3z = 8

-2x + z = 7

5. Show that the system of equations

3x + 2y +7z = 0

4x - 3y - 2z = 0

5x +9y +23z = 0

Has a non-trivial solution. Find the solution.

6. State the condition under which the following systems of linear equations has a unique set.

x + 2y - 2z + 5 = 0

-x + 3y + 4 = 0

2y + z - 4 = 0

Using matrix method, find the unique solution of the above systems of linear equation.

23

7. Show that each of the following system of equations is consistent and solve:

a) x + 5y = 3 b) x + y + z = 6

2x + 10y = 6 x + 2y + 3z = 14

x + 4y + 7z = 30

c) x - y = 1 d) 2x + 2y - 2z = 1

3x - 3y = 3 4x + 4y - z = 2

6x + 6y + 2z = 3

8. Solve (Matrix method)

a) 2x + 3y +3z = 5 b) x + y + z = 1

x - 2y + z = 6 x - 2y + 3z = 2

3x – y - 2z = 3 x - 3y + 5z = 3

9. Show that each of the following system of linear equations is inconsistent.

a) 2x + 5y = 5 b) x + y - 2z = 5

6x + 15y = 10 x - 2y + z = -2

-2x + y + 2 = 4

c) 3x - y +2z = 3

2x + y +3z = 5

x - 2y - z = 1

24

By using elementary row transformation.

Find the inverse of the matrix.

1) A = 1 −12 3

2) A = 1 22 −1

3) A = 4 33 2

4) A = 1 23 7

5) A = 2 0 −15 1 00 1 3

6) A = 1 2 3

−3 5 00 1 1

7) If A = 1 −1 12 −1 01 0 0

find A-1

and show that A-1

= A2

8) If f (α) = 𝑐𝑜𝑠 𝛼 −𝑠𝑖𝑛 𝛼 0𝑠𝑖𝑛 𝛼 cos 𝛼 0

0 0 1 , prove that [ f (𝛼)]

-1 = f (-𝛼)

9) Verify that (AB)-1

= B-1

A-1

for the matrix.

A = 3 27 5

B = 4 63 2

10) If A = 1 −1 12 −1 01 0 0

, find A3 and show that A

2 = A

-1

11) Let A be the Matrix = 3 82 1

, find A-1

and verify that A-1

= 1

13 A-

4

13 I, is a

2 X 2 unit matrix.

12) Show that A = 5 3

−1 −2 , satisfies the equation x

2 - 3x - 7 = 0. Thus find A

-1

13) A = 0 1 21 2 33 1 1

, and verify that A-1

. A = I3

14) For the matrix A = 3 17 5

, find x and y so that A2

+ xI = yA, Hence find A-1

.

15) If A-1 = 3 −1 1

−15 6 −55 −2 2

and B = 1 2 −2

−1 3 00 −2 1

find (AB)-1

.

25

RELATION AND FUNCTIONS

1. Let A and B be two sets, show that f: A X B → B X A such that f (a, b) = (b, a) is a bijections.

2. Show that the signum function f: R→R define by f (x)=

1 𝑖𝑓 𝑥 > 00 𝑖𝑓 𝑥 = 0

−1 𝑖𝑓 𝑥 < 0

is neither one-one nor on to.

3. If f : N→N be defined by f (n)= 𝑛+1

2 𝑖𝑓 𝜂 𝑖𝑠 𝑜𝑑𝑑

𝑛

2 𝑖𝑓 𝜂 𝑖𝑠 𝑒𝑣𝑒𝑛

∀ 𝑥 ∈ 𝑛. State whether the function f is bijection.

4. Consider f : R→ f [-5, ∞] given by f (x) = 9x2

+ 6x - 5, show that f is investible with

f -1

(y) = 𝑦+6−1

3

5. If f (x)= 27x3 and g(x) = 𝑥

13 find go f (x).

6. f : N→R be a function defined as f (x) = 4x2

+12x +15, Show that f : N→S Where S is the range

of f, is investible find the inverse of f.

7. Show that the relation R in the Set R of real numbers. Define as R = {(a1 b) : a ≤ b2} is neither

reflective nor symmetric nor transitive.

8. Let A= NXN and ∗be a binary operation on A defined by (a, b) ∗ (c, d) = (a+c, b+d).

Show that ∗ is commutative and associative. Also find the identity element for ∗ on A, if any.

9. If f (x) = 4𝑥+3

6𝑥−4, x ≠

2

3, show that to fof (x) = x ∀ x ≠

2

3, What is the inverse of f.

10. Show that f : N→N, given by f (x)= 𝑥 + 1, 𝑖𝑓 𝑥 𝑖𝑠 𝑜𝑑𝑑𝑥 − 1 𝑖𝑓 𝑥 𝑖𝑠 𝑒𝑣𝑒𝑛

is bijection.

11. Let A= R-{3} and B = R-{1}. Consider one function f : A→B defined by f (x) 𝑥−2

𝑥−3, Show that f is

one-one and on to and hence find f -1

.

12. If the binary operation ∗ on the set Z of integers in defined by a ∗ b = a + b - 5, They write the

identity element for the operation ∗ is Z.

13. Show that the relation R defined by (a, b) R (c, d) ⇒ a + d = b + c on the set N×N is an

equivalence relation.

26

14. Show that the relation R refined by R = {(a, b): a - b is divisible by 3, a, b∈N} is are equivalence

relation.

15. A binary operation ∗ on the set {0, 1, 2, 3, 4, 5} is defined as: a∗b = 𝑎 + 𝑏 𝑖𝑓 𝑎 + 𝑏 < 6

𝑎 + 𝑏 − 6 𝑖𝑓 𝑎 + 𝑏 > 6

Show that zero is the identity for this operation and each element a of the set in invertible with

6 - a, being the inverse of a.

27

Inverse Trigonometric functions (2007-2013)

1. Show that sin-1

(2x 1 − 𝑥2) = 2sin-1

x

2. Fine the principle value of sin-1

𝑠𝑖𝑛3𝜋

5

3. Write the principle value of sin -1

(- 32

)

4. Write one principal value of cos-1

(- 32

)

5. Write the principal value of sec -1

(-2)

6. Write the principal value of sin-1

𝑠𝑖𝑛 4𝜋

5

7. Find the value of cot (tan-1

α + cot -1

α)

8. Write the principal value of cos -1

1

2 -2 sin

-1 −1

2 .

9. Find the value of tan -1

𝑥

𝑦 - tan

-1

𝑥−𝑦

𝑥+𝑦

10. Prove that tan -1

(1) + tan -1

(2) + tan -1

(3) = π.

11. Solve of x: tan-1

(x+1) + tan-1

(x - 1) = tan-1

8

31

12. Prove that 2tan-1 1

5 + tan

-1 1

8 = tan

-1 4

7

13. Prove that sin -1 12

13 + cos

-1 4

5 + tan

-1 63

16 = π

14. Prove that sin-1

4

5 + sin

-1 5

13 + sin

-1

16

65 =

𝜋

2

15. Solve: cos -1

𝑥2−1

𝑥2+1 + tan

-1

2𝑥

𝑥2−1 =

2𝜋

3

16. Solve: tan -1 𝑥−1

𝑥−2 + tan

-1 𝑥+1

𝑥+2 =

𝜋

4

28

17. Prove that: tan -1

x + tan -1

2𝑥

1−𝑥2 = tan -1

3𝑥−𝑥3

1−3𝑥2

18. Prove that: cos {tan -1

[sin (cot – 1

x)]} = 1−𝑥2

2+𝑥2

19. Prove that: tan 𝜋

4+

1

2 cos−1 𝑎

𝑏 + tan

𝜋

4−

1

2cos−1 𝑎

𝑏 =

2𝑏

𝑎

20. Prove that: cot -1

1+𝑠𝑖𝑛𝑥 + 1−𝑠𝑖𝑛𝑥

1+𝑠𝑖𝑛𝑥 + 1−𝑠𝑖𝑛𝑥 =

𝑥

2, x < 0,

𝜋

4

21. Prove that: tan -1

1+𝑥 − 1−𝑥

1+𝑥+ 1−𝑥 =

𝜋

4 -

1

2 cos

-1 x,

1

2 ≤ x ≤ 1

22. Prove that: 9𝜋

8 -

9

4 sin

-1 1

3 =

9

4 sin

-1 2 2

3

23. Prove that: cos 𝑠𝑖𝑛 − 1 3

5 + cos−1 3

2 =

6

5 13

24. Solve for x: 2 tan-1

(sin x) = tan-1

(2sin x), x ≠ 𝜋

2

25. Find the value of tan -1

𝑥

𝑦 – tan

-1

𝑥−𝑦

𝑥+𝑦

26. Prove that: tan-1

𝑥 = 1

2 cos

-1 1−𝑥

1+𝑥 , x ∈ (0, 1)

27. Prove that: tan-1

1

4 + tan

-1 2

9 =

1

2 cos

-1 3

5

28. Show that: tan 1

2𝑠𝑖𝑛−1 3

4 =

4 − 7

3

29. Solve for x cos (2 sin-1

x) = 1

9, x > 0

30. cos {tan-1

[sin (cot -1

x)]}= 1 + 𝑥2

2 + 𝑥2

29

FUNDAMENTALS OF PARTNERSHIP FIRM

Q1. A and B are partners sharing profits in the ratio of 3:2 with their capitals on January 1st, 2016 as K 40,000 and K 30,000 respectively. Interest on capital is allowed at 5% p.a. B is allowed an annual salary of K 3,000 which he had not withdrawn. During 2016 the profits prior to calculation of interest on capital but after charging B’s salary amounted to K 12,000. A provision of 5% of profits is to be made in respect of commission to the manager. Prepare an account showing allocation of profits.

Ans. Divisible Profit K 7,750 i.e., K 12,000 -2,000 -1,500 – 750 being A’s share K 4,650 and B’s share K 3,100 Q2. Geeta and Meeta were partners in a firm sharing profits in the ration of 5:3. Their fixed

capitals were K 3,00,000 and K 2,00,000 respectively. The partnership deed provided that: i. Interest on capital should be allowed @ 12% p.a.

ii. Geeta should be allowed a salary K 40,000 p.a. iii. A commission of 5% of the net profit should be allowed to Meeta.

