|Unit-1 [ Relations & Functions ]||Relations|
|Mapping or Function|
|Trigonometric Inverse Circular Functions|
|Unit-2 [ Algebra ]||Types of Matrix Operations on Matrices|
|Adjoint and Inverse of a matrix and Solution of Lilnear Simultaneous equations by Matrix Method|
|Unit-3 [ Calculus ]||Limit|
|Continuity and Differentiability|
|Second Order Derivative|
|Method of Substitution|
|Integration by Parts|
|Integrals of Some Special Form of Functions|
|Order and Degree of Differential Equation|
|Differential Equations of the First Order and First Degree|
|Linear Differential Equation|
|Significance of Derivative as Rate of Change|
|Tangent and Normal|
|Increasing and Decreasing Function|
|Maxima and Minima|
|Definite Integral as an Area|
|Unit-4 [ Vector and Three Dimensional Coordinate Geometry ]||Vector|
|Products of Two Vectors|
|Direction Cosines and Direction Ratios|
|Straight Line in Three Dimensional Spaces|
|Unit-5 [ Linear Programming ]||Linear Programming Graphical Method|
|Unit-6 [ Probability ]||Probability|
|Random Variable and Its Distribution|
Syllabus for Class XII WBJEE :
Matrices : Concepts of m x n (m ≤ 3, n ≤ 3) real matrices, operations of addition, scalar multiplication and multiplication of matrices. Transpose of a matrix. Determinant of a square matrix. Properties of determinants (statement only). Minor, cofactor and adjoint of a matrix. Nonsingular matrix. Inverse of a matrix. Finding area of a triangle. Solutions of system of linear equations. (Not more than 3 variables).
Statistics and Probability : Addition and multiplication rules of probability, conditional probability and Bayes’ Theorem, independence of events, repeated independent trails and Binomial distribution.
Trigonometry : Inverse trigonometric functions and their properties.
Coordinate geometry :
Coordinate geometry of three dimensions : Equation of a straight line, equation of a plane, distance of a point from a plane.
Differential calculus : Functions, composition of two functions and inverse of a function, limit, continuity, derivative, chain rule, derivative of implicit functions and functions defined parametrically.
Rolle’s Theorem and Lagrange’s Mean Value theorem (statement only). Their geometric interpretation and elementary application. L’Hospital’s rule (statement only) and applications. Second order derivative.
Integral calculus : Integration as a reverse process of differentiation, indefinite integral of standard functions.
Integration by parts : Integration by substitution and partial fraction. Definite integral as a limit of a sum with equal subdivisions. Fundamental theorem of integral calculus and its applications. Properties of definite integrals.
Differential Equations : Formation of ordinary differential equations, solution of homogeneous differential equations, separation of variables method, linear first order differential equations. Application of Calculus: Tangents and normals, conditions of tangency. Determination of monotonicity, maxima and minima . Differential coefficient as a measure of rate. Motion in a straight line with constant acceleration. Geometric interpretation of definite integral as area, calculation of area bounded by elementary curves and Straight lines. Area of the region included between two elementary curves.
Vectors : Addition of vectors, scalar multiplication, dot and cross products, scalar triple product.