UNIT 1 : SETS, RELATIONS AND FUNCTIONS ( Marks : 06 )
Sets and their representation, finite and infinite sets, empty set subsets, subset of real numbers especially intervals, power set, universal set. Venn diagram, union and intersection of sets. Difference of sets, Compliment of a set. Ordered pairs, Cartesian product of sets, number of elements in the Cartesian product of two finite sets.
Relations, Domain, co-domain and range of relation, types of relations, reflexive, symmetric, transitive and equivalence relations.
Functions as special kind of relations from one set to another, domain, co-domain and range of a function. One to one, onto functions. Real valued functions of the real variable; constant, identity, polynomial, rational, modulus, signum and the greatest integer functions with their graphs. Sum, difference, product and quotients of functions. Composition of functions, inverse of a function, binary operations.
UNIT 2 : COMPLEX NUMBER; LINEAR INEQUATION; LINEAR PROGRAMMING ( Marks : 06 )
Complex Number : Conjugate of a complex number, modulus and amplitude ( argument ) of a complex number, Argand‘s plane and polar representation of complex numbers, algebraic properties of complex numbers. Fundamental theorem of algebra, solution of Quadratic equation in the complex number system. Square root of a complex number.
Linear Inequation : Algebraic solution of linear inequalities in one variable and two variables.
Linear programming : Introduction, definition of related terminology such as constraints, objective function, optimization, different type of linear programming problem ( L.P. ), mathematical formulation of L.P problem, graphical method of solution for problems in two variables, feasible and in feasible regions, feasible and infeasible solutions, optimal feasible solutions.
UNIT 3: SEQUENCE AND SERIES, PERMUTATION AND COMBINATION & BINOMIAL THEOREM ( Marks : 06 )
Sequence and series : Arithmetic progression ( A.P. ), arithmetic mean ( A.M. ), nth term, sum to n-terms of an A.P, Geometric progression ( G.P. ), Geometric Mean (G.M), nth term, sum to n-terms and sum to infinity of a G.P. Relation between A.M and G.M. Sum to n terms of Σn, Σn2, Σn3
Permutation and combination : Fundamental principle of counting, factorial n, permutations P(n,r) and combinations C(n,r), simple applications.
Binomial Theorem : Binomial theorem for positive integral power. general and middle terms in the Binomial expansion. Pascal‘s triangle and simple applications.
UNIT 4: TRIGONOMETRIC AND INVERSE TRIGONOMETRY FUNCTIONS ( Marks : 06 )
Positive and negative angles, measuring angles in radians and in degrees, Conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Periodicity of Trigonometric functions. Basic Trigonometric identities sin2x+cos2x=1 for all Sign of x etc. Trigonometric functions and their graphs. Expressions for sin (x±y), cos (x±y) tan (x±y), cot (x±y), sum and product formulae.
Identities related to Sin2x, Cos2x, tan2x, Sin3x, Cos3x, and tan3x. General and principal solutions of trigonometric equations of the type Sin x= Sin a, Cosx= Cos a , Tan x= Tan a.
Identities related to Sin2x, Cos2x, tan2x, Sin3x, Cos3x, and tan3x. General solution of trigonometric equations of the type Sin x= Sin a, Cos x= Cos a, Tan x= Tan a.
Inverse trigonometric functions, range, domain, principal value branches. Graphs of inverse trigonometric functions, elementary properties of inverse trigonometric functions.
UNIT 5: MATRICES AND DETERMINANTS ( Marks : 04 )
Matrices, concepts, notation, order, equality, types of matrices, Zero matrix, transpose of matrix, Symmetric and skew symmetric matrices. Addition, multiplication, scaler multiplication of matrices, simple properties of addition, multiplication and scaler multiplication of matrices. Non – commutativity of multiplication of matrices and existence of non – zero matrices whose product is the zero matrix ( order 2×2 ). Concept of elementary row and column operation, Invertible matrices and uniqueness of inverse, if it exists. ( Matrices with real entries ).
Determinants of square matrix ( upto 3×3 matrices ) properties of determinants, minors, co factors and applications of determinants in finding 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 using inverse of a matrix.