The net profit for the year ended 31.3.2016 was K 2,00,000. Prepare profit and loss appropriation account.

Ans. Divisible Profit K 90,000 being Geeta’s Share K 56,250 and Meeta’s K 33,750 Q3. What entries will be passed to record the following transactions in the books of the firm of A and B before distributing the profits earned?

a) Interest on capital: A- K 3,000 B – K 2,000

b) Interest on Drawing A – K 800 B – K 1,000

c) Salary payable A – K 3,000 (p.a.)

d) Transfer to General Reserve K 4,000

Ans. (a) (i) Dr. Interest on Capital K 5,000; Cr. A’s Capital K 3,000 and B’s Capital K 2,000 (ii) Dr. Profit & Loan Appropriation A/c, Cr. Interest on Capital by K 5,000

(b) (i) Dr. A’s Capital K800 and B’s Capital K1,000; Cr. Interest on Drawings by K 1,800. (ii) Dr. Interest on Drawings, Cr. Profit & Loss Appropriation A/c by K 1,800

(c) (i) Dr. A’s Salary A/c. Cr. A’s Capital A/c. by K 3,000. (ii) Dr. Profit & Loss Appropriation A/c, Cr. A’ salary by K 3,000

(d) Dr. Profit & Loss Appropriation A/c, Cr. General Reserve A/c by K 4,000

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Q4. Muskan and Surbhi are partners in a firm sharing profits in the ratio of 3:2. The partnership

deed provided that Muskan was to be paid of K 2,500 per month and Surbhi was to get a commission of K 10,000 per year. Interest on capital was to be allowed @5% per annum and interest on drawings was to charged @6% per annum. Interest on Muskan’s drawings was K 1,250 and on Surbhi’s drawing K 425. Capital of the partners were K 2,00,000 and K 1,50,000 respectively , and were fixed. The firm earned a profit of K 90,575 for the year ended on 31/3/2014. Prepare Profit and Loss Appropriation Account of the firm. Ans. Divisible Profit K 34,750 transferred to Muskan’s Current K 20,850 and Surbhi’s Current A/c K 13,900

Q5. On 1st January, 2015 A and B entered into partnership contributing K 60,000 and K 45,000

respectively. They agreed to share profit and losses in the ratio of 3:2. B is allowed a salary of K 12,000 per year. Interest on capital is to be allowed at 10% per annum. During the year, A withdrew K 9,000 and B K 18,000 as Drawings. Interest on Drawings of A and B was K 150 and K 210 respectively. Profit as on 31st December, 2015 before the above mentioned adjustments was K 35,000. Show the distribution of Profit by preparing Profit and Loss Appropriation A/c. of the firm and prepare Partners’ capital A/cs also. Ans. Divisible Profit K 12,860, Share of profit : A K 7,716 and B K 5,1444, Balance of Capital A/cs. A K 64,566 and B K 48,434.

INTEREST ON CAPITAL AND DRAWING

Q6. A and B started business on 1.1.17 with capital of K 60,000 and K 40,000 respectively. During the year A, introduction K 10,000 to the firm additional capital on 1.7.2017. They withdrew K 500 per month for the house expenses in lieu of profit. Interest on capital is to be allowed @ 10% per annum. Calculate the interest payable to A and B for the year ending 31/12/17.

Ans. (i) Interest on A’s Capital:

Interest on Opening Capital = 60,000 * 10/100 * 1 = K 6,000 Interest on Additional Capital = 10,000 * 10/100 * 6/2 = K 500

K 6,500

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IN THE ABSENCE OF PARTNERSHIP DEED

Q7. Bobby and Pawan were partners in a firm. The partnership agreement provided that

interest on drawing was to be charged @ 12% p.a. Bobby had withdraw the following amount during the year ended 31/12/2017.

Date Amount withdrawn

K

1/1/2017 10,000

31/3/2017 16,000

1/7/2017 20,000

31/12/2017 4,000

Calculate interest on bobby’s drawings.

Ans. Interest on Bobby’s Drawing= K 3,840 (3,84,000 * 12/100 * 1/12)

Q8. Hina and Rahim are partners in a firm. The partnership deed provided that interest on drawings will be charged @6% p.a. During the year ended December 31st, 2016 Hina withdrew K 5,000 at the beginning of the every month and Rahim withdrew K 5,000 at the end of each month. Calculate interest on the partner’s drawings. Ans. Interest on Hina’s Drawings = 60,000 * 6/100 * 6.5/12= K 1,950

Interest on Rahim’s Drawing = 60,000 * 6/100 * 5.5/12 = K 1,650 Q9. A and B are partners in a firm sharing profit equally. They had advance to the firm a sum

of K 30,000 as a loan in their profit sharing ratio on July 1st , 2016. The partnership deed is silent on the question of interest on loan from partners. Compute the interest payable by the firm to the partners, assuming the firm closes its books on December 31st each year. Ans. Interest on Partner’s loan = 15,000 * 6/100 * 6/12= K 450 each

Q10. Mahesh and Ramesh are partners with capitals of K 50,000 and K 60,000 respectively. On 1st January 2016, Mahesh gives a loan of K 10,000 and Ramesh introduced K 20,000 as additional capital. Profit for the year ending 31st March 2016 was K 15,200. There is no partnership deed. Both Mahesh and Ramesh Expect interest @ 10% p.a. on the loan and additional capital advanced by them. Show how the profits would be divided? Give reason.

Ans. Divisible Profit K 15,050 being Mahesh’s Share and Ramesh’s share K 7,525 each

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PAST ADJUSTMENT

Q11. A and B starts business on July 1, 2015, each partner contributing K 1,50,000 as his share of capital. Three months later, on October 1st, 2015, B makes an additional contribution of K 1,00,000 which is treated as a loan. The profit for the period ending March 2016 was K 85,000 before charging any interest. All the partners were entitled to a salary of K 3,000 each, per quarter. The partners had drawn K 24,000 each on 1st January 2016. Prepare the Profit and Loss Appropriation Account for the period ended March 31st, 2016.

Ans. Divisible Profit K 82,000 being A’s Share and B’s Share K 41,000 each.

Q12. Ram and Shayam were partners in a firm sharing profits in the ratio of 3:5. Their fixed capital were: Ram K 5,00,000 and Shayam K 9,00,000. After the accounts of the year had been closed, it was found that interest on capital at 10% per annum as provided in the partnership agreement has not been credited to the capital Accounts of the partners. Pass a necessary entry to rectify the error.

Ans. Dr. Ram’s Current A/c, Cr. Shyam Current A/c by K 2,500 Q13. Meenu, Reema and Kavita were sharing profits equally. Their capitals were K 40,000;

K 20,000 and K 30,000 respectively. After closing the accounts for the year 2015 it was found that the interest on capital @10%p.a. was not allowed before distributing the profits. It was decided to pass a single adjusting entry to rectify the accounts of the previous year. Journalise.

Ans. Dr. Reema’s Capital, Cr. Meenu’s capital by K 1,000 Q14. Anu, Beena, Ceena, Deepa share profits in the ratio of 5:3:2:2 and their capital are

K 5,000, K 6,500, K 6,000 and K 6,500 respectively. On 31st December, 2015 after closing the books ot is found that interest on capital @5%p.a. was omitted. Interest of altering the signed accounts, it was decided to pass a singly adjustment entry at the beginning of the next year. Give the necessary journal entry.

Ans. Dr. Anu’s Capital K 250; Cr. Beena’s Capital K 25, Ceema’s Capital K 100 and Deepa’s capital K 125

Q15. X, Y and Z are partners sharing profits and losses in the ratio of 3:2:1. After the final

accounts have been prepared, it was discovered that interest on drawings had not been taken into consideration. The interest on drawings of partners amounted to X K 250, Y K 180 and Z K 100. Give the necessary adjusting journal entry. Ans. Dr. Y’s Capital K 3 and Z’s Capital K 12; Cr. X’s Capital K 15

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Q16. Ram and Mohan were partners in a firm sharing profits in 3:2 ratio. Their fixed capital were: Ram K 1,20,000 and Mohan K 90,000. For the year 2017, interest on capital was credited to them @6% instead 5%. Give necessary adjusting entry for the rectification of the error. Show also the working noted clearly.

Ans. Dr. Monah’s Current A/c, Cr. Ram’s Current A/c by 60 Q17. X, Y and Z are partners in a firm, sharing profits in the ratio of 5:3:2. Their fixed capital

were K 3,00,000, K 2,00,000 and K 1,00,000 respectively. For the year 2015, interest on capital was credited to their capitals accounts @ 8% p.a. instead of 10% p.a. showing your working clearly, pass the necessary adjusting journal entry.

Ans. Dr. Z’s Current A/c. Cr. Y’s Current A/c by K 400 Q18. Malti, Paro and Arti are partners in a firm having fixed capitals of K 80,000; K 40,000

and K 50,000 respectively sharing profits as 7:6:4. The rate of interest on capital was agreed at 10% per annum, but was wrongly credited to them as 12% per annum. Give the necessary adjustment entry to adjust the balances of partner’s capital accounts.

Ans. Dr. Malti’s Current A/c, and Arti Current A/c by K 200 each; Cr. Paro’s Current A/c. K 400

Q19. X, Y and Z are partners in a firm who share profits in the ratio of 2:3:5. The firm earned a profit of K 1,50,000 for the year ended December 31st , 2015. The profit by mistake was distributed among X, Y and Z in the ratio of 3:2:1 respectively. This error was noted only in the beginning of the next year. Pass necessary entry to rectify the error.

Ans. Dr. X’s Capital K 45,000 and Y’s Current K 5,000; Cr. Z’s Capital K 50,000 Q20. S, K and R are partners in a firm sharing profits in the ratio of 3:2:1 respectively. R wants

that he should share profits of the firm equally in future. He further wants that change profit sharing ratio should be applicable retrospectively for the last three years others partners have no objection to this. This profit for last three years were K 60,000, K 47,000 and K 55,000. Record the adjustment by means of journal entry. Give Workings.

