![]() ![]() ![]() Partial fractions: Partial fractions of f(x)/g(x) when g(x) contains non–repeated linear factors - Partial fractions of f(x)/g(x) where both f(x) and g(x) are polynomials and when g(x) contains repeated and/or non-repeated linear factors - Partial fractions of f(x)/g(x) when g(x) contains irreducible factors Permutations and Combinations: Fundamental Principle of counting – linear and circular permutations - Permutations of ‘n’ dissimilar things taken ‘r’ at a time - Permutations when repetitions allowed - Circular permutations - Permutations with constraint repetitions - Combinations-definitions, certain theorems, and their applicationsīinomial Theorem: Binomial theorem for positive integral index - Binomial theorem for rational Index (without proof) - Approximations using Binomial theorem Theory of Equations: The relation between the roots and coefficients in an equation - Solving the equations when two or more roots of it are connected by certain relation - Equation with real coefficients, the occurrence of complex roots in conjugate pairs and its consequences - Transformation of equations - Reciprocal Equations Quadratic Expressions: Quadratic expressions, equations in one variable - Sign of quadratic expressions – Change in signs – Maximum and minimum values - Quadratic Inequations Matrices: Types of matrices - Scalar multiple of a matrix and multiplication of matrices - Transpose of a matrix - Determinants (excluding properties of determinants) - Adjoint and Inverse of a matrix - Rank of a matrix - Solution of simultaneous linear equations (ExcludingĬomplex Numbers: Complex number as an ordered pair of real numbers- fundamental operations - Representation of complex numbers in the form a+ib - Modulus and amplitude of complex numbers –Illustrations - Geometrical and Polar Representation of complex numbers in Argand plane- Argand diagramĭe Moivre’s Theorem: De Moivre’s theorem- Integral and Rational indices - nth roots of unity-Geometrical Interpretations – Illustrations ![]() Functions: Types of functions – Definitions - Domain, Range ![]()
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