Maths Question Paper for CBSE Class 12 - 2016 Set 1 S

Unit I: Relations and Functions

Chapter 1: Relations and Functions: Types of relations − Reflexive relation, Symmetric relation, transitive relation and equivalence relation, One to one and onto functions, composite functions, the inverse of a function and Binary operations.

Chapter 2: Inverse Trigonometric Functions: Definitions of range, domain, principal value branch, graphs of inverse trigonometric functions, Elementary properties of inverse trigonometric functions.

Unit II: Algebra

Chapter 1: Matrices: Concepts, notations, order, equality, types of matrix, zero and identity matrices, transpose of matrices, symmetric and skew symmetric matrices. Operations on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication and Non-Commutativity of the multiplication of matrices and the existence of non-zero matrices whose product is the zero matrices (restricted to square matrices of order. Concept of elementary row and column operations. Invertible matrix and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

Chapter 2: Determinants: Determinant of the square matrix, properties of the determinants, minors, cofactors 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 a system of linear equations with examples, solving system of linear equations in two or three variables having unique solution using the inverse of a matrix

Unit III: Calculus

Chapter 1: Continuity and Differentiability: The concepts of Continuity and differentiability, the 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. The Logarithmic differentiation and derivative of functions are expressed in parametric forms. Second-order derivatives. Rolle's and Lagrange's Mean Value Theorems and their geometric interpretations. 

Chapter 2: Applications of Derivatives: Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in approximation, maxima and minima. Simple numerical problems.

Chapter 3: Integrals: Integration as an 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 types and problems based on them. Definite integrals as a limit of a sum, Fundamental Theorem of Calculus Basic properties of definite integrals and evaluation of definite integrals

Chapter 4: Applications of the Integrals: Applications in finding the area under some of the simple curves, especially lines, circles, parabolas, ellipses. The area between any of the two above-said curves. 

Chapter 5: Differential Equations: Definitions, the concepts of order and degree and the general and the particular solutions of a differential equation. Formation of differential equations whose general solution is given. Solutions of the differential equations by the method of separation of variables solutions of homogeneous differential equations of the first order and first degree. Solutions of the linear differential equation of the type − dy/dx + py = q, where p and q are the functions of x or constants, dx/dy + px = q, where p and q are the functions of y or constants.

Unit IV: Vectors and Three-Dimensional Geometry

Chapter 1: Vectors: Vectors and scalars, magnitude and direction of a vector. Directional cosines and the direction ratios of a vector. Types of vectors position vectors of a point, negative of a vector, components of a vector, the 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 application of scalar (dot) product of vectors, vector (cross) product of vectors, the scalar triple product of vectors

Chapter 2: Three-dimensional Geometry: Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, coplanar and skew lines, the shortest distance between two lines. Cartesian and vector equation of a plane Angle between Two lines, Two planes, A-line and a plane, Distance of a given point from a plane. 

Unit V: Linear Programming

Chapter 1: Linear Programming: Introduction, 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 (bounded and unbounded) Feasible and infeasible solutions. Optimal feasible solutions (up to three non-trivial constraints)

Unit VI: Probability

Chapter 1: Probability: The concept of Conditional probability, multiplication theorem on probability, independent events, total probability, the Bayes theorem, Random variable and its probability distribution, Mean and variance of the random variable, Repeated independent (Bernoulli) trials and Binomial distribution

Conclusion 

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