Ans. Dr. S’ Capital; Cr.R’s Capital by K 27,000 Q21. Preeti, Mona and Nisha shared profits in the ratio of 3:2:1. The profits of the last three

years were K 1,40,000, K 84,000 and K 1,06,000 respectively. These profits were by mistake, shared equally for all the three years. It is now decided to correct the error. Give necessary journal entry for the same.

Ans. Dr. Nisha Capital, Cr.Preeti Capital by K 55,000

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Q22. Jagdish, Ashish and Deepak are partners sharing profits in the ratio of 3:2:1. The firm

has been in existence for many year now the partners decided to share profits in the ratio of 2:2:1. They have also decided that the change shall be carried out with retrospective effect from 1995. The profits and losses during the last few years have been 2012: K 16,000, 2013: K 12,000, 2014: K 14,000, 2015: K 19,000 and 2016: (loss) K 15,000. Show the adjustment of the profit for the last 4 years by means of a single adjustment entry. Ans. Dr. Jagdish’s Capital A/c K 3,000; Cr. Ashish’s Capital A/c K 2,000 and Deepak’s Capital A/c K 1,000

Q23. A, B and C were partners in a firm sharing profits of 5:3:2. On 1/1/2016 they decided to a

share the profits equally. It was also agreed that the change be carried out retrospectively for the last 4 years. The profits of the last 5 years were as follows:

Year Ended: 2013 2014 2015 2016 2017

Profits (K) 50,000 40,000 10,000 (Loss) 60,000 1,00,000

Pass necessary adjusted entry.

Ans. Dr. A’s Capital K 31,666; Cr. B’s Capital K 6,333 and C’s Capital K 25,333. Q24. After including the profits for the year ended 31st March 2011 the capital accounts of

Savitri, Savita and Santosh stood at K 20,000, K 15,000 and K 10,000 respectively. Subsequently, it was discovered that interest on capitals at 10% p.a. had inadvertently been ignored. The profit for the year in arriving at the above figures of capitals amounted to K 10,000. They shared profits and losses in the ratio 2:1:1 respectively. Give the necessary journal entry to rectify the above.

Ans. Dr. Savitri’s Capital K 250 and Santosh’s Capital K 125; Credit Savita’s Capital K 375

Q25. On March 31, 2016 after the close of books of accounts, the capital accounts of, A, B and C

stood at K 24,000; K 20,000 and K 12,000 respectively. The profit for the year K 36,000 was distributed equally. Subsequently it was discovered that interest on capital @5% p.a. had been omitted. The profit sharing ratio was 2:2:1. Pass an adjustment journal entry. Ans. Opening Capital: A K 12,000, B K 8,000 and C nil; Dr. C’s Capital K 5,000; Cr. A’s Capital K 2,600 and B’s Capital K 2,400

35

Q26. On 31st December 2015 after closing account, capitals of X, Y and Z stood at K 80,000,

K 60,000 and K 40,000 respectively. It was subsequently discovered that interest @5% p.a. on capitals at the beginning of the year was left out. Their drawing during the year were K 20,000, K 15,000 and K 9,000 respectively. Profit for the year was K 1,20,000. Partners share profits as 3:2:1.Give necessary adjustment entry and show the working notes. Ans. Opening Capital: X K 40,000; Y K 35,000; Z K 29,000; K X Rs.600; Cr. Y K 17 and Z K 583.

Q27. A, B and C were partners in a firm. On 1/4/2016 their capital stood at K 50,000; K 25,000 and K 25,000 respectively. As per the provisions of the partnership deed:

i. C was entitled for a salary of K 5,000 p.a. ii. Partners were entitled to interest on capital at 5%

iii. Profit were to be shared in the ratio of partners’ capita.

The net profit for the year 2016-17 of K 33,000 was divided equally without providing for the above terms. Pass an adjustment entry in journal to rectify the above error. Ans. Dr. B’s Capital K 4,000; Cr. A’s Capital K 3,000 and C’s Capital K 1,000.

Q28. P, Q and R were partners in a firm sharing profits in the ratio of 1:2:2. After division of

the profits for the year ended 31/3/2017 their capitals were : P K 1,50,000; Q K 1,80,000; and R K 2,10,000. During the year they withdrew K 20,000 each. The profit of the year was K 60,000. The partnership deed provided that interest on capital will be allowed @ 10% p.a. While preparing the final accounts, interest on partner’s capital was not allowed. You are required to calculate the capital of P, Q and R as on 1.4.2000 and pass the necessary adjustment entry for providing interest on capital. Show your working clearly. Ans. Opening Capital as on 1.4.2000; P K 1,58,000, Q K 1,76,000 and R K 2,06,000 Adjustment entry: Dr. Q’s Capital K 3,000 and C’s Capital K 1,000

36

Guarantee of Partners

Q29. X, Y and Z were partners, sharing profits in the ratio of 2:2:1. Z was guaranteed a

minimum profit of K 20,000. The profits of the firm for the year ended 31/3/2017 were K 80,000. Prepare P & L Appropriation A/c.

Ans. Share of Profit: X K 30,000 (32,000-2,000) and Z K 20,000(16,000 + 2,000 + 2,000)

Q30. A, B and C were partners in a firm sharing profits in 2:3:5 ratio. A was guaranteed a minimum profit of K 1,00,000. Any deficiency on this account was to be borne by C. The net profit of the firm for the year ended 31/3/2016 was K 4,50,000. Prepare Profit and Loss Appropriation Account of A, B and C for the year ended 31/3/2016.

Ans. Dr. C’s Capital and Cr. A’s Capital by K 10,000 Q31. A, B and Care partners sharing profits in the ratio of 5:4:1. C is given a guarantee that his

share of profit in any given year would be K 5,000. Deficiency, if any, would be borne by A and B equally. The profits for the year 2016 amounted to K 40,000. Pass necessary entries in the books of the firm.

Ans. (i) Dr. Profit & Loss Appropriation A/c by K 40,000; Cr, A’s Capital A/c K 20,000, B’s Capital A/c K 16,000 and C’s Capital A/c K 4,000

(ii) Dr. A’s Capital A/c K 500,B’s Capital A/c K 500 and Credit C’s Capital A/c. K 1,000 Q32. P, Q and Rare partners in a firm. Their profit sharing ratio is 3:2:1. However, R is

guaranteed a minimum amount of K 10,000 as share of profit every year. Any deficiency arising on that shall be met by Q. The profits for two years ending December 31st, 2013 and 2014 were K 45,000 and K 75,000 respectively. Prepare Profit and Loss Appropriation Account for the two years.

Ans. 1993- Share of Profit: P K 22,500, Q K 12,500 (i.e., K 15,000 – K 2,500); R. K 10,000 i.e., (K 7,500 – K 2,500)

Q33. A, B and C are partners in a firm sharing profits in the ratio of 2:2:1. C is guaranteed a

minimum amount of K 10,000 as his share of profit every year. Deficiency if any, on that account shall be borne by B. The profits for two years ending 31.3.2014 and 31.2.2015 were K 50,000 and K 60,000 respectively. Prepare Profit and Loss Appropriation account for two years.

Ans. 31/3/2003 Share of Profit = A K 20,000; B K 20,000 and C K 10,000

31/3/2015 Share of Profit = A K 24,000; B K 24,000 and C K 12,000

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Q34. Rajat, Nimesh and Vishesh entered into a partnership on April 1st 2016 to share profits

and losses in the ratio of 4:3:3. Rajat, however, personally guaranteed that Vishesh’s share of profit after charging interest on capitals at 5% p.a. would not be less that K 40,000 p.a. The capital contributions were K 3 lakhs, Nimesh K 2 lakhs and Vishesh K 1 lakh. The profits for the period ended December 31st 2016 were K 1,20,000. Show the distribution of profits.

Ans. Divisible Profit K 90,000; Share of Profits: Rajat K 23,000 (K 36,000 – 13,000), Nimesh K 27,000 and Vishesh K 40,000(K 27,000 + 13,000)

Q35. A, B and C entered into a partnership on October 1, 2015 to share profits and losses in the

ratio of 3:2:1. A, however personally guaranteed that C’s share of profit after charging interest on capitals at 5% p.a. would not be less than K 30,000 in any year. The capital contributions were A: K 3 lakhs, B K 2 lakhs and C : K 1 lakh. The profits for the period ended March 31, 2016 were K 1,20,000. Show the distribution of profits.

Ans. Divisible Profit K 1,05,000 (K 1,20,000- K 15,000) being share of profits. A K 52,000; B K 35,000 and C K 17,500.

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ACCOUNTING RATIOS

Q1. Calculate Current Ratio and Quick Ratio: Sundry Trade Receivables K 4,00,000; Prepaid Expenses K 40,000; Debenture K 2,00,000; Inventory K 1,60,000; Bills Payable K 80,000; Marketable Securities K 80,000; Sundry Creditors K 1,60,000; Cash K 1,20,000; Expenses Payable K 1,60,000.

Ans. Current Ratio 2:1, Quick Ratio 1.5:1 Q2. A firm has current of 4:1and quick ratio of 2.5:1. Assuming inventories (Inventory) are K 22,500, find out total current assets and total current liabilities.

Ans. Current Assets K 65,000 Current Liabilities K 15,000 Q3. X Ltd. has a liquid ratio of 7:3. If its Inventory is Rs.25,000 and its current liabilities are K 75,000, find out the current ratio.

Ans. Current Ratio = 2.67:1 Q4. Priya Ltd. has a current ratio of 3:1. If its Inventory is K 40,000 and total current liabilities are K 75,000, find out its quick ratio.

Ans. Quick Ratio = 2.47:1 Q5. Current assets of a company are K 5,00,000; current ratio = 2.5:1 and Quick Ratio = 1:1. Calculate the amount of current liabilities, liquid assets and Inventory.

Ans. Current Liabilities K 2,00,000 Liquid Assets K 2,00,000 Inventory K 3,00,000 Q6. Current liabilities of a company are K 1,20,000. Its current ratio is 3.00 and liquid ratio is 0.90. Calculate the amount of Current Assets; liquid Assets and Inventory.

Ans. Current Assets K 3,60,000 Liquid Assets K 1,08,000 Inventory K 2,52,000 Q7. Current ratio of a company is 3:1, working capital is K 30,000. Calculate the amount of current assets and current liabilities.

