SAMPLE PAPERS MATHEMATICS

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$Inner Math XII BW 05 Final.ps D:\Vashist System-Data\Vashist\Final 04-5\MBD\Sample Paper 04-5\MBD S.P. Mathematics-XII (E)-04-5\Prilim page\inner Math XII BW 03 Final.$ 35406 RS VE CO 04 ERS AP D P ED) R A V BO (SOL Sure Shot CBSE SAMPLE PAPERS d e v l So MATHEMATICS CLASS XII 05 MALHOTRA BOO DEPOT An ISO 900:008 Certified Company MBD House, Gulab

35406 RS VE CO 04 ERS AP D P ED) R A V BO (SOL Sure Shot CBSE SAMPLE PAPERS d e v l So MATHEMATICS CLASS XII 05 MALHOTRA BOO DEPOT An ISO 900:008 Certified Company MBD House, Gulab

2 Inner Math XII BW 05 Final.ps D:\Vashist System-Data\Vashist\Final 04-5\MBD\Sample Paper 04-5\MBD S.P. Mathematics-XII (E)-04-5\Prilim page\inner Math XII BW 03 Final.cdr Friday, July 8, 04 3:00:37 PM Color profile: Disabled Composite 50 lpi at 45 degrees Regd. Trade Mark No RS VE CO 04 ERS AP D P ED) R A V BO (SOL Sure Shot CBSE SAMPLE PAPERS d e v l So MATHEMATICS CLASS XII 05 MALHOTRA BOO DEPOT An ISO 900:008 Certified Company MBD House, Gulab Bhawan, 6, Bahadur Shah Zafar Marg, New Delhi-000 MB 6, Street No. 4, Shakarpur Delhi-009 Ph.: 58, MBD House, 4587/5, Opp. Times of India, Daryaganj, New Delhi-000 Ph.: Plot No. 5, Industrial Area, Patparganj, Delhi-009 Ph.: 4969, ewy; Price 90.00

3 OUR ADDRESSES IN INDIA New Delhi : MBD House, Gulab Bhawan, 6, Bahadur Shah Zafar Marg Ph , Mumbai : A-683, T.T.C. Industrial Area, M.I.D.C. Off. Thane-Belapur Road, Navi Mumbai Ph , 77808, Chennai : No. 6 B/ SIDCO Estate, North Phase, Pataravakkam, Ambattur Industrial Estate, Ambattur Ph , Chennai : 5A, Ground Floor, Tiruvenkatapuram, st Street, Near Nungambakkam Railway Station, Choolaimedu Ph olkata : Satyam Building, 46-D, Rafi Ahmed idwai Marg Ph , 6670 Jalandhar City : MBD House, Railway Road Ph , , Bengaluru : 4/3, st Main, Industrial Town (Near Chowdeshwari alyan Mantap), West of Chord Road, Rajajinagar Ph , Hyderabad : , Varun Towers, Barkatpura Ph , Ernakulam : Surabhi Building, South Janatha Road, Palarivattom Ph , Pune : aul Building No., IInd Floor, Flat C, Guru Nanak Nagar, Shankar Sheth Road Ph , Nagpur : Near N.I.T. Swimming Pool, North Ambazari Road, Ambazari Layout Ph. 4804, 4806, 48649, Ahmedabad : Godown No. 0, Vedant Prabha Estate, Opp. ONGC Pumping Station, Sarkhej Sanand Road, Sarkhej Ph Cuttack : Badam Bari, Link Road Ph , 36779, 3303 Guwahati : Chancellor Commercial, Hem Baruah Road, Paan Bazar Ph. 5049, Lucknow : 73/5, Dr. B. N. Verma Road, Old 30 utchery Road Ph , Patna : Ist Floor, Annapurna Complex, Naya Tola Ph. 6773, , 6647 Bhopal : Plot No. 37, 38, 39, Sector-, Special Industrial Area, Govindpura Ph , Jabalpur : 840, Palash Chamber, Malviya Chowk Ph Goa : H. No. 93, Plot No. 66, ranti Nagar (Behind Azad Bhawan), Alto Porvorim, Bardez Ph. 4398, Jaipur : G-, artarpura Industrial Area, Baees Godown Ph. 058, 059 Raipur : Behind ailash Provision Store, Ravi Nagar Ph , 454 arnal : Plot No. 03, Sector-3, HSIDC, Near Namaste Chowk, Opp. New World Ph. 0006, 0009 Shimla (H.P.) : C-89, Sector-I, New Shimla-9 Ph. 670,67068 Jammu (J&) : MBD Office, 48 Gurjjar Colony, C/o Gurjar Desh Charitable Trust, N.H. Bye Pass Road Ph , Ranchi (Jharkhand) : Shivani Complex, nd Floor, Jyoti Sangam Lane, Upper Bazar Ph Sahibabad (U.P.) : B-9 & 0, Site IV, Industrial Area Ph , Dehradun (Uttarakhand) : Plot No. 37, Bhagirathipuram Niranjanpur, GMS Road Ph , 074 DELHI LOCAL OFFICES : Delhi (Shakarpur) : MB 6, Street No. 4 Ph , 58 Delhi (Daryaganj) : MBD House, 4587/5, Opp. Times of India Ph Delhi (Patparganj) : Plot No. 5, Industrial Area Ph. 4969, We are committed to serve students with best of our knowledge and resources. We have taken utmost care and attention while editing and printing this book but we would beg to state that Authors and Publishers should not be held responsible for unintentional mistake that might have crept in. However, errors brought to our notice shall be gratefully acknowledged and attended to. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise without the prior written permission of the publisher. Any breach will entail legal action and prosecution without further notice. Published by : Printed at : MALHOTRA BOO DEPOT MBD House, Railway Road, Jalandhar M. GULAB SINGH & SONS (P) LTD. B-5/4 Site IV, Industrial Area, Sahibabad (U.P.) Address Page-0x30=8(04).9.04.pmd 9//04, 0:5 AM

