Theory of Calculus:

Functions, composition of two functions and inverse of a function, limit, continuity,

derivative, chain rule, derivative of implicit functions and functions defined parametrically.

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.

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.

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). Combinations of n

different things taken r at a time (r ≤ n). Combination of n things not all different. Basic properties. Problems

involving both permutations and combinations.

Statistics and Probability:

Measure of dispersion, mean, variance and standard deviation, frequency

distribution. Addition and multiplication rules of probability, conditional probability and Bayes’ Theorem,

independence of events, repeated independent trails and Binomial distribution.

Aptitude:

Mathematical reasoning

: Statements, logical operations like and, or, if and only if, implies, implied by.

Understanding of tautology,

converse, contradiction and contrapositive.

Sets and Relations:

Idea of sets, subsets, power set, complement, union, intersection and difference of sets,

Venn diagram, De Morgan's Laws, Relation and its properties. Equivalence relation definition and

elementary examples

and it's also good to study quantitative aptitude as several questions had appeared from previous year question paper.

here is a good website to study quantitative aptitude (please note that some of the questions are quite advanced on this website you can concentrate on the basics)- https://www.indiabix.com/aptitude/questions-and-answers/