joint entrance exam

Probability : Classical definition, addition rule, conditional probability and Bayes’ theorem, independence, multiplication rule.

Sets, Relations and Mappings : Idea of sets, subsets, power set, complement, union, intersection and difference of sets, Venn diagram, De Morgan’s Laws, Inclusion / Exclusion formula for two or three finite sets, Cartesian product of sets.

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.

Infinite series : Binomial theorem for negative and fractional index. Infinite G.P. series, Exponential and Logarithmic series with range of validity (statement only), simple applications.

Binomial theorem (positive integral index) :Statement of the theorem, general term, middle term, equidistant terms, properties of binomial co-efficients.

Principle of Mathematical Induction : Statement of the principle. Proof by induction for the sum of squares, sum of cubes of first n natural numbers, divisibility properties like 2²ⁿ–1 is divisible by 3 (n≥1), 7 divides 3²ⁿ⁺¹+2ⁿ⁺²(n≥1).

Permutation and combination : Permutation of n different things taken r at a time (r≤n). Permutation of n things not all different. Permutation with repetitions (circular permutation excluded).

Quadratic Equations : Quadratic equations with real coefficients; Relations between roots and coefficients; Nature of roots; Formation of a quadratic equation, sign and magnitude of the quadratic expression ax²+bx+c (a,b,c are rational numbers and a≠0).

Complex Numbers: Definition and properties of complex numbers; Complex conjugate; Triangle inequality; Square root of complex numbers; Cube roots of unity; D’Moivre’s theorem (statement only) and its elementary applications.

Logarithms :Definition; General properties; Change of base.