OSWAAL BOOKS“Oswaal House” 1/11, Sahitya Kunj, M.G. Road, AGRA-282002Ph.: 0562-2857671, 2527781, Fax : 0562-2854582, 2527784

email : contact@oswaalbooks.com, website : www.oswaalbooks.com

Published by :

with Complete SolutionsQUESTION BANK

Includes Solved Paper (KVS) 2016

CLASS 11

MathematicsStrictly Based on the Latest Syllabus issued by CBSE Board

For

MARCH2017Exam

© Publisher

Oswaal Books

2004

MADHYA PRADESHGWALIOR Krishna Sons, (0751) 2320431INDORE Arun Prakashan, (0731) 2454372, 2459448, 3244544 Akruti Publishing House, (0731) 2456024, 25 Student Book Depot, (0731) 2535892 S.P. & Sons, (0731) 2452680 Akshar Sansar Publisher & Dist., (0731) 2453161BHOPAL UBS Publisher & Dist., 97547535412JABALPUR Sangam General Store, (0761) 2313592, 6538467 Akash Book Distributor, (0761) 4063099KATNI Agrasen Stationers, (07622) 403377REWA Siddharth Enterprises, (07662) 404019UJJAIN Sri Nath Book Depot, (0734) 2556903, 2556902 MAHARASHTRAAHMEDNAGAR Heera Stationers, (0241) 2418774AKOLA Book Emporium, (022) 2436460 Rathi Paper Traders, (0724) 2452679, 2452979AURANGABAD Maya Book Centre, (0240) 2360150BHUSAWAL Anil Book Depot, (02582) 225412CHANDRAPUR Novelty Book Depot, (07172) 277418JALGAON Sharma Book Depot, (0257) 6958794 Vidyadhan Book House, (0257) 2225548KOLHAPUR Jai Book Co., (0231) 2651008MUMBAI Shivam Book & Stationers, (022) 28381014, 28236000 Reshma Agency, (022) 23070853NAVI MUMBAI Krishna Book Store, (022) 27744962, 32980838NAGPUR Novelty Book Depot, (0712) 2534884 Vijay Book Depot, (0712) 2534217, 2520496 Shree Balaji Agency, (0712) 2452361 UBS Publisher & Dist., (0712) 6437909, 2736010 Laxmi Pustakalya, (0712) 2720379NANDED India Book Agencies, 9890489460 Vijay Book Centre, 9872994436PUNE Sai Shubham, (020) 69498635, 9975687687 UBS Publisher & Dist., 9860288838SOLAPUR Mahavir General Store, (0217) 2723405WARDHA Unique Traders, (07152) 243617, 9960644752YAVATMAL Dilip Book Agencies, (07232) 245450 ODISHABHUBANESWAR Sagar Book Store, (0674) 2516040, 2506040 Pragnya Book Store, (0674) 2405757 UBS Publishers & Dist., (0674) 2314446 PUNJABBARNALA Bhaian Di Hatti, (01679) 2321717BHATINDA Janta Book Depot, (0164) 2253993 Krishna Book Depot, (0614) 2237611LUDHIANA Chhabra Book Depot, (0161) 2405427 Amit Book Depot, (0161) 2727038 Bhatia Book Centre, (0161) 2747713 RAJASTHANBHARATPUR Sunil Book Centre, (05644) 233777, 220650BHILWARA Nakoda Book Depot, (01482) 239653JAIPUR Goyal Book Distributors, (0141) 2571673 SIKKIMGANGTOK Kwality Store, (03592) 202992 TAMIL NADUCOIMBATORE UBS Publisher & Dist., (0422) 2499914 Sapna Book House, (0422) 4629999CHENNAI Indian Book House, (044) 24327784 Ruby Books, (044) 26425958 UBS Publisher & Dist., (044) 2374622TRICHY Rasi Publication, (0431) 2703692 TRIPURAAGARTALA Book Corner, (0381) 2301945 UTTAR PRADESHAGRA Ajay Book, (0562) 2254621 Om Pustak Mandir, (0562) 2464014, 3059218ALIGARH Shaligram & Sons, (0571) 2421887ALLAHABAD Mehrotra Book Depot, (0532) 2400129, 2266128AZAMGARH Sasta Sahitya Sadan, (05462) 224421BILASPUR Raj Agencies, 9412150750BALIA Saraswati Shishu, (05498) 221042 Vidya Kendra, 9415281234LUCKNOW VBS Publication, (0522) 4025144 Rama Book Depot (Retail), (0522) 4080133MEERUT Mahi Book Palace, (0121) 2541791, 2649644 Ideal Book Depot, (0121) 2660648NOIDA UBS Publisher & Dist., (0120) 4205516VARANASI Bokaro Student Friends, (0542) 2401250 Gupta Books, (0542) 2413017 WEST BENGALKOLKATA Oriental Publishers, (033) 22191591, 22198367 Saha Book House, (033) 22193671 Eureka Book Emporium, (033) 25934001 Katha–O–Kahani Pvt. Ltd., 22419071, 22196313 Every Book, (033) 22418590SILIGURI Agarwal Book House, (0353) 2535274 Novelty Books, (0353) 2525445

