SYLLABI OF SUBJECTS FOR REE - 99
Mathematics ( 150 Marks - 3 Hours )
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.
Addition and multiplication theorems of probability and their applications. Binomial distribution.
Trigonometric identities and equations. Properties of triangles. Solution of triangles. Heights and distances. Inverse trigonometric functions.
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.