### University of Pune MCA Entrance Exam Syllabus

Mathematics

• Set theory: Set operations, relations, functions.
• Propositional logic: Formulation, deduction, evaluation, puzzles.
• Linear Algebra: Solution of a system of linear equations. Determinant and inverse of a matrix, basic properties of matrices.
• Co-ordinate Geometry and Conic Sections: Equations of lines and planes, vector products; definitions and properties of conic sections.
• Trigonometry: Identities, computation of heights and lengths.
• Differential Calculus: Total and partial differentiation, limit of a function.
• Integral Calculus: Definite and indefinite integrals, solution of differential equations, computation of areas and volumes.
• Series and sequences: sum, mean, convergence, limit.
• Real and complex numbers: surds, solution of equations on complex domain.
• Polynomials: solution of quadratic equations, properties of roots of polynomials with real coefficients, binomial expansion, Taylor series.
• Permutations and Combinations.
• Elementary Probability Theory: Computing probability from combinatorial reasoning, conditional probability.

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