ISI Kolkata Previous Years Sample Question Papers : Indian Statistical Institute

Name of the Organization : Indian Statistical Institute (isical.ac.in)
Type of Facility : Previous Years Sample Question Papers
Location : Bangalore

Website : http://www.isical.ac.in/

Previous Years Sample Question Papers :
Sample Question Papers For Junior Research Fellowship (JRF) in Computer Science :
The candidates for Junior Research Fellowship in Computer and Communication Sciences will have to take two tests – Test MMA (objective type) in the forenoon session and Test CSB (short answer type) in the afternoon session.

The CSB test booklet will have two groups as follows :
Group- A :
A test for all candidates in the basics of computer programming and discrete mathematics.

Group- B :
A test, divided into five sections in the following areas atM.Sc./M.E./M.Tech. level :
** Mathematics,
** Statistics,
** Physics,
** Electrical and Electronics Engineering, and
** Computer Science.

A candidate has to answer questions from only one of these sections in Group B, according to his/her choice. Group A carries 20 marks and Group B carries 80 marks.

The syllabi and sample questions of the CSB test are given overleaf.

Syllabi
Group- A :
Logical reasoning elementary combinatorics including inclusion-exclusion principle and pigeonhole principle; basics of programming (using pseudocode); elementary data structures including array, stack and queue; Boolean algebra.

Group- B :
Mathematics :
Graph theory and combinatorics :
Graphs, paths and cycles, trees, Eulerian graphs, Hamiltonian graphs, chromatic numbers, planar graphs, digraphs and tournaments.

Linear algebra :
Vector spaces, basis and dimension, linear transformations, matrices, rank, inverse, determinant, systems of linear equations, eigenvalues and eigenvectors, orthogonality.

Abstract algebra :
Groups, subsubgroups, 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, congruences, primality.

Calculus and real analysis :
Real numbers, convergence of sequences and series, limits, continuity, uniform continuity of functions, differentiability of functions of one or more variables, indefinite integral, fundamental theorem of integral calculus, Riemann integration, improper integrals, sequences and series of functions, uniform convergence.

Statistics :
Probability theory and distributions :
Basic probability theory, discrete and continuous distributions, moments, characteristic functions, Markov chains.

Estimation and inference :
Sufficient statistics, unbiased estimation, maximum likelihood estimation, consistency of estimates, most powerful and uniformly most powerful tests, unbiased tests and uniformly most powerful unbiased tests, confidence sets, Bayesian methods.

Linear models :
Gauss-Markov set up and least squares theory, multiple linear regression, one and two way analysis of variance.

Multivariate analysis :
Multivariate normal distribution, principal component analysis, multiple and canonical correlations, discriminant analysis

Downloads :
Previous Year : http://www.isical.ac.in/~deanweb/SAMPLEQUESTIONS.HTML
2013 : http://www.isical.ac.in/~deanweb/sample2013.html