Unit 4 Combinatorics

Factorials - definition and examples; Permutations - fundamental principle of counting, permutation of distinct objects, not all distinct objects,

simple problems; Combinations - definition, relation between Permutation and combinations, properties, simple problems

Mathematical Induction - principles, simple problems

Unit 5 Finite and Infinite Series

Binomial theorem - Binomial theorem for positive integral index (proof using combinations and also by induction), applications of binomial theorem;

Sequence and Series - AP, GP, HP: Terms and Sum of AP and GP, Arithmetic and Geometric means. Problems on sum of finite series, Arithmetico-geometric progression

telescopic sums for series

Unit 5 Finite and Infinite Series

Infinite Geometric Series; Infinite Arithmetico - Geometric Series; Infinite series using principle of telescopic sums; Exponential and logarithmic series (without proof); Binomial theorem for all rational index as an infinite series (without proof)

Unit 6 : Two Dimensional Analytic geometry – I

Locus of a point - definition and simple examples;Straight lines - various forms of equation: Slope – point,Slope – intercept, two points, intercepts

normal and parametric forms; general form; related problems

Pair of Straight lines - equation of a pair of straight lines, problems related with:distance of a point from a line, distance between two parallel lines, equation of a line bisecting the angle between two lines

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