Ans. Current Assets K 45,000 Current Liabilities K 15,000 Q8. A business has a current ratio of 3:1. Its net working capital is K 4,00,000 and its Inventory is valued at K 2,50,000. Calculate liquid ratio.

Ans. Liquid Ratio K 1.75:1

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Q9. The current ratio of a company is 2:1. State giving reasons which of the following would improve, reduce or not change the ratio:

(a) Repayment of a current liability (b) Purchasing goods on credit, (c) Sale of Office equipment for K 4,000 (Book Value K 5,000), (d) Sale of goods K 11,000(Cost K 10,000), (e) Payment of dividend

Ans. (a) Improve (b) Reduce (c) Improve (d) Improve (e) Improve

Q10. The current ratio of a company is 2:1. State which of the following would improve, reduce or not change the ratio:

(i) Repayment of a current liability (ii) Purchasing goods on credit (iii) Sale of Motor vehicles at a loss of 20% (iv) Sale of goods at a profit of 10%. (v) Payment of dividend. (vi) Redemption of debentures at a premium. Ans. (i) Improve (ii) Reduce (iii) Improve (iv) Improve (v) Improve (vi) Reduce.

Q11. Calculate Current Assets from the following information:

(i) Inventory Turnover: 4 times (ii) Inventory at the end is K 20,000 more than the Inventory in the beginning. (iii) Sales K 3,00,000 (iv) Gross Profit Ratio 25% (v) Current Liabilities K 40,000 (vi) Quick Ratio 0.75

Ans. Current Assets K 96,250.

Q12. Calculate Debt Equity Ratio:

K Equity Share Capital

General Reserve Accumulated Profits

10% Debentures Current liabilities

Preliminary Expense

5,00,000 1,00,000

50,000 1,30,000 1,00,000

10,000 Ans. Debt Equity Ratio 0.203:1

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Q13. From the following information, calculation the Debt Equity Ratio and Current Ratio:

K Share Capital Bills Payable

Creditors Trade Receivables 12% Debentures

Bank Balance Long term Loan General Reserve

2,50,000 15,000 45,000 60,000

2,80,000 30,000

1,10,000 25,000

Ans. Debt Equity Ratio 1.4:1; Current Ratio 1.5:1

Q14. Calculate Debt Equity Share Ratio and Proprietary Ratio from the following data:

K

Equity Share Capital Reserve and Surplus

Debentures Loan for ICICI

Current Liabilities Fixed Assets

Goodwill Current Assets

75,000 20,000 40,000 30,000 15,000 82,000 48,000 50,000

Ans. Debt Equity Ratio 0.74:1 ; Proprietary Ratio K 0.53:1

Q15. The debt equity ratio of a company is 1:2. Which of the following transaction would increase, decrease and not change it?

(a) Issue of Equity Shares (b) Cash Received from Trade Receivables (c) Redemption of Debentures (d) Purchased Goods on Credit?

Ans. (a) Decrease (b) No change (c) Decrease (d) No Change

41

Q16. Calculate Inventory Turnover Ratio from the following:

K K

Opening Inventory` Purchases

Carriage Inward Wages

Manufacturing Expenses Gross Profit

75,000 1,00,000

4,000 11,000

9,000 61,000

Sales Less: Returns 3,00,000 Closing Inventory 50,000

2,50,000

10,000

2,60,000 2,60,000

Ans. Inventory Turnover Ratio Rs.4.45 times

Q17. From the following information, calculate Inventory Turnover Ratio:

K

Sales Purchase

Opening Inventory Closing Inventory

2,00,000 1,69,000

35,500 44,500

Ans. 4 Times

Q18. From the given information, calculation the Inventory Turnover Ratio:

Sales: K 3,00,000; GP : 25% on cost; Opening Inventory was 1/3rd of the value of the Closing Inventory. Was 30% of Sales. Ans. Inventory Turnover Ratio 4 times

Q19. From the following information, determine the opening and closing Inventory:

Inventory Turnover Ratio 4 times Total Sales K 3,00,000 Rate of Gross Profit on Sales 20%

Closing Inventory is more by K 6,000 than the opening and closing Inventory. Ans. Opening Inventory K 57,000, Closing Inventory K 52,000

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Q20. Find out the value of opening Inventory from the following particulars: Total Sales K 3,00,000 Gross Profit 20% of sales Inventory Turnover Ratio 5 times

You are informed that opening Inventory is K 8,000 less than the closing Inventory. Ans. Opening Inventory K 44,000, Closing Inventory K 52,000 Q21. Inventory Turnover Ratio is 6 times. Average Inventory is K 80,000. Calculate the amount of gross profit, if profit is 25% above cost. Ans. Gross Profit K 1, 20, 000 Q22. Operating Ratio 60%. Office and Selling Expenses to Sales Ratio is at 5%. Calculate Gros Profit Ratio.

Ans. Profit K 2,40,000

Q23. Determine the sales if: Average Inventory K 1, 60, 000 Inventory Turnover Ratio 6 times Gross Profit K 1, 20, 000

Ans. Cost of Goods sold K 9,60,000, Sales K 10,80,000

Q24. From the following information, calculate:

(i) Opening Inventory, (ii) Closing Inventory Details : Inventory Turnover 6 times Gross profit was K 80,000 which was 20% of sales

Closing Inventory was K 15,000 more than opening Inventory. Ans. Cost of revenue from operations K 3, 20, 000, Average Inventory K 53, 333, Opening Inventory K 45,833, Closing Inventory K 60,833.

Q25. K 2, 00, 000 is the cost of revenue from operations, inventory turnover 8 times; Inventory at the beginning is 1.5 times more than the Inventory at the end. Calculate the values of opening and closing Inventory. Ans. Opening Inventory K 35,714.2; Closing Inventory K 14,285.7.

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Q26. Net credit sales of M.S. Limited during the year were K 1, 80,000. If Trade Receivables

turnover ratio is 4 times, calculate Trade Receivables in the beginning and at the end of the year. You are informed that closing Trade Receivables are two times in comparison to opening Trade Receivables. Ans. Opening Inventory K 30,000 Closing Inventory K 60,000

Q27. Calculate Trade Receivables Turnover Ratio and Average Collection Period in terms of months from the following:

K

Credit sales for the year Trade Receivables Bills Receivable

60,000 5,000 5,000

Ans. Trade Receivables Turnover Ratio 6 times; Average Collection Period 2 months. Q28. Calculate the amount of closing Trade Receivables from the following data:

K

Total Sales Cash Sales Credit Collection Period Trade Receivables at the beginning of the year

25,00,000 12,22,500

52 days 1,74,000

Ans. Closing Trade Receivables K 1, 90, 000

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Q29. Calculate Operating Ratio, Gross Profit Ratio, Net Profit Ratio and Return on Investment

from the following Trading and Profit & Loss Account of M/s Sudhir Ltd. for the year ending 31st December, 1994:

K K

To Inventory (1-1-1994) To Purchases To wages To Gross Profit c/d

45,000 1,10,000

15,000 1,85,000

By sales (Less: Sale Returns) By Inventory (31-12-1994)

3,00,000 55,000

3,55,000 3,55,000

To Administrative Expense To Selling Expenses To Interest Paid To Net Profit

6,000 8,000

14,000 1,67,000

By Gross Profit By Rent Received

1,85,000 10,000

1,95,000 1,95,000

Capital employed K 9,00,000

Ans. (i) Operation Ratio 43% (ii) Gross Profit Ratio 61.67%

(iii) Net Profit Ratio =55.67% (iv) ROI =20.11%

Q30. Calculate the Gross Profit Ratio based on the following information:

Cash Sales: 25% of Total Sales; Purchases: K 2,76,000; Credit Sales: K 2,40,000; Excess of Closing Inventory over Opening Inventory : K 20,000 Ans. Gross Profit Ratio 20%.

Q31. Compute the gross profit ratio from the following information: Sales K 5,00,000 and Gross

Profit 25% on Cost. Ans. Gross Profit Ratio 20%.

Q32. A company earns a gross profit of 20% on cost. Its credit sales are twice its cash sales. If

the credit sales are K 4,00,000 calculate the gross profit ratio of the company. Ans. Gross Profit Ratio 16.67%

45

Q33. The operating ratio of a company is 80%. State, giving reasons, which of the following transactions will (a) increase (b) decrease or (c) not alter the opening ratio:

(i) Credit Purchase of Goods K 5,000

(ii) Sales Return K 200 (iii) Payments to Creditors K 1,000 (iv) Selling Expenses K 800 (v) Cash Sales K 10,000 (vi) Purchase Returns K 100 Ans. (i) Increase (ii) Increase (iii) No Change

(iv) Increase (v) Decrease (vi) Decrease Q34. State with reasons whether the operating ratio of a company will increase, decrease or not change due to the following transaction:

(i) Paid wages K 1,000

(ii) Issued K 1,00,000 12% debentures

(iii) Sold goods on credit K 15,000

(iv) Paid K 5,000 commission on sales.

(v) Paid K 4,000 for advertisement.

Ans. (i) Increase (ii) No Change (iii) Decrease

(iv) Increase (v) Increase. Q35. Calculate cost of revenue from operations from the following information:

Sales K 12,00,000; Sales Returns K 80,000; Operating Expenses K 1,82,000; Operating Ratio 92%.

Ans. COGS K 8,48,400

46

Q36. The Profit and Loss Account of Surya Ltd. for the year ended 31/3/2006 and the Balance

Sheet of the Company as on 31/3/2006 is given below: Profit and Loss Account

for the year ended 31/3/2006

K K

Opening Inventory Purchases Direct Expense Gross Profit

40,000 2,50,000

30,000 1,40,000

Sales Closing Inventory

4,00,000 20,000

4,60,000 4,60,000

Salary Loss on Sale of Building Net Profit

32,000 8,000

1,00,000

Gross Profit 1,40,000

1,40,000 1,40,000

Balance Sheet as on 31st March, 2006 Liabilities K Assets K

Equity Share Capital Profit and Loss Account Creditors Outstanding Salary

3,00,000 1,00,000 1,50,000

50,000

Land Inventory Trade Receivables Cash

4,00,000 20,000

1,00,000 80,000

6,00,000 6,00,000

On the Basis of the information given in these two statements, calculate any two of the following ratios:

(i) Current Ratio, (ii) Inventory Turnover Ratio, and (iii) Proprietary Ratio.

