QUESTION BANK. with Complete Solutions CLASS 11. Mathematics. Strictly Based on the Latest Syllabus issued by CBSE Board. For.

Size: px

Start display at page:

Download "QUESTION BANK. with Complete Solutions CLASS 11. Mathematics. Strictly Based on the Latest Syllabus issued by CBSE Board. For."

Theodore Hood
5 years ago
Views:

2 QUESTION BANK with Complete Solutions CLASS 11 Mathematics Strictly Based on the Latest Syllabus issued by CBSE Board For MARCH 017 Exam Includes Solved Paper (KVS) 016 Published by : OSWAAL BOOKS Oswaal House 1/11, Sahitya Kunj, M.G. Road, AGRA-800 Ph.: , 57781, Fax : , contact@oswaalbooks.com, website :

3 OUR DISTRIBUTORS MADHYA PRADESH GWALIOR Krishna Sons, (0751) INDORE Arun Prakashan, (0731) 45437, , Akruti Publishing House, (0731) 45604, 5 Student Book Depot, (0731) S.P. & Sons, (0731) Akshar Sansar Publisher & Dist., (0731) BHOPAL UBS Publisher & Dist., JABALPUR Sangam General Store, (0761) 31359, Akash Book Distributor, (0761) KATNI Agrasen Stationers, (076) REWA Siddharth Enterprises, (0766) UJJAIN Sri Nath Book Depot, (0734) , MAHARASHTRA AHMEDNAGAR Heera Stationers, (041) AKOLA Book Emporium, (0) Rathi Paper Traders, (074) 45679, AURANGABAD Maya Book Centre, (040) BHUSAWAL Anil Book Depot, (058) 541 CHANDRAPUR Novelty Book Depot, (0717) JALGAON Sharma Book Depot, (057) Vidyadhan Book House, (057) 5548 KOLHAPUR Jai Book Co., (031) MUMBAI Shivam Book & Stationers, (0) , Reshma Agency, (0) NAVI MUMBAI Krishna Book Store, (0) , NAGPUR Novelty Book Depot, (071) Vijay Book Depot, (071) 53417, Shree Balaji Agency, (071) UBS Publisher & Dist., (071) , Laxmi Pustakalya, (071) NANDED India Book Agencies, Vijay Book Centre, PUNE Sai Shubham, (00) , UBS Publisher & Dist., SOLAPUR Mahavir General Store, (017) WARDHA Unique Traders, (0715) 43617, YAVATMAL Dilip Book Agencies, (073) ODISHA BHUBANESWAR Sagar Book Store, (0674) , Pragnya Book Store, (0674) UBS Publishers & Dist., (0674) PUNJAB BARNALA Bhaian Di Hatti, (01679) BHATINDA Janta Book Depot, (0164) Krishna Book Depot, (0614) LUDHIANA Chhabra Book Depot, (0161) Amit Book Depot, (0161) Bhatia Book Centre, (0161) RAJASTHAN BHARATPUR Sunil Book Centre, (05644) 33777, 0650 BHILWARA Nakoda Book Depot, (0148) JAIPUR Goyal Book Distributors, (0141) SIKKIM GANGTOK Kwality Store, (0359) 099 TAMIL NADU COIMBATORE UBS Publisher & Dist., (04) Sapna Book House, (04) CHENNAI Indian Book House, (044) Ruby Books, (044) UBS Publisher & Dist., (044) 3746 TRICHY Rasi Publication, (0431) TRIPURA AGARTALA Book Corner, (0381) UTTAR PRADESH AGRA Ajay Book, (056) 5461 Om Pustak Mandir, (056) , ALIGARH Shaligram & Sons, (0571) ALLAHABAD Mehrotra Book Depot, (053) 40019, 6618 AZAMGARH Sasta Sahitya Sadan, (0546) 441 BILASPUR Raj Agencies, BALIA Saraswati Shishu, (05498) 104 Vidya Kendra, LUCKNOW VBS Publication, (05) Rama Book Depot (Retail), (05) MEERUT Mahi Book Palace, (011) , Ideal Book Depot, (011) NOIDA UBS Publisher & Dist., (010) VARANASI Bokaro Student Friends, (054) Gupta Books, (054) WEST BENGAL KOLKATA Oriental Publishers, (033) , Saha Book House, (033) Eureka Book Emporium, (033) Katha O Kahani Pvt. Ltd., , Every Book, (033) SILIGURI Agarwal Book House, (0353) Novelty Books, (0353) Publisher Oswaal Books 004

4 CONTENTS Syllabus v viii Solved Paper (KVS), 016 Agra Region ix xviii Solved Paper (KVS), 016 Mumbai Region xix xxx Solved Paper (KVS), 016 Guwahati Region xxxi xl Solved Paper (KVS), Sets 1 1. Relations and Functions Trigonometric Functions Principle of Mathematical Induction Complex Numbers and Quadratic Equation Linear Inequalities Permutations and Combinations Binomial Theorem Sequences and Series Coordinate Geometry Conic Sections Introduction to Three Dimensional Geometry Limits and Derivatives Mathematical Reasoning Statistics Probability Note : BSM - Board Supplementary Material, NCT - National Capital Territory, KVS - Kendriya Vidyalaya Sangathan

5 PREFACE CBSE always believes in Global Trends of Educational Transformation. The CBSE curriculum gets its lead from National Curriculum Framework 005 and Right to Free and Compulsory Education Act 009. 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)

