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TEST PAPER: MATHEMATICAL STATISTICS (MS) The Mathematical Statistics (MS) Test Paper comprises following topics of Mathematics (about 30% weight) and Statistics (about 70% weight).   Mathematics Sequences and Series of real numbers: Sequences of real numbers, their convergence, and limits. Cauchy sequences and their convergence. Monotonic sequences and their limits. Limits of standard sequences. Infinite series and its convergence, and divergence. Convergence of series with nonnegative terms. Tests for convergence and divergence of a series. Comparison test, limit comparison test, D’Alembert’s ratio test, Cauchy’s root test, Cauchy’s condensation test and integral test. Absolute convergence of series. Leibnitz’s test for the convergence of alternating series. Conditional convergence. Convergence of power series and radius of convergence.   Differential Calculus of one and two real variables: Limits of functions of one real variable. Continuity and differentiabi...