Ans. (i) Current ratio = 1:1

(ii) Inventory Turnover =10 Times (iii) Proprietary ratio = 0.67 or 67%

47

Q37. From the details given below, calculate the following ratios:

(i) Current Ratio (ii) Acid Test Ratio (iii) Working Capital Turnover Ratio

K Fixed Assets Inventory Trade Receivables Cash Prepaid Expenses Creditors Bank Overdraft Reserves Revenue from operations

1,00,000 37,200 19,200 39,600 10,000 36,000 17,000 10,000 31,800

Ans. (i) Current ratio =2:1

(ii) Acid Test Ratio 1.10:1; (iii) Working Capital turnover 0.6 times

Q38. From the following information, calculate:

(i) Gross Profit Ratio, (ii) Inventory Turnover Ratio (iii) Trade Receivables Turnover Ratio (iv) Operating Ratio

K Sales Cost of revenue from operations Opening Inventory Closing Inventory Trade Receivables Operating Expense Net Fixed Assets

1,50,000 1,20,000 27,000 33,000 20,000 16,000 1,10,000

Ans. (i) K 30,000 (ii) 4 times (iii) 7.5 times (iv) 90.66%

48

Q39. On the basis of following information, calculate:

(i) Gross Profit Ratio (ii) Working Capital Turnover Ratio

(iii) Debt Equity Ratio (iv) Proprietary Ratio.

K Revenue from operations Cost of revenue from operations Current Assets Current Liabilities Paid up share capital Debentures Loan

30,00,000 20,00,000

6,00,000 2,00,000 5,00,000 2,50,000 1,25,000

Ans. (i) 33 1/3 % (ii) 5 Times (iii) 0.75:1 (iv) 0.57:1

Q40. With the help of the given information calculate the following ratios:

(i) Operating Ratio, (ii)Current Ratio,

(iii) Inventory Turnover Ratio, (iv) Debt Equity Ratio,

(v) Current Assets Turnover Ratio

K Equity share Capital 9% Preference Share Capital 12% Debentures General Reserve Sales Opening Inventory Purchases Wages Closing Inventory Selling and Distribution Expenses Other Current Assets Current Liabilities

5,00,000 4,00,000 2,40,000

40,000 8,00,000

48,000 5,00,000

30,000 52,000

6,000 2,00,000 1,50,000

Ans. (i) 66.5 Ratio (ii) 1.68:1 (iii) 10.52 times

(iv) 33.05% (v) 0.31 times

49

Q41. With the help of the given information calculate the ratios:

(i) Operating Ratio, (ii) Quick Ratio, (iii) Inventory Turnover Ratio, (iv) Proprietary Ratio (v) Fixed Assets Turnover Ratio.

K Sales Opening Inventory Purchases Carriage Inwards Closing Inventory 9% Preference Shares Capital Securities Premium General Reserve Other Current Assets Current Liabilities Fixed Assets Opening Expenses

5,00,000 40,000

2,30,000 10,000 60,000

4,00,000 30,000 10,000

1,10,000 1,80,000 3,50,000

25,000

Ans. (i) 49% (ii) 0.61:1 (iii) 4.4 times (iv) 85% (v) 0.7 times

Q42. From the following information, calculate Inventory Turnover ratio, Operating Ratio

and Gross Ratio:

K Opening Inventory Closing Inventory Purchases Inventory Sales Returns Carriage inwards Office expenses Selling & Distribution Expenses Capital Employed

28,000 22,000 46,000 90,000 10,000 4,000 4,000 2,000 2,00,000

Ans. (i) Inventory Turnover Ratio 2.24 times,

(ii) Operating Ratio 77.57%, (iii) Gross Profit Ratio 30%

50

Q43. Calculate the following ratios from the given information:

(i) Gross Profit Ratio (ii) Inventory Turnover Ratio

(iii) Proprietary Ratio (iv) Operating Ratio

Information: Revenue from operations K 4,00,000; Cost of goods of sold K 2,00,500; Administrative expenses K 45,000; Selling expenses K 57,000; Share Capital K 8,50,000; Reserve and Surplus K 3,00,000; Long-term loans K 8,20,000; Fixed assets (net) K 4,62,000; Investment K 2,42,500; Trade Receivables K 72,000; Opening Inventory K 2,40,000; Closing Inventory K 2,10,000 and Bank Balance K 3,00,000. Ans. (i) Gross Profit Ratio = 49.88%

(ii) Inventory Turnover Ratio = 0.89 times

(iii) Proprietary Ratio = 1.17:1

(iv) Operating Ratio = 75.63%

Q44. Following is the Balance Sheet of Title Machine Ltd. as on March 31, 2006.

Liabilities K Assets K Equity Share Capital 8% Debentures Profit and Loss Bank Overdraft Creditors Provision for Taxation

24,000 9,000 6,000 6,000

23,400 600

Building Inventory Trade Receivables Cash in Hand Prepaid Expense

45,000 12,000

9,000 2,280

720

69,000 69,000 Calculate Current Ratio and liquid Ratio. Ans. Current ratio 8:1; Liquid Ratio 0.37:1

Q45. Handa Ltd. has Inventory of K 20,000. Total liquid assets are K 1,00,000 and quick ratio

2:1. Calculate current ratio.

Ans. Current Ratio 2.4:1 Q46. Calculate debt equity ratio from the following information: Total Assets K 15,00,000 Current Liabilities K 6,00,000 Total Debts K 12,00,000

Ans. Debt Equity Ratio 2:1

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Q47. From the following information calculate:

(i) Gross Profit Ratio (ii) Inventory Turnover Ratio (iii) Current Ratio (iv) Liquid Ratio (v) Net Profit Ratio (vi) Working Capital Ratio:

K Sales Net Profit Cost of Sales Long –term Debt Creditors Average Inventory Other Current Assets Fixed Assets Current Liabilities Net Profit before Interest and Tax

25,20,000 3,60,000

19,20,000 9,00,000 2,00,000 8,00,000 7,60,000

14,40,000 6,00,000 8,00,000

Ans. Gross profit Ratio 40%; Working Capital Ratio 2.4 times; Current Ratio 2.6:1;

Liquid Ratio 1.27:1; Net Profit Ratio 14.21%; Working Capital Ratio 2.625 times.

Q48. Compute Gross Profit Ratio, Working Capital Turnover Ratio, Debt Equity Ratio and Proprietary Ratio from the following information:

K Paid –up Capital Current Assets Revenue from operations 13% Debentures Current Liability Cost of revenue from operations

5,00,000 4,00,000

10,00,000 2,00,000 2,80,000 6,00,000

Ans. Gross Profit Ratio 40%; Working Ratio 8.33 times; Debt Equity Ratio 2:5;

Proprietary Ratio 25:49. Q49. Calculate the Inventory Turnover Ratio from the following information:

K Annual Sales Gross Profit Opening Inventory Closing Inventory

2,00,000 25% on Cost 38,500 41,500

Ans. Inventory Turnover Ratio = 4 Times.

52

Q50. Find out the value of Closing Inventory if: Cost of Sales K 5,60,000 Inventory Turnover Ratio 7 times

Opening Inventory is K 10,000 more than the closing Inventory. Ans. Average Inventory K 80,000; Closing Inventory K 75,000

Q51. From the following particulars, determine the amount of sales: Opening Inventory K 50,000 Inventory Turnover Ratio 4 times Gross Profit 20% of Sales

You are informed that closing Inventory was two times in comparison to opening Inventory. Ans. Average Inventory K 75,000; COGS K 3,00,000; Sales K 3,75,000

Q52. Compute Trade Receivables Turnover from the following:

K Gross Sales Trade Receivables at the beginning of year Trade Receivables at the end of year Sales Return

9,00,000 83,000

1,17,000 1,00,000

Ans. Trade Receivables Turnover Ratio = 8 Times

Q53. From the following information, calculate Trade Receivables Turnover Ratio and Average Collection Period:

K Opening Trade Receivables Closing Trade Receivables Sales Cash Sales

37,000 43,000

6,00,000 80,000

Ans. Trade Receivables Turnover Ratio 13 times, Average Collection Period 28 days.

53

Q54. From the following information, calculate: (i) Trade Receivables Turnover Ratio (ii) Average Collection Period (iii) Payable Turnover Ratio (iv) Average Payment Period

K Sales Creditors Bills Receivable Bills Payable Purchases Trade Receivables

8,75,000 90,000 48,000 52,000

4,20,000 59,000

Ans. (i) 8.18 times (ii) 45 days (iii) 3 times (iv) 122 days.

Q55. The following is the summarised Profit and Loss account and the Balance Sheet of

Nigam limited for the year ended March 31, 2017:

Expenses/Losses K Revenue/Gains K Opening Inventory Purchases Direct Expenses Gross Profit

50,000 2,00,000

16,000 1,94,000

Sales Closing Inventory

4,00,000 60,000

4,60,000 4,60,000 Salary Loss on Sale of Furniture Net Profit

48,000 6,000

1,40,000

Gross Profit 1,94,000

1,94,000 1,94,000 Balance Sheet of Nigam Limited as on March 31st, 2017

Liabilities K Assets K Profit and Loss Creditors Equity Share Capital Outstanding Expenses

1,40,000 1,90,000 2,00,000

70,000

Inventory Land Cash Trade Receivables

60,000 4,00,000

40,000 1,00,000

6,00,000 6,00,000 Calculate: (i) Quick Ratio (ii) Inventory Turnover Ratio (iii) Return on Investment

Ans. (i) 7:13; (ii) 3.74 times; (iii) 41.17%

54

Q56. The following is the summarised transactions and Profit and Loss Account for the year

ending March 31, 2017 and the Balance Sheet as on that date. Expenses/ Losses K Revenue/ Gains K

Opening Inventory Purchases Direct Expenses Gross Profit

5,000 25,000

2,500 25,000

Sales Closing Inventory

50,000 7,500

57,500 57,500 Administrative Expense Interest Selling Expenses Net Profit

7,500 1,500 6,000

10,000

Gross Profit 25,000

25,000 25,000

Liabilities K Assets K Share Capital Current Liabilities Profit and Loss

50,000 20,000 10,000

Land And Building Plant and Machinery Inventory Sundry Trade Receivables Bills Receivables Cash in Hand and at Bank Furniture

25,000 15,000

7,500 7,500 6,250 8,750

10,000 80,000 80,000

Calculate : (i) Gross Profit Ratio

(ii) Current Ratio

(iii) Acid Test Ratio

(iv) Inventory Turnover Ratio

(v) Fixed Turnover Ratio.

