• Matrix operation, Adjoint and inverse of a matrix, Rank of a Matrix; Cayley Hamilton Theorem, Eigen Values, Eigen Vectors, Latent Vectors, Linear System of equations, properties of determinants, Cramer’s rule.

• Continuity and Limits, Total and Partial Differentiation,Properties of continuous Functions, Rolle’s Theorem, L.M.V. Theorem, Cauchy’s generalized mean value theorem,Taylor’s and Maclaurin’s Series, Maxima and Minima,Indeterminate form, L. Hospital’s rule, Curvature,Asymptotes, Tangent & normal, Tracing of curves,Successive Differentiation, Functions of two or more variables, Applications of derivatives such as tangent and normal, rate as a measure, increasing and decreasing functions etc.

• Definite and Indefinite Integral, Evaluvation of Length, Area and Volume of Curves, Multiple Integration, Change of order, Change of Variables, Application to find Area, Volume.

• Differential equations of first order and their solutions, Linear differential equations with constant coefficients, Homogenous Linear Differential Equations, Orthogonal Trajectories, Introduction to Differential Equations of Second order, Complimentary Function, Particular Integrals.

• Real Number system, concept of neighbourhood and limit points, order completeness property, Archemedian Property, Sequence, Sequences of real Numbers, Bounded sequences, Covergent sequences, Cauchy Sequences, Monotonic sequences, Infinite series of positive terms and their different tests of convergence, Alternating series, Leibnitz’s test, Absolute convergence. Conditional Convergence

• Sets, Relations, functions, Simultaneous linear equations,Quardratic Equations, Indices, Logarithms, A.P., G.P., H.P.,Inequalities, Surds, Binomial Theorem, Complex numbers, Demoivere’s Theorem, Roots of unity, Roots of a complex number,geometry of complex numbers.

• Polynomials and their characteristics, Roots of an equation, Relation between Roots and coefficients, Transformation of equations.

• Slope of a line, Different forms of a straight line, Family of lines, Pair of straight lines, Translation of Axes, Circles, Family of circles, coaxial system of circles, Parabola, Ellipse, Hyperbola, Equation of Tangent, Pair of tangents from a point, Chord of contact, Equation of chord in terms of middle point, Pole and polar of a conic, Diameter of a conic, Conjugate Diameter, Classification of curves of second degree.

• Straight Line, Plane, Sphere, Right Circular Cylinder, Cone.

• Groups, Permutation groups, Subgroups, Lagrange’s theorem, Order of an element of a group, Normal subgroups, Quotient Groups, Homomorphism, Isomorphism, Automorphism, Endomorphism, Rings, Field, Vector spaces, Linear Dependence and Linear Independence of vectors, Basis, Dimension,Linear Transformation, Quardratic Forms, Diagonalisation of matrices.

• Interpolation, Extrapolation, Simpson’s 1/3rd rule, Trapezoidal rule, Numerical differentiation, Numerical Integration, Use of Iterative Methods (Bisection Method, Newton- Raphson method, Gauss Method, Gauss-Jacobi Method etc.) to solve system of equations, Convergence of various iterative methods, Rate of Convergence etc.

• Classifications of Data and Frequency distribution, Calculation of measures of Central tendency and measures of dispersion, Skewness & Kurtosis, Correlation & Regression, Index numbers, Time Series Analysis

• Permutation & combination, Probability, Random Variables & distribution functions, Mathematical Expectations & generating functions, Binomial, Poisson, Geometric, Exponential & Normal Distributions, Sampling & large sample tests, Tests of significance based on t, Chi-square and F distributions.

• Trigonometric Functions, Trigonometric Identities,Trigonometric Equations, Properties of triangles, Solution of triangles, Properties of Triangle, Height and distance; Inverse trigonometric function, Applications of trigonometry in coordinate geometry.

• Organization of a computer, Central Processing Unit (CPU), Structure of instructions in CPU, input / output devices,computer Memory, memory organization, back-up devices.

• Venn Diagrams in logic, Logical operators, Negations, Logical Equivalence and Tautology, Flow Chart and Algorithms.

• Representation of characters, integers, and fractions, binary and Hexadecimal representations.

• Addition, subtraction, division, multiplication, single arithmetic and two complement arithmetic, floating point representation of numbers, normalized floating point representation, Boolean algebra, Truth tables, Venn diagrams.

• Block Structure of computers, communication between processor and I / O devices, Interrupts.

• Set theory and its simple applications. Basic concepts of groups, fields and vector spaces.

• Rank of a matrix. Existence and uniqueness of solution of a system of linear equation. Eigen values and Eigen vectors. Inverse of a matrix by elementary transformations.

• Differentiation, Partial differentiation, Taylor series and approximate calculations. Maxima and minima of functions of one and two variables.

• Single and multiple integration. Definite integrals, Change of order and change of variables. Application to evaluation of area, surface and volume.

• First order differential equations, linear differential equations of higher order with constant coefficients.

• Vector algebra, Gradient.

• Solution of non linear equations using iterative methods. Interpolation (Lagrange’s formula and Newtons formulae for equidistant points). Numerical differentiation and integration (Trapezoidal and Simpson rules)

• Basic concepts of probability theory. Binomial and Poisson distributions.

• Formulation and its graphical solution for two variable problems.

• Number systems. Basic electronic gates. Boolean algebra. Flip-Flops. Algorithmic approach to solve problems. Fundamentals of C language.

MATHEMATICS

General Aptitude

Computer Science