MATHEMATICS XII (04-5) One Paper Three Hours Marks : 00 Units No. of Periods Marks I. RELATIONS AND FUNCTIONS 30 0 II. ALGEBRA 50 3 III. CALCULUS 80 44 IV.

4 MATHEMATICS XII (04-5) One Paper Three Hours Marks : 00 Units No. of Periods Marks I. RELATIONS AND FUNCTIONS 30 0 II. ALGEBRA 50 3 III. CALCULUS IV. VECTORS AND THREE-DIMENSIONAL GEOMETRY 30 7 V. LINEAR PROGRAMMING 0 6 VI. PROBABILITY 30 TOTAL UNIT I : RELATIONS AND FUNCTIONS. Relations and Functions : (5 Periods) Types of relations : reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations.. Inverse Trigonometric Functions : (5 Periods) Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions. UNIT II : ALGEBRA. Matrices : (5 Periods) Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric and skew-symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication. Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order ). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists ; (Here all matrices will have real entries).. Determinants : (5 Periods) Determinant of a square matrix (up to 3 3 matrices), properties of Syllabus 05.pmd 9//04, 6:53 PM

5 determinants, minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix. UNIT III : CALCULUS. Continuity and Differentiability : (0 Periods) Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives. Rolle s and Lagrange s Mean Value Theorems (without proof) and their geometric interpretation.. Applications of Derivatives : (0 Periods) Applications of derivatives : rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations). 3. Integrals : (0 Periods) Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts. Evaluation of simple integrals of the following type and problems based on them: dx dx dx dx dx,,,, x ± a ax bx c x ± a a x + + ax + bx+ c px + q px + q dx, dx, a ± x dx, x a dx ax + bx + c ax + bx + c ax bx c dx, ( px q) ax bx c dx Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals. 4. Applications of the Integrals : (5 Periods) Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only). Area between the two above said curves (the region should be clearly identifiable). Syllabus 05.pmd 9//04, 6:53 PM

6 5. Differential Equations : (5 Periods) Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations of first order and first degree by method of separation of variables of homogeneous differential equations. Solutions of linear differential equation of the form : dy py q dx + =, where p and q are functions of x or constant dx dy + px = q, where p and q are functions of y or constant. UNIT IV : VECTORS AND THREE-DIMENSIONAL GEOMETRY. Vectors : (5 Periods) Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties and applications of scalar (dot) product of vectors, vector (cross) product of vectors, scalar triple product of vectors, projection of a vector on a line.. Three-dimensional Geometry : (5 Periods) Direction cosines and direction ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane. Angle between (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a point from a plane. UNIT V : LINEAR PROGRAMMING. Linear Programming : (0 Periods) Introduction, related terminology such as constraints, objective function, optimization. Different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints). UNIT VI : PROBABILITY. Probability : (30 Periods) Conditional probability, multiplication theorem on probability, Independent events, total probability, Baye s theorem, Random variable and its probability distribution, mean and variance of a random variable. Repeated independent (Bernoulli) trials and Binomial distribution. Syllabus 05.pmd 3 9//04, 6:53 PM

