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Unformatted text preview: Test Code : RC (Short Answer Type) 2008 JRF in Computer and Communication Sciences The Candidates for Junior Research Fellowship in Computer Science and Communication Sciences will have to take two tests  Test MIII (objective type) in the forenoon session and Test RC (short answer type) in the after noon session. The RC test booklet will have two groups as follows: GROUP A A test for all candidates in logical reasoning and basics of programming, carrying 20 marks. GROUP B A test, divided into five sections, carrying equal marks of 80 in the following areas at M.Sc./M.E./M.Tech. level: (i) Mathematics, (ii) Statistics, (iii) Physics, (iv) Radiophysics/ Telecommunication/ Electronics/ Electrical Engg., and (v) Computer Science. A candidate has to answer questions from only one of these sec tions, according to his/her choice. The syllabi and sample questions of the RC test are given overleaf. 1 Syllabus Elements of Computing: Logical reasoning, basics of programming (using pseudocodes), Elementary data types and arrays. Mathematics: Graph theory and combinatorics: Graphs and digraphs, paths and cycles, trees, Eulerian graphs, Hamiltonian graphs, chromatic numbers, planar graphs, tournaments, inclusionexclusion principle, pigeonhole principle. Linear programming: Linear programming, simplex method, duality. Linear algebra: Vector spaces, basis and dimension, linear transformations, matrices, rank, inverse, determinant, systems of linear equations, character istic roots (eigen values) and characteristic vectors (eigen vectors), orthog onality and quadratic forms. Abstract algebra: Groups, subgroups, cosets, Lagrange’s theorem, normal subgroups and quotient groups, permutation groups, rings, subrings, ideals, integral domains, fields, characteristic of a field, polynomial rings, unique factorization domains, field extensions, finite fields. Elementary number theory: Elementary number theory, divisibility, congru ences, primality. Calculus and real analysis: Real numbers, basic properties, convergence of sequences and series, limits, continuity, uniform continuity of functions, differentiability of functions of one or more variables and applications, in definite integral, fundamental theorem of calculus, Riemann integration, im proper integrals, double and multiple integrals and applications, sequences and series of functions, uniform convergence. Differential equations: Solutions of ordinary and partial differential equa tions and applications. Statistics: Probability Theory and Distributions: Basic probability theory, discrete and continuous distributions, moments, characteristic functions, Markov chains. Estimation and Inference: Sufficient statistics, unbiased estimation, max imum likelihood estimation, consistency of estimates, most powerful and uniformly most powerful tests, unbiased tests and uniformly most powerful unbiased tests, confidence sets....
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 Winter '11
 PhanThuongCang
 Normal Distribution, probability density function, maximum likelihood estimator, Elementary number theory

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