OUR DISTRIBUTORS

CONTENTS

• Syllabus v – viii

• Solved Paper (KVS), 2016 – Agra Region ix – xviii

• Solved Paper (KVS), 2016 – Mumbai Region xix – xxx

• Solved Paper (KVS), 2016 – Guwahati Region xxxi – xl

• Solved Paper (KVS), 2015 9 – 16

1. Sets 1 – 12

2. Relations and Functions 13 – 20

3. Trigonometric Functions 21 – 37

4. Principle of Mathematical Induction 38 – 46

5. Complex Numbers and Quadratic Equation 47 – 57

6. Linear Inequalities 58 – 69

7. Permutations and Combinations 70 – 79

8. Binomial Theorem 80 – 91

9. Sequences and Series 92 – 107

10. Coordinate Geometry 108 – 126

11. Conic Sections 127 – 145

12. Introduction to Three Dimensional Geometry 146 – 150

13. Limits and Derivatives 151 – 163

14. Mathematical Reasoning 164 – 171

15. Statistics 172 – 184

16. Probability 185 – 199

qq

Note : BSM - Board Supplementary Material, NCT - National Capital Territory, KVS - Kendriya Vidyalaya

Sangathan

PREFACE

CBSE always believes in Global Trends of Educational Transformation. The CBSE curriculum gets its lead from National Curriculum Framework – 2005 and Right to Free and Compulsory Education Act – 2009. The aim of CBSE Curriculum is not just to let learners obtain basic knowledge but to make them life-long learners. CBSE always updates and reviews the syllabus to make it more relevant with educational transformation and in last few years the chapters and topics which CBSE has added are very interesting and increase practical knowledge.

Oswaal Question banks are designed to nurture individuality and thus enhance one's innate potentials which help in increasing the self-study mode for students. This book strengthens knowledge and attitude related to subject. It is designed in such a way that students can set their own goals and can improve their problem solving and thinking skills.

The journey of this book is never ending as this book is reviewed every year and new questions, previous year's examination questions, new HOTS or any change in syllabus is updated time to time. Also regular review and reader's feedback increase the efficiency of this book gradually.

Moreover, every Question Bank strictly follows the latest syllabus and pattern, and contains more than sufficient questions and brief description of chapters, which help students in practicing and completing the syllabus. Higher Order Thinking Skills (HOTS) questions, Value Based Questions, Previous Year Questions and Important Questions from NCERT make this book complete and very efficient. Solutions are always checked twice and tried to make precise as per marking scheme. Practically, this book provides students everything they need to learn.

At last we would like to thank our authors, editors, reviewers and specially students who regularly send us suggestions which help in continuous improvement of this book and make this book stand in the category of “One of the Best”. Wish you all Happy Learning.

–Publisher

(iv)

Latest Syllabus for Academic Year 2016-17Course Structure

One Paper Total Hours—Periods of 35 Minutes eachThree Hours Max. Marks. 100

No. Units No. of Periods Marks

I. Sets and Functions 60 29

II. Algebra 70 37

III. Coordinate Geometry 40 13

IV. Calculus 30 06

V. Mathematical Reasoning 10 03

VI. Statistics and Probability 30 12

Total 240 100

*No chapter/unit wise weightage. Care to be taken to cover all the chapters.

Unit-I : Sets and Functions

1. Sets 20 Periods

Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of aset of real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams.Union and Intersection of sets. Difference of sets. Complement of a set. Properties of Complement Sets.

2. Relations & Functions 20 Periods

Ordered pairs, Cartesian product of sets. Number of elements in the cartesian product of two finitesets. Cartesian product of the sets of reals with itself (upto R x R x R). Definition of relation, pictorialdiagrams, domain, co-domain and range of a relation. Function as a special type of relation. Pictorialrepresentation of a function, domain, co-domain and range of a function. Real valued functions,domain and range of these functions; constant, identity, polynomial, rational, modulus, signum,exponential, logarithmic and greatest integer functions, with their graphs. Sum, difference, productand quotient of functions.