7 MATHEMATICS (CODE NO. 04) QUESTION PAPER DESIGN CLASS-XII (04-5) Time-3 Hours Max. Marks-00 S. Learning Very Short Long Long % No. TYPOLOGY OF QUESTIONS outcomes Answer Answer-I Answer-II Marks Weightage and testing ( mark) (4 marks) (6 marks) 3 4 Remembering (nowledge 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). 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) 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) competencies 3 0 0% 6 6% 3 5 5% % % Evaluation and Multi-Disciplinary (Appraise, judge, and/or justify the value or worth of a decision or outcome, or to predict outcomes based on values) Reasoning Analytical Skills Critical thinking Derivative (values based) Total 6 = = = % Questions Paper Designs 04-5(Maths-XII).pmd 9//04, 7:0 PM

8 CONTENTS CBSE Question Papers 04 (Delhi) Solved 35 CBSE Question Papers 04 (Outside Delhi) Solved CBSE Question Papers 03 (Delhi) Solved 3 CBSE Question Papers 03 (Outside Delhi) Solved 33 6 CBSE Question Papers 0 (Delhi) Solved 30 CBSE Question Papers 0 (Outside Delhi) Solved 3 58 Fast Track Revision F- F- Other Sample Papers (Solved) 3 MBD Sample Question Paper MBD Sample Question Paper 45 MBD Sample Question Paper MBD Sample Question Paper MBD Sample Question Paper Model Question Papers for Practice Model Question Paper Model Question Paper Model Question Paper 3 Model Question Paper 4 Model Question Paper 5 Model Question Paper 6 Model Question Paper 7 Model Question Paper 8 Model Question Paper 9 Model Question Paper 0 Model Question Paper Model Question Paper M- M-4 M-5 M-8 M-9 M-3 M-4 M-7 M-8 M- M- M-5 M-6 M-9 M-30 M-33 M-34 M-37 M-38 M-4 M-4 M-45 M-46 M-49 Contents 05.pmd 7/8/04, : AM

9 Model Question Paper 3 Model Question Paper 4 Model Question Paper 5 Model Question Paper 6 Model Question Paper 7 Model Question Paper 8 Model Question Paper 9 Model Question Paper 0 M-50 M-53 M-54 M-57 M-58 M-6 M-6 M-65 M-66 M-69 M-70 M-73 M-74 M-77 M-78 M-8 Contents 05.pmd 7/8/04, : AM

10 C.B.S.E. QUESTION PAPERS 04 (SOLVED) MATHEMATICS CLASS XII (C.B.S.E.) (DELHI) Series : OSR / Code No. 65 / / Time Allowed : 3 Hours Maximum Marks : 00 General Instructions:. All questions are compulsory.. The question paper consists of 9 questions divided into three sections A, B and C. Section A comprises of 0 questions of one mark each, section B comprises of questions of four marks each and section C comprises of 07 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 question. 4. There is no overall choice. However, internal choice has been provided in 04 questions of four marks each and 0 questions of six 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. SET I SECTION A (Question numbers to 0 carry mark each). Let '*' be a binary operation on the set of all non-zero real numbers, given by ab a * b = for all a, b R {0}. Find the value of x, given that * (x * 5) = 0. 5 Answer. x = 5. Solution. * (x * 5) = 0 * ( x)(5) 0 5 ()( x) * x = x = 50. Hence, x = 5. Sample Paper.p65 7/6/4, 8:3 AM

11 MBD Sample Paper Math CBSE (English Medium) 40% OFF Publisher : MBD Group Publishers ISBN : Author : Panel Of Experts Type the URL : Get this ebook

All Questions of. JEE-Main 2016 Included. Joint Entrance Examination (Main) (All India Common Engineering Entrance Test)

All Questions of. JEE-Main 2016 Included. Joint Entrance Examination (Main) (All India Common Engineering Entrance Test) All Questions of JEE-Main 06 Included PART II Joint Entrance Eamination (Main) (All India Common Engineering Entrance Test) By J.P. Mohindru (Author of Modern's abc + of Mathematics Series) & Bharat Mohindru