Ans. (i) 50% (ii) 3:2 (iii) 1.125:1 (iv) 4 Times (v) 1:1

55

Q57. You are able to collect the following information about a company for two years:

2014 K

2015 K

Book Debts on Apr.01 Book Debts on Mar.30 Inventory-in-trade on Mar.31 Sales (at gross profit of 25%)

4,00,000

6,00,000 3,00,000

5,00,000 5,60,000 9,00,000

24,00,000 Calculate Inventory Turnover Ratio and Trade Receivables Ratio if in the year 2014 Inventory-in-trade increased K 2,00,000. Ans. Inventory Turnover Ratio 2.4 times, Trade Receivables Turnover Ratio 4.53

times. Q58. Calculate current ratio from the following : Working Capital K 5,00,000 Bills Payable K 50,000 Sundry Creditors K 2,00,000

Ans. 3:1

Q59. Calculate the current ratio from the following information:

Liabilities K Assets K Total assets Long Term Liabilities Shareholder’s Fund

4,50,000 1,20,000 3,00,000

Fixed Assets Investment Miscellaneous Expenditure

2,40,000 1,50,000 NIL

Ans. 2:1

Q60. A firm has a current ratio of 3:1. Its current liabilities are K 20,000. What are the current

assets and working capital? Ans. Current Assets K 60,000, Working Capital K 40,000

Q61. A Business has current ratio of 3:1. Its current ratio 1.2:1. If the working capital is

K 1,80,000, calculate the current liabilities, current assets and Inventory. Ans. Current Liabilities K 90,000,

Current Assets K 2,72,000, Inventory K 1,62,000

56

Q62. X Ltd. has a current ratio of 3.5:1 and quick ratio of 2:1. If excess of current assets over

quick assets represented by Inventory is K 24,000, calculate current assets and current liabilities.

Ans. Current Assets K 56,000 Current Liabilities K 16,000

Q63. The ratio of current assets (K 3,00,000) to current liabilities (K 2,00,000) is 1.5:1. The

accountant of the firm is interested in maintaining a current ratio of 2:1, by paying off a part of the current liabilities. Compute the amount of current liabilities that should be paid, so that the current ratio at the level of 2:1 may be maintained. Ans. K 1,00,000

Q64. Compute Inventory Turnover Ratio from the following information: Revenue from operations K 2,00,000 Gross Profit K 50,000 Closing Inventory K 60,000

Excess of Closing Inventory over Opening Inventory K 20,000 Ans. 3 Times

Q65. Calculate the current assets of a Company from the following information:

(i) Inventory Turnover Ratio 6 Times (ii) Inventory in the beginning is K 8,000 more than Inventory at the end (iii) Sales K 2,16,000 (iv) Gross Profit 20% on Cost (v) Current Liabilities K 80,000 (vi) Acid Test Ratio 0.75:1.

Ans. Current Assets K 86,000

Q66. Calculate Debt Equity Ratio from the following information:

K Balance Sheet Total Fictitious Assets Long Term Liabilities Current Liabilities

30,30,000 30,000

15,00,000 3,00,000

Ans. 0.8:1

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Q67. From the following information, calculate Debt Equity Ratio, Proprietary Ratio and Ratio

of Total Assets to Debt. Balance Sheet as on December 31st,2015

Liabilities K Assets K

Preference Share Capital Equity Share Capital Reserves and Surplus Secured and Surplus Current liabilities

1,00,000 3,00,000 1,10,000 1,50,000

50,000

Fixed Assets Investment Current Assets Preliminary Expense

4,00,000 1,00,000 2,00,000

10,000

7,10,000 7,10,000 Ans. Debt Equity Ratio = 0.3

Proprietary Ratio = 0.77% Total Assets to Debt Ratio = 4.67%

Q68. Following information is available for the year 2016. Calculate gross profit ratio:

K

Cash sales Cash Purchases Credit Purchases Freight inwards Purchases Return Salaries Decrease in Inventory Wages Ratio of Cash Sales and Credit Sales

50,000 30,000

1,20,000 4,000 4,000

50,000 20,000 10,000

1:3 Ans. Gross Profit Ratio 10%.

Q69. Net Profit ratio of a company was 20%. Its indirect expenses were K 80,000 and cash

sales were K 3,00,000. The credit sales were 80% of the total sales. Calculate the Gross Profit Ratio of the company. Ans. Gross Profit Ratio =25.33%

58

Q70. Following information is available for the year 2015, calculate gross profit ratio:

K

Cash sales

Credit

Purchases : Cash

Credit

Carriage Inwards

Salaries

Decreases in Inventory

Return Outwards

Wages

25,000

75,000

15,000

60,000

2,000

25,000

10,000

2,000

5,000

Ans. Gross Profit Ratio = 10%

Q71. Gross Profit ratio of a company was 25%. Its sales were K 18,00,000 and its cash sales

were 10% of the total sales. If the indirect expenses of the company were K 50,000, calculate its net profit ratio. Ans. Net Profit Ratio = 22.50%

Q72. From the following information calculate Inventory Turnover Ratio: Sales K 5,00,000 Average Inventory K 68,750 Gross Loss Ratio 10%

Ans. Inventory Turnover Ratio = 8 Times.

Q73. From the following information, find out the cost of revenue from operations; sales and

closing Inventory.

(i) Inventory Velocity = 6 times

(ii) Gross Profit = 20%

(iii) Gross Profit = K 60,000

(iv) Closing Inventory was K 5,000 in excess of opening Inventory.

Ans. COGS = K 2,40,000; Sales K 3,00,000; Closing Inventory K 42,500

59

Q74. Calculate Trade Receivables Turnover Ratio from the following:

Particulars K Total sales for the year

(Credit Sales : 70% of Total Sales)

Sales Return (4/5th out of credit Sales)

Opening Trade Receivables

Closing Trade Receivables

12,00,000

50,000

73,250

86,750

Ans. Trade Receivables Turnover Ratio = 10 Times

Q75. Cash Sales= K 2,00,000; Credit Sales= K 4,00,000; Gross Profit = K 1,00,000 and

Inventory Turnover Ratio = 5times.

Calculate the value of Opening and Closing Inventory in each of the following alternatives cases: Case I : If closing Inventory was K 80,000 in excess of opening Inventory

Case II : If closing Inventory was 3 times that in the beginning.

Case III : If closing Inventory was 3 times more than that in the beginning

Case IV : If closing Inventory was 1/3rd of Inventory at the beginning.

Ans. Case I : opening Inventory K 60,000, Closing Inventory K 1,40,000

Case II : opening Inventory K 50,000, Closing Inventory K 1,50,000

Case III : opening Inventory K 40,000, Closing Inventory K 1,60,000

Case IV : opening Inventory K 1,50,000, Closing Inventory K 50,000

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Q76. The profit and loss account and balance sheet of Bakshish Ltd. is given below: Profit and Loss Account for the year ended 31st March, 2016

Liabilities K Assets K To opening Inventory To purchases To wages To gross profit c/d

90,000 5,60,000 2,14,000 1,26,000

By sales By closing Inventory

9,00,000 90,000

9,90,000 9,90,000 To Salaries To Electricity To Miscellaneous Expenses To Depreciation To Net Profit

16,000 10,000 10,000 30,000 60,000

By Gross profit b/d 1,26,000

1,26,000 1,26,000 Balance Sheet as on 31s,March, 2016

Liabilities K Assets K Share capital Equity Shares Reserves and Surplus Secured Loans Current Liabilities Sundry Creditors

1,80,000 1,20,000 2,10,000

90,000

Fixed Assets 5,40,000 Less: Depreciation 1,50,000 Current Assets Inventory 90,000 Trade Receivables 1,05,000 Cash 15,000

3,90,000

2,10,000 6,00,000 6,00,000

From the above figures, calculate the following ratio: (a) Liquidity Ratios (b) Solvency Ratios (c) Turnover Ratios (d) Profitability Ratios Ans. (a) (i) Current ratio 233:1 (ii) Liquid Ratio=1.33:1

(b) (i) Debt Equity Ratio 7:1 (ii) Total Assets to Debt Ratio =2.86:1

(c) (i) Inventory Turnover Ratio =8.6 Times (ii) Trade Receivables Turnover Ratio =8.57 Times

(iii) Average Collection Period = 43 days (iv) Working Capital Period =6.45 Times (v) Fixed Assets Turnover Ratio = 1.98 Times (vi) Capital Turnover Ratio = 1.52 Times

(d) (i) Gross Profit Ratio = 14% (ii) Net Profit Ratio = 6.67% (iii) Operating Ratio =90% (iv) Return on Equity = 33.33% (v) Return on Investment = 11.76%

61

Q77. The Current ratio and Liquidity ratios are 2.10:1 and 1.90: 1 respectively. Current assets

include Inventory of K 16,000. There is no bank overdraft in current liabilities. Find out liquid assets and working capital.

Ans. Liquid Assets K 1,52,000; Working Capital K 88,000 Q78. On the basis of the information given below calculate the following ratios: (i) Operating ratio (ii) Liquid ratio (iii) Proprietary ratio

Cash sales K 3,00,000; Credit Sales K 2,80,000; Sales Returns K 20,000; Cost of revenue from operations K 4,00,000; Selling and Distribution Expenses K 7,000; Administrative Expenses K 8,000; Current Liabilities K 2,30,000; Current Assets K 4,00,000; closing Inventory K 40,000; Equity Share Capital K 5,00,000; 8% Preference Share Capital K 2,00,000; Fixed Assets K 5,50,000

Ans. (i) 74.1% (ii) 1.57:1 (iii) .74:1 Q79. Following are the details available:

Current Assets Current Liabilities Total Sales Cost of revenue from operations Operating Expenses Inventory Turnover Ratio

K 1,00,000 K 70,000

K 2,00,000 K 1,50,000

K 20,000 5 times

If the closing Inventory is more by K 4,000 than opening Inventory, determine the following: (i) Opening Inventory (ii) Liquidity Ratio.

