## Syllabus  ( for Entrance)

 b) MATHEMATICS ALGEBRA : Algebra of complex numbers, modulus and argument, triangle inequality, nth roots of unity. Theory of quadratic equations and quadratic expressions, relationship between the roots and coefficients, sign of a quadratic expression, greatest and least values of quadratic expression. Arithmetic geometric and harmonic progressions, sums of arithmetic, geometric and harmonic progressions, infinite geometric series, sums of the squares and cubes of the first n natural numbers. Mathematical induction, permutations and combinations, Binomial theorem for a positive integral index. Determinants of order two and three, solutions of simultaneous linear equations in two and three variables. TRIGONOMETRY : Trigonometric functions and their graphs, addition and subtraction formulae, formula involving multiple and sub multiple angles, general solution of trigonometric equations, relations between the sides and angles of triangle, properties of a triangle, solutions of triangles, heights and distances, trigonometric functions. ANALYTICAL GEOMETRY OF TWO DIMENSIONS : Equation of straight line in various forms, angle between tow lines, distance of a point from a line, line through the point of intersection of two given lines, concurrency of lines. Equation of a circle in various forms, equations of tangent and normal, intersection of a circle with a straight line, equation of a circle through the points of intersection of two circles and that of a circle and a straight, line. Equations of the conic sections in the standard form, focus, directrix, eccentricity of the conic section, parametric equations, equations of tangent and normal CALCULUS : Into, onto and one-to-one functions, Sum, difference, product and quotient of two functions, composite function; absolute value, greatest integer, polynomial, rational, trigonometric, exponential and logarithmic functions, even and odd functions, inverse of a function. Limit and continuity of a function, limit and continuity of the sum, difference, product and quotient of two functions, continuity of composite function. Derivative of a function, derivative of composite and implicit functions, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions. Geometrical interpretation of derivative, tangents and normal. Monotonicity, maximum and minimum values of a function. Derivatives upto order three. INTEGRATION, DIFFERENTIAL EQUATIONS : Integration as the inverse proves of differentiation, integration by parts, integration by the methods of substitution and partial fraction, Definite integral and its application for the determination of areas. Properties of definite integrals. Formational of differential equations. First order equation, variables separable and homogeneous equations. PROBABILITY : Addition and multiplication laws of probabilities, conditional probabilities. VECTORS : Addition and vectors, scalar products, cross product, scalar and vector triple products, applications in geometry. PAPER 2 a) APTITUDE TEST It will consist of analytical and logical reasoning. b) GENERAL KNOWLEDGE It will consist of General Knowledge related to Information Technology. c) ENGLISH It will consist of English (language) to test the communication skills of candidates.