CBSE Mathematics Question Paper

Can you provide me the previous year CBSE (Central Board of Secondary Education) Mathematics question paper of class 12th as I need it for preparation?

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The question paper of CBSE (Central Board of Secondary Education) Mathematics of class 12th is as follows:
CBSE Mathematics Question Paper






CBSE Mathematics Syllabus

Unit - I: Relations and Functions
1. Relations and Functions: 15 Periods
Types of relations: reflexive, symmetric, transitive and equivalence relations. Functions: 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 identity 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 2). 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).
2. Determinants: 25 Periods
Determinant of a square matrix (up to 3 x 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.
2. Applications of Derivatives: 10 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: 20 Periods
Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial
fractions and by parts. Evaluation of simple intergrals of the following type and problems based on them:
2 2 2
2 2
2
2
d d d d d , , , ,
± a a + b + c ± a a - a + b + c
p + q p + q d , d , a ± d , - a d
a + b + c a + b + c
a + b + c d , (p + q) a + b + c d .
2 2 2 2 2
2 2
2
2
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: 15 Periods
Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form
only), Area between any of the two above said curves (the region should be clearly identifiable).
5. Differential Equations: 15 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.
+ py = q, where p and q are functions of x or constants
+ px = q, where p and q are functions of y or constants
Unit-IV: Vectors and Three-Dimensional Geometry
1. Vectors: 15 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, Geomertrical 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 aline.
2. Three - dimensional Geometry: 15 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
1. Linear Programming: 20 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
1. 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.
Prescribed Books:
1) Mathematics Part I - Textbook for Class XI, NCERT Publication
2) Mathematics Part II - Textbook for Class XII, NCERT Publication
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