6 Latest Syllabus for Academic Year Course Structure One Paper Total Hours Periods of 35 Minutes each Three Hours Max. Marks. 100 No. Units No. of Periods Marks I. Sets and Functions 60 9 II. Algebra III. Coordinate Geometry IV. Calculus V. Mathematical Reasoning VI. Statistics and Probability 30 1 Total *No chapter/unit wise weightage. Care to be taken to cover all the chapters. Unit-I : Sets and Functions 1. Sets 0 Periods Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of a set 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.. Relations & Functions 0 Periods Ordered pairs, Cartesian product of sets. Number of elements in the cartesian product of two finite sets. Cartesian product of the sets of reals with itself (upto R x R x R). Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Function as a special type of relation. Pictorial representation 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, product and quotient of functions. 3. Trigonometric Functions 0 Periods Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin x + cos x=1, for all x. Signs of trigonometric functions. Domain and range of trignometric functions and their graphs. Expressing sin (x ± y) and cos (x ± y) in terms of sinx, siny, cosx & cosy and their simple application. Deducing the identities like the following : tan (x ± y) = tan x tan y 1 tan x tan y, cot (x ± y) = cot x cot y 1 cot y cot x sin ± sin = sin 1 ( ± ) cos 1 ( ) cos + cos = cos 1 ( + ) cos 1 ( - ),

7 cos cos = sin 1 ( + ) sin 1 ( - ), Identities related to sin x, cos x, tan x, sin 3x, cos 3x and tan 3x. General solution of trigonometric equations 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 natural numbers as the least inductive subset of real numbers. The principle of mathematical induction and simple applications.. Complex Numbers and Quadratic Equations 15 Periods Need for complex numbers, especially? 1, to be motivated by inability to solve some of the quardratic equations. Algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations (with real coefficients) 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 representation on the number line. Graphical representation of linear inequalities in two variables. Graphical method of 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 of formulae for n and n and their connections, simple applications. p r c r 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. n n n 3, and k k k k 1 k 1 k 1 Unit-III : Coordinate Geometry 1. Straight Lines 10 Periods Brief recall of two dimensional geometry from earlier classes. Shifting of origin. Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axis, point-slope form, slopeintercept form, two-point form, intercept form and normal form. General equation of a line. Equation of family of lines passing through the point of intersection of two lines. Distance of a point from a line.. Conic Sections 0 Periods Sections of a cone: circles, ellipse, parabola, hyperbola a point, a straight line and a pair of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle. [ vi ]

8 3. Introduction to Three dimensional Geometry 10 Periods Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula. Unit-IV : Calculus 1. 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 and logarithmic functions. Definition of derivative, relate it to slope of tangent of a curve, Derivative of sum, difference, product and quotient of functions. Derivative of polynomial and trignometric functions. Unit-V : Mathematical Reasoning 1. Mathematical Reasoning 10 Periods Mathematically acceptable statements. Connecting words/phrases - consolidating the understanding of 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. Validating the statements involving the connecting words, Difference between contradiction, converse and contrapositive. Unit-VI : Statistics and Probability 1. 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.. Probability 15 Periods Random 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, probability of not, and and or events. [ vii ]

9 Mathematics (Code No. 041) Question Paper Design Class XI (016-17) 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 Simple recall questions, to know specific facts, terms, concepts, principles, or theories, % Identify, define, or recite, information). Understanding-(Comprehension to be familiar with meaning and to understand % conceptually, interpret, compare, contrast, explain, paraphrase information) 3. Application (Use abstract information in concrete situation, to apply knowledge to % new situations, Use given content to interpret 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 % information, Organize and/or integrate unique pieces of information from a variety of sources) 5. Evaluation -(Appraise, judge, and/or justify the value or worth of a decision % or outcome, or to predict outcomes based (Value on values) based) TOTAL 6x1=6 13x4=5 7x6= % QUESTION WISE BREAK UP Type of Question Mark per Question Total No. of Questions Total Marks VSA LA-I LA-II Total No chapter wise weightage. Care to be taken to cover all the chapters.. 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. [ viii ]

10 KENDRIYA VIDYALAYA SANGATHAN [AGRA REGION] SESSION ENDING EXAMINATION 016 SUBJECT : MATHEMATICS CLASS XI (SOLVED PAPER) Time : 3 Hrs. M.M. : 100 Instructions : 1. All questions are compulsory.. The question paper consists of 6 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 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, 7, 81} in set builder form. 1. Find the fourth term in the expansion of x x Find the centre of the circle x + y + y = 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 (, ) and cutting off intercepts on the axes whose sum is Let N be the set of all natural numbers and let R be the relation defined by {(a, b) : a, b N and a + b = 10} Find (i) R in Roster form (ii) Domain of R (iii) Range of R (iv) co-domain of R Prove that (cosx + cosy) + (sinx siny) = 4 cos x+ y 10. Let A = {1,, 3}, B = {3, 5} and C = {4, 5, 6}. Find (i) A (B C) (ii) (A B) (A C) Find the Square root of complex number 3 4i 4 OR Convert complex number 3 + i in polar form. 1. 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) = ( 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. 1 4

11 Oswaal CBSE Question Bank With Complete Solutions for Class 11 Mathematics (For 017 Exams) 51% OFF Publisher : Oswaal Books ISBN : Author : Panel Of Experts Type the URL : Get this ebook

OSWAAL CBSE Strictly Based on Latest Syllabus Issued by CBSE for 2017 Examination SAMPLE QUESTION PAPERS CLASS 10 TERM 1 SEPTEMBER 2016 EXAMINATION

OSWAAL CBSE Strictly Based on Latest Syllabus Issued by CBSE for 2017 Examination SAMPLE QUESTION PAPERS CLASS 10 TERM 1 SEPTEMBER 2016 EXAMINATION SCIENCE *Solutions for SQP 6-10 can be downloaded from