Ans. (i) K 28,000 (ii) 0.97:1 Q80. Calculate the Creditors Turnover Ratio and Creditors Payment Period form the

following figures:

Total Purchases during 2006

Return outwards

Cash Purchases

Creditors on 1/1/2006

B/P on 1/1/2006

Creditors on 31/12/2006

B/P on 31/12/2006

K 15,00,000

K 1,00,000

K 2,00,000

K 1,50,000

K 2,50,000

K 40,000

K 1,60,000

Ans. Creditors Turnover Ratio = 4 Times Creditors Payment Period = 3 months

62

Q82. From the following information, calculate (i) Current Assets Turnover (ii) Fixed Assets Turnover and (iii) Working Capital Turnover Ratios:

Particulars K Particulars K

Preference Share Capital Equity Share capital General Reserve Profit and Loss account 15% Debentures 14% Loan Creditors Bills Payable Outstanding Expenses

4,00,000 6,00,000 1,00,000 3,00,000 2,00,000 2,00,000 1,40,000

50,000 10,000

Plant and Machinery Land and Building Motor Car Furniture Inventory Trade Receivables Bank Cash

8,00,000 5,00,000 2,00,000 1,00,000 1,80,000 1,10,000

80,000 30,000

Sales for the year 2016 were K 30,00,000 Ans. (i) 7.5 Times (ii) 1.88 Times (iii) 15 Times

Q83. A company has inventory of K 1,80,000, Trade Receivables of K 1,20,000 and Inventory

Turnover Ratio 6 Times. The gross Profit margin of the company is 10% and its credit sales are 20% of the total sales. Calculate the average collection period (Assume 360 days in a year) Ans. 180 days.

Q84. Calculate the amount of Opening Trade Receivables and Closing Trade Receivables from

the following figures: Trade Receivables Turnover Ratio 4 Times

Cost of revenue from operations K 6,40,000

Gross Profit Ratio 20%

Closing Trade Receivables were K 20,000 more than at the beginning. Cash Sales being 331/3 % of Credit Sales. Ans. Opening Trade Receivables K 1,40,000 Closing Trade Receivables K 1,60,000

63

Q85. From the following details, Calculate Return on Investment (ROI)

Share Capital : Equity (K 10) 12% Preference General Reserve 10% Debentures Declared and Dividend Paid Current Liabilities Discount on Debentures Net Profit after Debenture Interest but before tax

K 4,00,000 K 1,00,000 K 1,89,000 K 4,00,000

K 50,000 K 1,00,000

K 5,000 K 80,000

Also calculate the Earning Per Share (EPS), Dividend Per Share and Price Earning Ratio (P/E Ratio) if the market price of the shares is K 34. Ans. ROI = 11.07% EPS= K 1.70

Dividend Per Share = K 1.25 P/E Ratio 20 times Q86. From the following details, calculate Return on Investment:

Share Capital : Equity (K 10) 12% Preference Current Liabilities Discount on Shares General Reserve Fixed Assets 10% Debenture Current Assets

K 4,00,000 K 1,00,000 K 1,00,000

K 5,000 K 1,89,000 K 9,50,000 K 4,00,000 K 2,34,000

Also calculate Return on Shareholder’s Funds, EPS and P/E ratio if the market price of the share is K 34 and the net profit after tax was K 1,50,000, and the tax had amounted to K 50,000 Ans. Return of Investment 22.14%

Return on Shareholder’s Funds =21.9% EPS= K 3.45, P/E Ratio = 9.86 Times

64

CHAPTER: BUSINESS ENVIRONMENT 1. Why is business environment uncertain?

2. What is meant by Market Orientation?

3. How can environment awareness help managers?

4. How can political stability be beneficial to the economy?

5. What was the immediate cause of economic reforms in 1991?

6. What is meant by threats?

7. Give one of the most important objectives of Indian development programmes at the time of independence.

9. Business environment or Environmental Scanning helps in the identification of threats and early warning signals." Explain?

10. What is meant by liberalization? List the impact of changes in government policy on business and industry.

11. Explain the meaning of the term Privatisation? List any two reforms made under Privatisation. -

12. Enumerate the various ways in which managers respond to changes In business environment.

13. Mention four examples of acquisitions and mergers.

14. Explain the changes initiated by the Government of India since 1991.

15. Explain the meaning of the term Privatisation? List any two reforms made under Privatisation.

16. Explain the changes initiated by the Government of India since 1991. Explain any five ways in which managers have responded to changes in business environment. 17. Explain 'fiscal reforms' and 'monetary reforms' as per economic change initiated by Government of India since 1991.

65

CHAPTER: PLANNING 1. What is planning?

2. Which function of management bridges the gap between where we are and where we want to go to?

3. Name the primary function of management.

4. One of the functions of Management is considered as base' for all other functions. Name that function.

5. What all qualities are required for doing planning?

6. Name the feature of planning which says planning is a forward looking function?

7. How does planning create rigidity?

8. What is the basis for creating future course of action?

9. Give one limitation of planning function.

10. Which is the most crucial step in planning process?

11. Define 'Objective'?

12. Define 'Strategy'.

13. Define 'Policy'.

14. Define 'Rules'.

15. Give anyone example of 'budget'.

16. What do you mean by planning?

17. What do you mean by a plan?

18. Enumerate six points of importance of planning.

19. How is planning a pervasive function of management?

20. How is planning forward looking? OR

Planning is futuristic' explain?

21. Planning involves decision making". Explain.

22. 'Planning reduces creativity'. How?

23. 'Planning does not guarantee success'. Comment.

24. Enumerate the steps involved in the planning process.

25. What do you mean by objectives?

66

26. Explain the meaning of policies.

27. What is meant by procedures?

28. What do you mean by methods?

29. What do you mean by rules?

30. What do you mean by programmes?

31. What is meant by budget?

32. Defining 'organizational objectives' is the first step in the process of planning. Explain, in brief, the other steps of this process.

OR Explain the steps involved in the process of planning.

33. Differentiate between procedures and rules.

34. How does planning reduce the risk of uncertainty?

35. A company wants to increase sales; the alternatives may be reducing prices hanging packaging, improving packaging, etc. Which step of planning process relates with the above example?

36. Write anyone difference between policies and procedures.

37. A company needs a detailed plan for its new project? ‘Construction of a Shopping Mall'. What type of plan is it?

38. Give anyone difference between Policy and Rule.

39. "These are general statements that guide thinking and channelise energise towards a particular direction and help in solving routine problems”. Identify the type of plan

40. 'Planning promotes innovative ideas’. Explain?

41. 'Planning focuses on achieving objectives'. Explain.

42. 'Planning is the basic function on of management'. Comment.

43. Why is planning considered as a mental exercise?

44. Give an example each of any three limitations of planning which are beyond the control of an organization.

45. How can (i) Political climate and (ii) Policies of competitors obstruct planning?

46. What do you mean by planning premises?

47. Distinguish between Policies and Rules.

48. 'Though planning is an important tool of management, yet it is not a remedy for all types of problems", Do you agree with this statement? Give any five reasons in support of your answer.

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CHAPTER: ORGANISING 1) Name the organization which is deliberately created? 2) Enumerate the steps in the process of organizing? 3) Organizing helps in optimum utilization of resources. Which type of resources does it refer? 4) Give any one importance of organizing? 5) Divisional structure is more suitable for the firms having several products and each product

has distinct features. Do you agree? 6) Distinguish between functional structure and divisional structure. 7) What are the advantages and disadvantages of divisional structure? 9) Distinguish between formal and informal organizations 10) Which term denotes “The number of subordinates that can be effectively managed by a

superior? 11) What are the elements of delegation of authority? 12) Distinguish between authority and responsibility? 13) “A manager is of the view that he is not responsible for the quality of work that he has

delegated to his subordinate”. Do you agree with his view points? Justify your answer by giving arguments

14) Scope of decentralization of authority is wider than delegation. Why? 15) Distinguish between ‘delegation’ and ‘decentralisation’ of authority on the basis of 16) Name of the function of management which co-ordinates the physical, financial and human

resources and establishes productive relations among them for achievement of specific c goals.

17) Name and explain the two steps in the process o organizing which come after

‘Identification and division of work’ and ‘Departmentalization’.

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18) Organising leads to a systematic allocation of jobs amongst the workforce. Which importance of organizing is stated here? 19) Organising clarifies lines of communication and specifies who is to report to whom.

Mention the importance of organizing indicated here. 20) Aman Ltd. Is manufacturing toys and has production, sales, Purchase and Finance

Departments. Which type of organization structure would you suggest to them? State any three advantages of this organization structure.

21) Hindustan Ltd., is manufacturing computers, soaps and textiles. Which type of

organizational structure would suit the requirements of such organization? State any three advantages of this organization structure.

22) It is a network of personal and social relations not established or required by the formal

organization but arising spontaneously as people associate with one another. Name this organization and give its three advantages.

23) It merely means the granting of authority to subordinates to operate within prescribe limits. Mention the concept referred here. 24) Delegation provides a ready workforce to take up leading positions in new ventures. Which importance of delegation is stated here? 25) “Authority can be delegated but accountability cannot.” Explain the statement. 26) The Marketing Manager of an organization has been asked to achieve a target sales of 100

generators per day. He delegates the task to 10 sales managers working under him. Two of them could not achieve their respective targets. Is the marking manager responsible? Briefly explain the relevant principle in support of your answer.

27) It refers to the systematic delegation of authority from top management to the lower level managers. Mention it. 28) If we delegate the authority we multiply it by two, If we decentralize it, we multiply it by money.