3. Trigonometric Functions 20 Periods

Positive and negative angles. Measuring angles in radians and in degrees and conversion from onemeasure to another. Definition of trigonometric functions with the help of unit circle. Truth of theidentity sin2 x + cos2 x=1, for all x. Signs of trigonometric functions. Domain and range of trignometricfunctions and their graphs. Expressing sin (x ± y) and cos (x ± y) in terms of sinx, siny, cosx & cosyand their simple application. Deducing the identities like the following :

tan (x ± y) =

tan tan

1 tan tanx y

x y , cot (x ± y) = cot cot 1

cot cotx yy x

sin ± sin = 2sin12 ( ± ) cos

12 ( )

cos + cos = 2cos12 (+ ) cos

12 (- ),

[ vi ]

cos – cos = – 2sin12 (+ ) sin

12 (- ),

Identities related to sin 2x, cos 2x, tan 2x, sin 3x, cos 3x and tan 3x. General solution of trigonometricequations of the type sin y = sin a, cos y = cos a and tan y = tan a.

Unit-II : Algebra

1. Principle of Mathematical Induction 10 Periods

Process of the proof by induction, motivating the application of the method by looking at naturalnumbers as the least inductive subset of real numbers. The principle of mathematical induction andsimple applications.

2. Complex Numbers and Quadratic Equations 15 Periods

Need for complex numbers, especially 1? , to be motivated by inability to solve some of the quardraticequations. Algebraic properties of complex numbers. Argand plane and polar representation of complexnumbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations (with realcoefficients) in the complex number system. Square root of a complex number.

3. Linear Inequalities 15 Periods

Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representationon the number line. Graphical representation of linear inequalities in two variables. Graphical methodof finding a solution of system of linear inequalities in two variables.

4. Permutations and Combinations 10 Periods

Fundamental principle of counting. Factorial n. (n!)Permutations and combinations, derivation offormulae for

rpn and rcn and their connections, simple applications.

5. Binomial Theorem 10 Periods

History, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle,General and middle term in binomial expansion, simple applications.

6. Sequence and Series 10 Periods

Sequence and Series. Arithmetic Progression (A.P.). Arithmetic Mean (A.M.) Geometric Progression(G.P.), general term of a G.P., sum of first n terms of a G.P., infinite G.P. and its sum, geometric mean(G.M.), relation between A.M. and G.M. Formula for the following special sum.

2 3

1 1 1, and

n n n

k k kk k k

Unit-III : Coordinate Geometry1. Straight Lines 10 Periods

Brief recall of two dimensional geometry from earlier classes. Shifting of origin. Slope of a line andangle between two lines. Various forms of equations of a line: parallel to axis, point-slope form, slope-intercept form, two-point form, intercept form and normal form. General equation of a line. Equationof family of lines passing through the point of intersection of two lines. Distance of a point from aline.

2. Conic Sections 20 PeriodsSections of a cone: circles, ellipse, parabola, hyperbola a point, a straight line and a pair ofintersecting lines as a degenerated case of a conic section. Standard equations and simple propertiesof parabola, ellipse and hyperbola. Standard equation of a circle.

[ vii ]

3. Introduction to Three–dimensional Geometry 10 PeriodsCoordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance betweentwo points and section formula.

Unit-IV : Calculus1. Limits and Derivatives 30 Periods

Derivative introduced as rate of change both as that of distance function and geometrically.Intutive idea of limit. Limits of polynomials and rational functions, trignometric, exponential andlogarithmic functions. Definition of derivative, relate it to slope of tangent of a curve, Derivative ofsum, difference, product and quotient of functions. Derivative of polynomial and trignometricfunctions.

Unit-V : Mathematical Reasoning1. Mathematical Reasoning 10 Periods

Mathematically acceptable statements. Connecting words/phrases - consolidating the understandingof “if and only if (necessary and sufficient) condition”, “implies”, “and/or”, “implied by”, “and”, “or”,“there exists” and their use through variety of examples related to real life and Mathematics. Validat-ing the statements involving the connecting words, Difference between contradiction, converse andcontrapositive.

Unit-VI : Statistics and Probability1. Statistics 15 Periods

Measures of dispersion: Range, mean deviation, variance and standard deviation of ungrouped/grouped data. Analysis of frequency distributions with equal means but different variances.

