SYLLABI OF SUBJECTS FOR REE - 99

 Mathematics ( 150 Marks - 3 Hours ) Algebra Sets, union, intersection, relation, equivalence relation, mapping (function). Algebra of complex numbers. DeMoiver's Theorem and simple applications. Determinants and matrices of order two and three and their elementary properties . Inverse of a matrix, Rank of a matrix, Consistency of simultaneous linear equations using determinants and matrices. Theory of quadratic equations and expressions. Relation between roots and coefficients. Partial fractions. Permutations and combinations. Mathematical induction and its simple applications. Binomial theorem for a positive integral index and its simple applications. Arithmetic, geometric and harmonic progressions. Exponential and logarithmic series. Probability Addition and multiplication theorems of probability and their applications. Binomial distribution. Trigonometry Trigonometric identities and equations. Properties of triangles. Solution of triangles. Heights and distances. Inverse trigonometric functions. Coordinate Geometry Straight line, pair of straight lines. Distance of a point from a straig ht line. Angle between two lines. Bisectors of angles. Area of a triangle. Circle, tangent and normal. Family of Circles, radical axis. Parabola, ellipse and hyperbola in standard forms, their tangents and normals. Vector Algebra Definition of a vector. Addition of vectors. Components in three dimensional space. Scalar and vector products. Scalar and vector triple products. Simple applications. Calculus Function: Polynomial, rational, trigonometric, logarithmic and exponenti al functions. Inverse function. Graphs of simple functions. Limit, Continuity and differentiability of functions. Derivatives of composite and implicit functions. Differentiation of rat ional, trigonometric, inverse trigonometric, logarithmic and exponential functions. Tangent and normal. Sign of derivative and monotonicity. Simple problems of maxima and minima. Integration by parts, by substitution and by partial fractions. Definite integral. Integral as limit of a sum. Fundamental theorem of calculus. Areas under simple curves. Ordinary differential equations : First order and first degree differential equations - variable separable, homogenous and linear. Statics and Dynamics Resultant of coplanar forces. Moments and couples. Equilibrium of coplanar forces. Velocity and acceleration. Relative velocity. Rectilinear motion under uniform acceleration. Projectiles.