1. ALGEBRA: a) Functions – Types of functions – Algebra of real valued functions b) Mathematical induction and applications c) Permutations and Combinations – linear and circular permutations – combinations. d) Binomial theorem – for a positive integral index – for any rational index – applications – Binomial Coefficients. e) Partial fractions f) Exponential and logarithmic series g) Quadratic expressions, equations and inequations in one variable. h) Theory of equations – Relations between the roots and Coefficients in any equation – Transformation of equations – reciprocal equations. i) Matrices and determinants – Types of matrices – Algebra of matrices – Properties of determinants – simultaneous linear equations in two and three variables – Consistency and inconsistency of simultaneous equations. j) Complex numbers and their properties – De Moivre’s theorem – Applications – Expansions of trigonometric functions.
2. TRIGONOMETRY: a) Trigonometric functions – Graphs – periodicity b) Trigonometric ratios of compound angles, multiple and sub-multiple angles, Transformations – sum and product rules. c) Trigonometric equations d) Inverse trigonometric functions e) Hyperbolic and inverse hyperbolic functions f) Properties of Triangles g) Heights and distances (in two-dimensional plane)
3. VECTOR ALGEBRA: a) Algebra of vectors – angle between two non-zero vectors – linear combination of vectors – vector equation of line and plane b) Scalar and vector product of two vectors and their applications c) Scalar and vector triple products, Scalar and vector products of four vectors .
4. PROBABILITY: a) Random experiments – Sample space – events – probability of an event – addition and multiplication theorems of probability – Conditional event and conditional probability – Baye’s theorem b) Random variables – Mean and variance of a random variable – Binomial and Poisson distributions .
5. COORDINATE GEOMETRY: a) Locus, Translation of axes, rotation of axes b) Straight line c) Pair of straight lines d) Circles e) System of circles f) Conics – Parabola – Ellipse – Hyperbola – Equations of tangent, normal, chord of contact and polar at any point of these conics, asymptotes of hyperbola. g) Polar Coordinates h) Coordinates in three dimensions, distance between two points in the space, section formula, centroid of a triangle and tetrahedron. i) Direction Cosines and direction ratios of a line – angle between two lines j) Cartesian equation of a plane in (i) general form (ii) normal form and (iii) intercept form – angle between two planes k) Sphere – Cartesian equation – Centre and radius.
6. CALCULUS: a) Functions – limits – Continuity b) Differentiation – Methods of differentiation c) Successive differentiation – Leibnitz’s theorem and its applications d) Applications of differentiation e) Partial differentiation including Euler’s theorem on homogeneous functions f) Integration – methods of integration g) Definite integrals and their applications to areas – reduction formulae h) Numerical integration – Trapezoidal and Simpson’s rules Differential equations – order and degree – Formation of differential equations – Solution of differential equation by variables separable method – Solving homogeneous and linear differential equations of first order and first degree.
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