2. Probability 15 PeriodsRandom experiments; outcomes, sample spaces (set representation). Events; occurrence of events,‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Axiomatic (set theoretic)probability, connections with theories studied in earlier classes. Probability of an event, probabilityof ‘not’, ‘and’ and ‘or’ events.

[ viii ]

Mathematics (Code No. 041)

Question Paper DesignClass XI (2016-17)

Time : 3 Hours Max. Marks. 100

S. Typology of Questions Very Long Long Marks %No. Short Answer I Answer Weightage

Answer (4 marks) II(1 marks) (6 marks)

1. Remembering-(Knowledge based Simplerecall questions, to know specific facts,terms, concepts, principles, or theories, 2 3 1 2 0 20%Identify, define, or recite, information)

2. Understanding-(Comprehension to befamiliar with meaning and to understand 2 2 2 2 2 22%conceptually, interpret, compare, contrast,explain, paraphrase information)

3. Application (Use abstract information inconcrete situation, to apply knowledge to 1 4 2 2 9 29%new situations, Use given content tointerpret a situation, provide an example,or solve a problem)

4. High Order Thinking Skills (Analysis& Synthesis- Classify, compare, contrast,or differentiate between different pieces of 1 2 1 1 5 15%information, Organize and/or integrateunique pieces of information from a varietyof sources)

5. Evaluation -(Appraise, judge, and/orjustify the value or worth of a decision – 1+1 1 1 4 14%or outcome, or to predict outcomes based (Valueon values) based)

TOTAL 6x1=6 13x4=52 7x6=42 100 100%

QUESTION WISE BREAK UP

Type of Question Mark per Question Total No. of Questions Total Marks

VSA 1 6 06

LA-I 4 13 52

LA-II 6 7 42

Total 26 100

1. No chapter wise weightage. Care to be taken to cover all the chapters.2. The above template is only a sample. Suitable internal variations may be made for generating similar templates

keeping the overall weightage to different form of questions and typology of questions same.

KENDRIYA VIDYALAYA SANGATHAN[AGRA REGION]

SESSION ENDING EXAMINATION 2016SUBJECT : MATHEMATICS

CLASS–XI(SOLVED PAPER)

Time : 3 Hrs. M.M. : 100

Instructions : 1. All questions are compulsory. 2. The question paper consists of 26 questions divided into three sections A, B and C. Section A comprises of 6 questions

of one mark, Section B comprises of 13 questions of four marks each and Section C comprises of 7 questions of six marks each.

3. All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the questions. 4. There is no overall choice. However internal choice has been provided in 4 questions of 4 marks each and 2 questions of 6

marks each. You have to attempt only one of the alternatives in all such questions. 5. Use of calculator is not permitted. You may ask for logarithmic tables, if required.

SECTION A 1. Write the set {3, 9, 27, 81} in set builder form. 1

2. Find the fourth term in the expansion of 7

21

–xx

1

3. Find the centre of the circle x2 + y2 + 2y = 0 1 4. Write the negation of following statement 1 "There exists a capital for every state in India." 5. Write the converse of following statement 1 'If you live in Agra, then you have winter clothes." 6. Write the contrapositive of following statement 1 "If x is a prime number, then x is odd."

SECTION B 7. Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9. 4 8. Let N be the set of all natural numbers and let R be the relation defined by {(a, b) : a, b ∈N and 2a + b = 10} Find (i) R in Roster form (ii) Domain of R (iii) Range of R (iv) co-domain of R. 4

9. Prove that (cosx + cosy)2 + (sinx – siny)2 = 4 cos2

2x y+

4

10. Let A = {1, 2, 3}, B = {3, 5} and C = {4, 5, 6}. Find (i) A × (B ∩ C) (ii) (A × B) ∩ (A × C) 4 11. Find the Square root of complex number 3 – 4i 4

OR

Convert complex number – 3 + i in polar form. 12. Find the general solution of the equation cot q + 3 tan q = 5 cosec q 4

OR

If, A + B + C = p, then prove that; sin sin (B – C)sin (B + C) =

2 2

2( – )b c

a

13. Find the number of arrangements of the letters of the word INDEPENDENCE. In how many of these arrangements 4

(i) Do all the vowels always occur together ? (ii) Do all the words begin with I and end in P.

Oswaal CBSE Question Bank WithComplete Solutions for Class 11Mathematics (For 2017 Exams)

Publisher : Oswaal Books ISBN : 9789351278221 Author : Panel Of Experts

Type the URL : http://www.kopykitab.com/product/7988

Get this eBook

51%OFF