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OBJECTIVE TYPE QUESTIONS

1. What is decrease in supply?

2. What is market equilibrium?

3. State two features of resources that give rise to an economic problem.

4. What is market demand?

5. Why does AFC fall with the increase in output.

6. What is meant by an economic problem?

7. The demand for product x is perfectly inelastic. Its price falls from K 8 to K 6 per unit? What will be the change in the quantity demanded by the Consumer?

8. What happens to the price when the demand for a commodity increases and supply also increases but in a relatively greater proportion?

9. Give the meaning of excess demand for a product?

10. Give two examples of implicit cost?

SHORT ANSWER QUESTIONS

11. The demand for a good doubles due to a 25 percent fall in its price. Calculate its price elasticity of demand.

12. Price elasticity of supply of a commodity is 1. its price rises from K 20 to K 24 per unit and its supply rises by 300 units. calculate its supply at its original price of K 20.

13. Complete the following table: Output TR Price MR

1 6 ---- ----

2 ---- 5 ----

3 ---- ---- 2

14. Complete the following table: Output TC AVC MC

0 24 ---- ----

1 44 ---- ----

2 ---- 15 -----

3 ----- ---- 15

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15. Define a budget line. Explain the reasons responsible for the shift of the Budget Line. Use appropriate diagram.

16. Define an economy. Explain its vital processes.

17. State any three causes responsible for the rightward shift in the demand curve of a commodity?

18. How does the imposition of a unit tax affect the supply curve of a firm?

19. Explain the problem of “What to produce”?

20. Explain why PPC curve is concave to the origin? Under what circumstances the shape of PPC will resemble i) a straight line, ii) convex shape.

21. Explain the relationship between Price and total expenditure

22. Price elasticity of demand of a good is (-)1. At a given price, Gautam buys 60 units of the good. How many units will the consumer buy if the price falls by 10%.

23. Calculate Total Cost and Average Variable Cost of a firm at each given level of output from its cost schedule as given below:

Output (in units) Average Fixed Cost (in K) Marginal Cost (in K) 1 60 32 2 30 30 3 20 28 4 15 30 5 12 35 6 10 43

24. Draw TR and MR of a firm which is free to sell any quantity of the product at a given price. Explain.

25. Explain the implications of single seller under monopoly market and product differentiation under monopolistic market.

26. State the causes of rightward shift in the supply curve and explain any one.

27. Distinguish between Collusive and Non-collusive oligopoly? Explain why the oligopoly firms are interdependent while taking price and output decision? 28. Explain the implications of the following features under Perfect Competition:

a) Large No. of Buyers and sellers. b) Homogeneous Product.

29. Total Revenue is K 400/- when the price of the commodity is K 2/- per unit. When price rises to K 3/- per unit then the quantity supplied increases to 300 units. Calculate Price elasticity of supply using percentage method?

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30. Complete the following table:

Output(in units) Total Cost Average Variable Cost Marginal Cost

1 90 --- 30 2 --- 27 --- 3 --- --- 27 4 180 30 ---

LONG ANSWER QUESTIONS 31. Explain the conditions of consumer equilibrium using indifference curve analysis. 32. In a market the equilibrium price is set below the market price. Using chain of effects explain how will the market attain its equilibrium. 33. In a market the equilibrium price is set above the market price. Using chain of effects explain how will the market attain its equilibrium. 34. When more units of variable factor are combined with the same units of the Fixed factor, explain using diagram and schedule behavior of Total Product and Marginal Product. 35. A Producer is producing at a level of output where MR=MC. If he continues to increase

production Marginal Cost becomes lower than Marginal Revenue. Is the producer at equilibrium. Explain using diagram.

36. Explain the following:

a) Why are Indifference curves convex to the origin? b) Why does a higher indifference curve represent a higher level of satisfaction?

37. For the consumer to be in equilibrium, why must the marginal rate of substitution be equal to the prices of the two goods? 38. Distinguish between Monopoly and Monopolistic Competition? Why AR and MR curves under Monopoly appear to be steeper than Monopolistic Competition. 39. Market for an inferior good is in equilibrium and there is an increase in the income of the

buyers consuming that inferior good? Using chain of effects, explain how will the new equilibrium be reached?

40. Why does the difference between the AC and AVC curves decrease with an increase in the level of output? Can they be equal at some level of output? Explain.

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MySQL

1) What is a Foreign Key Constraint? Can you define multiple foreign key constraints for a

table?

2) What must exist in the parent table before MySQL will allow you to create a Foreign Key constraint from a child table?

3) Which function returns:

a) The length of a string (b) The roundup value of any fractional number

4) How many fields can have i) NOT NULL ii) FOREIGN KEY iii) UNIQUE iv) PRIMARY KEY constraint applied to them?

5) Primary Key of a table can be a. Defined at the time of table creation only. b. Defined after table creation only. c. Can be changed after table creation d. Cannot be changed after table creation

6) In a database there is a table Cabinet. The data entry operator is not able to put NULL in a column of Cabinet? What may be the possible reason(s)?

7) At the time of creation of table X, the data base administrator specified Y as the Primary key. Later on he realized that instead of Y, the combination of column P and Q should have been the primary key of the table. Based on this scenario, answer the following questions: Is it possible to keep Y as well as the combination of P and Q as the primary key? What statement(s) should be entered to change the primary key as per the requirement?

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8)

Write SQL commands for table FURNITURE

ITEMNO ITEMNAME TYPE DATEOFSTOCK PRICE DISCOUNT

INT VARCHAR VARCHAR DATE INT INT 5 20 20 - 6 2

Primary Key Not Null Not Null Default ’10-03-10’ Price < 40,000

-

a). Write a MYSQL Command to create a furniture table including all constraints.

b). Write a MYSQL command to insert data in FURNITURE table as follows. ITEM

NO ITEMNAME TYPE

DATE OF STOCK

PRICE DISCOUNT

1 White lotus Double Bed 2002/02/23 30000 25

2 Pink feather Baby cot 2002/01/02 7000 30

3 Dolphin Baby cot 2004/02/19 9500 7

c). Write a MYSQL command to change TYPE “Rolling Table” of FURNITURE where ITEMNO not more than 3.

d). Write a MYSQL query to Calculate the discount from the specified percentage and PRICE column.

e). Write a MYSQL query to display ITEMANME (in lower case) and DATEOFSTOCK from FURNITURE table.

9) Predict the output of the following: a) SELECT ROUND(124.44) + POW(4,3) ;

b) SELECT LOWER(SUBSTR(TRIM(‘THE JAIN INTERNATIONAL SCHOOL’),4,10));

c) SELECT LEFT(TRIM(‘IPL2010-12MAR’),5);

d) SELECT DAYOFMONTH(“2010-03-04”);

e) SELECT MID(‘ABS Public School’ ,11,8);

f) SELECT SUBSTR(‘INDIA IS GREAT ‘,3,9);

g) SELECT CONCAT(UPPER (‘xiHum’), LOWER(’xiSc’),LOWER(‘xiCom’));

h) SELECT POW(5,5);

i) SELECT TRUNCATE(919.09,2);

j) SELECT CHAR( 70,65,67,69);

k) SELECT LEFT(‘We are’,2), RIGHT(‘here to study’,5);

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10) Consider the following tables ACTIVITY and COACH. Write SQL commands for the following statements.

TABLE: ACTIVITY

Acode Activity Name Stadium Participants

Num Price

Money Schedule Date

1001 Relay 100 x 4 Star Annex 16 10000 2004-4-23

1002 High Jump Star Annex 10 12000 2003-12-3

1003 Shot Put Super Power 12 8000 2004-2-14

1005 Long jump Star Annex 12 9000 2004-01-1

1008 Discuss Throw Super Power 10 15000 2004-03-19

TABLE : COACH

Pcode Name Acode

1 Ahmad Hussain 1001

2 Ravinder 1008

3 Janila 1001

4 Naaz 1003

a) To display the names of all activities with their Acodes in descending order.

b) To display sum of PriceMoney for the Activities played in each of the Stadium separately.

c) To display the coach’s names and Acodes in ascending order of Acode from the table COACH

d) To display the content of all activities for which ScheduleDate is earlier than 01-01-2004 in ascending order of ParticipantsNum.

e) Give the output of the following SQL queries:

1. SELECT COUNT(DISTINCT ParticipantNum) FROM ACTIVITY;

2. SELECT MAX(ScheduleDate), MIN(ScheduleDate) FROM ACTIVITY;

3. SELECT Name, ActivityName FROM ACTIVITY A, COACH C WHERE A.Acode = C.Acode AND A.ParticipantNum = 10;

4. SELECT DISTINCT ParticipantNum FROM ACTIVITY;

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NetBeans

1) Create a Java Desktop Application to find the Discount of an item on the basis of Category of item (Electrical Appliance / Electronic Gadget / Stationary). The Categories will be implemented in J Radio Button controls. The Discount will be calculated as follows:

COST DISCOUNT (%)

<=1000 5

Otherwise 10

The extra Discount will be calculated as follows:

CATEGORY DISCOUNT (%) Electrical Appliance 3

Electrical Gadget 2 Stationary 1

Write the code to display the caption of the first label. Write the code to make the first radio button the default selected option. Disable the discount text field. Calculate the total discount as : Discount on cost +Discount on Category. Calculate the discount amount as : cost * discount. On clicking of Exit Button, it will exit the application after displaying a message of exiting.

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Unit: 1 Planning in sports

What is the meaning & objective of planning?

What do you mean by intramurals?

What is special seeding?

What do you mean by a ‘bye’?

Explain about league tournament.

What is the advantages and disadvantages of knockout tournament?

Explain about any tow specific sports programmes.

Draw a fixture of 13 teams on knockout basis.

Uint: 2 Adventure sports & leadership training

What are adventure sports?

What is camping?

What is rock climbing?

What is good leadership?

Discuss about meaning of conservation of environment in brief.

Enlist the material or requirement for rock climbing.

Mention the three objective of sports adventure.

Unit: 3 Postures

What do you mean by correct posture?

What are the posture deformities?

What is scoliosis?

What is lordosis?

Explain the correct posture of standing

Mention the corrective exercise related to lordosis.

Project: Practical: measurement of muscular strength- Kraus Weber test Draw a diagram of Basket ball field, measurement, history, timing of match, officials, terminology.