SAMPLE QUESTION PAPERS CLASS 12 MARCH 2017 EXAMINATION

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2 OSWAAL CBSE Strictly Based on Latest Syllabus Issued by CBSE for 2017 Examination SAMPLE QUESTION PAPERS CLASS 12 MARCH 2017 EXAMINATION Strictly designed as per the latest CBSE notification Circular No. Acad-32/2016 dated MATHEMATICS *SolutionsforSQP6-10canbedownloaded fromwww.oswaalbooks.com Published by : OSWAAL BOOKS 1/11, Sahitya Kunj, M.G. Road, Agra (UP) India , , contact@oswaalbooks.com

3 ANDAMAN & NICOBAR PORT BLAIR Mitali Enterprises, (03192) Kumar General Store, ANDHRA PRADESH GUNTOOR Y. Renuka Devi, (0863) HYDERABAD Himalaya Book World, (040) , UBS Publisher & Dist., VIJAYAWADA Sri Kanka Durga Book Stall, Vijaysai Book Centre, (0866) VISHAKHAPATNAM Sri Rajeshwari Book Link, (891) ASSAM BONGAIGAON Raju Pustak Sadan, (03664) GUWAHATI Book Emporium, Manika Books, UBS Publisher, BIHAR MUNGER New Aman Book & Stationers, (06344) MUZAFFARPUR Pustak Bhandar, PATNA Gyan Ganga, (0612) , Nova Publisher & Distributors, (0612) UBS Publisher, Shri Durga Pustak Mandir, (0612) Vikas Book Depot, (0612) Sharda Pustak Bhandar, (0612) Bokaro Student Friends, PURNEA Chaurasia Book Centre, CHATTISGARH DURG Bhagwati Bhawani Book Depot, (0788) RAIPUR Shri Ramdev Traders, (0771) DELHI DELHI Mittal Books, (011) Prozo (Global Educa Share Pvt. Ltd) R.D. 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Publishers, (0495) , THRISSUR Minerva Books, (0457) TRIVANDRUM Acedemic Book House, (0471) H & C Store, (0471) OUR DISTRIBUTORS MADHYA PRADESH GWALIOR Krishna Sons, (0751) INDORE Arun Prakashan, (0731) , , Student Book Depot, (0731) BHOPAL UBS Publisher & Dist., JABALPUR Akash Book Distributor, (0761) Vinay Pustak Sadan, (0761) KATNI Agrasen Stationers, (07622) REWA Siddharth Enterprises, (07662) MAHARASHTRA AHMEDNAGAR Heera Stationers, (0241) AKOLA Harney Book Depot, Rathi Paper Traders, (0724) , AMRAVATI Delta Pen House, (0721) AURANGABAD Aarti Book Centre, (0240) Maya Book Centre, (0240) BHUSAWAL Anil Book Depot, (02582) CHANDRAPUR Novelty Book Depot, (07172) KOLHAPUR Jai Book Co., (0231) MUMBAI Shivam Book & Stationers, (022) , Reshma Agency, (022) NAVI MUMBAI Krishna Book Store, (022) , NAGPUR Laxmi Pustakalya, (0712) Novelty Book Depot, (0712) Renuka Book Distributor, Shree Balaji Agency, (0712) UBS Publisher & Dist., (0712) , Vijay Book Depot, (0712) , NANDED India Book Agencies, Maheshwari General & Gift Centre, Vijay Book Centre, PUNE New Venture Natraj Book Shop, (020) Sai Shubham, (020) , UBS Publisher & Dist., SANGLI G. 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Tamhankar Books, (0233) SOLAPUR Mahavir General Store, (0217) WARDHA Unique Traders, (07152) , YAVATMAL Dilip Book Agencies, (07232) ODISHA BHUBANESWAR Sagar Book Store, (0674) , UBS Publishers & Dist., (0674) PUNJAB BARNALA Bhaian Di Hatti, (01679) Nav Chetan Book, (01679) BHATINDA Janta Book Depot, (0164) LUDHIANA Amit Book Depot, (0161) Bhatia Book Centre, (0161) RAJASTHAN BHARATPUR Sunil Book Centre, (05644) , BHILWARA Nakoda Book Depot, (01482) JAIPUR Goyal Book Distributors, (0141) Saraswati Book House, (0141) TAMIL NADU COIMBATORE CBSE Book Shop, (0422) UBS Publisher & Dist., (0422) Sapna Book House, (0422) CHENNAI Indian Book House, (044) Ravi Book House, (044) Ruby Books, (044) UBS Publisher & Dist., (044) PONDICHERRY Sri Laxmi Book Stall, TRICHY Rasi Publication, (0431) TRIPURA AGARTALA Balaji Book House, Book Corner, (0381) UTTAR PRADESH AGRA Ajay Book, (0562) Govind Book Shopee, (0562) Manav Book Dist., (0562) , Om Pustak Mandir, (0562) , ALIGARH Shaligram & Sons, (0571) ALLAHABAD Mehrotra Book Depot, (0532) , AZAMGARH Sasta Sahitya Sadan, (05462) BALIA Saraswati Shishu, (05498) Vidya Kendra, LUCKNOW UBS Publication, (0522) MATHURA Vishnu Book Depot, (0565) NOIDA UBS Publisher & Dist., (0120) VARANASI Bokaro Student Friends, (0542) WEST BENGAL KOLKATA Chukervertty Chatterjee, (033) Eureka Book Emporium, (033) Katha O Kahani Pvt. Ltd., , Krishna Book House, Oriental Publishers, (033) , Saha Book House, (033) SILIGURI Agarwal Book House, (0353) Novelty Books, (0353) Publisher Oswaal Books 1608

