Paper Code : BCA-03 Paper Title : Mathematics Theory.

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Paper Code : BCA-03 Paper Title : Mathematics Theory

SECTION-A Fundamental Principles of Counting : Permutation as an arrangement, meaning of P (n, r) and c (n, r), simple applications. Binomial Theorem: Statement of principle of Mathematical Induction, Proof of the Binomial Theorem of positive index using the principle of induction, general and middle terms. Binomial Theorem for Any index (Without Proof) applications of Binomial Theorem for approximation and properties of Binomial Coefficients. Trigonometry-I Trigonometric Ratios of allied angles, Trigonometric ratios of Compound angles or addition and subtraction formulae.

SECTION-B Trigonometry-II : Transformation Formulae, Trigonometric ratios of multiple and sub-multiple angles, Inverse Trigonometric functions. Limit and Continuity : Rules for finding Limits, Infinite Limits, Continuity at a point, Rules of continuity, Continuity on an Interval.

SECTION-C Derivatives : The derivative of a function, Calculating derivatives from the definition, Differentiability on an interval, Differentiation Rules, Rates of Change, Derivatives of Trigonometric Functions, The Chain Rule, Derivative of Implicit, Rational, and Exponential Functions. Application of Derivatives : Rolle’s theorem, Lagrange Mean Value Theorem and their applications, Extreme values of Functions, the first derivative test for Local Extreme Values. Integration-I : Indefinite Integrals, Integration by substitution, Integration of Transcendental Functions: Inverse Functions, Natural Logarithm, The Exponential Function.

SECTION-D Integration-II :Inverse Trigonometric functions, Integration by parts, Partial fractions, Trigonometric substitutions, Definite Integrals, Properties, Area under the curve. Matrix Operations : Introduction and definition of matrix, types of matrices, Matrix addition, Subtraction and scalar multiplication, Matrix multiplication, Transpose of a matrix, adjoint of a matrix and inverse of a matrix, solution of system of linear equations, definition and properties of a determinant.