4 CONTENTS l Syllabus 5-8 l On Tips Notes 9-41 q Sample Question Papers (Solved) Sample Question Paper - 1 (Issued by CBSE for Exams) with CBSE Marking Scheme Sample Question Paper with Topper Answers (CBSE Examination Paper 2015) Sample Question Paper Sample Question Paper Sample Question Paper q Sample Question Papers (Self Assessment) Sample Question Paper Sample Question Paper Sample Question Paper Sample Question Paper Sample Question Paper q Solutions Sample Question Paper Sample Question Paper Sample Question Paper * SOLUTIONS for Sample Question Paper 6 to 10 can be downloaded from qq (3)

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6 Latest Syllabus for Academic Year Mathematics (Code 041) Class-XII One Paper Time : Three Hours Marks : 100 Units No. of Periods Marks I. Relations and Functions II. Algebra III. Calculus IV. Vectors And Three - Dimensional Geometry V. Linear Programming VI. Probability Total Unit I : Relations and Functions 1. Relations and Functions : (15 Periods) Types of relations : reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations. 2. Inverse Trigonometric Functions : (15 Periods) Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions. Unit II : Algebra 1. Matrices : (25 Periods) Concept, notation, order, equality, types of matrices, zero and identify matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices; Addition and multiplication and multiplication with a scalar, 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 2). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matricecs will have real entries). 2. Determinants : (25 Periods) Determinant of a square matrix (up to 3 3 matrices), properties of 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 1. Continuity and Differentiability : (20 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. (5)

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8 3. Mathematics Exemplar Problem for Class XII, Published by NCERT (7)

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laxbu) f'k{kk lnu] 17] bulfvv~;w'kuy {ks=]

9 dsuæh; ek/;fed f'k{kk cksmz (ekuo lalk/ku fodkl ea=ky;] Hkkjr ljdkj] ds v/khu,d Lok;Ùk laxbu) f'k{kk lnu] 17] bulfvv~;w'kuy {ks=] jkmt,osu;q] fnyyhµ CENTRAL BOARD OF SECONDARY EDUCATION (An Autonomous Organization under the Union Ministry of Human Resource Development, Govt. of India) Shiksha Sadan, 17, Institutional Area, Rouse Avenue, New Delhi b 2 8=16 (8)

10 ON TIPS NOTES Note Making is a skill that we use in many walks of life : at school, university and in the world of work. However, accurate note making requires a thorough understanding of concepts. We, at Oswaal, have tried to encapsulate all the chapters from the given syllabus into the following ON TIPS NOTES. These notes will not only facilitate better understanding of concepts, but will also ensure that each and every concept is taken up and every chapter is covered in total. So, go ahead and use it to your advantage... go get the OSWAAL ADVANTAGE!! CHAPTER 1 : Relations And Functions ¾ Fundamentals A relation R from a non-empty set A to a non-empty set B is a subset of the Cartesian product A B. The set of all the first elements of the ordered pairs in a relation R from a set A to a set B is called the domain of the relation R. The set of all second elements in a relation R from a set A to a set B is called the range of the relation R. The whole set B is called the co-domain of the relation R. ¾ Types of Relation Empty Relation : A relation R in a set A is called empty relation, if no element of A is related to any element of A, i.e., R = f A A. Universal Relation : A relation R in a set A is called universal relation, if each element of A is related to every element of A, i.e., R = A A. A relation R in a set A is called (i) reflexive., if (a 1, a 2 ) R, for every a A. (ii) symmetric, if (a 1, a 2 ) R implies that (a 2, a 1 ) R, for all a 1, a 2 A. (iii) transitive, if (a 1, a 2 ) R and (a 2, a 3 ) R implies that (a 1, a 3 ) R, for all a 1, a 2, a 3 A. Equivalence Relation : A relation R in a set A is said to be an equivalence relation if R is reflexive, symmetric and transitive. ¾ Types of Function One-One(Injective) and Many-One : A function f : X Y is defined to be one-one(or injective), if the images of distinct elements of X have distinct images in Y under f., i.e. for every x 1, x 2 X, f(x 1 ) = f(x 2 ) implies x 1 = x 2. Otherwise, f is called many-one. Y Onto (Surjective) : A function f : X Y is said to be onto (or surjective), if every element of Y is the image of some element of X under f, i.e., for every y Y, there exists an element x in X such that f(x) = y. Y

Books ISBN : 9789351278801 Author : Panel Of Experts

11 Oswaal CBSE Sample Question Papers For Class 12 Mathematics (For 2017 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 9 TERM 2 MARCH 2017 EXAMINATION

OSWAAL CBSE Strictly Based on Latest Syllabus Issued by CBSE for 207 Examination SAMPLE QUESTION PAPERS CLASS 9 TERM 2 MARCH 207 EXAMINATION SCIENCE *Solutions for SQP 6-0 can be downloaded from www.oswaalbooks.com