CSIR University Grants Commission NET JRF Mathematical Science previous year question

Will you please give me the CSIR University Grants Commission NET JRF Mathematical Science previous year question papers?

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Contact Details:
University Grants Commission New Delhi
Bahadur Shah Zafar Marg,
Balmiki Basti,
Vikram Nagar,
New Delhi,
Delhi 110002 ‎
093 33 778791 ‎
India

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Hello sir I am preparing for the NET JRF exam so please provide me the previous years papers of Mathematical Science paper.

National eligibility test is conducted by the University Grants Commission for Junior Research Fellow and Lecturer ship.

Eligibility for CSIR-JRF(NET)

Educational Qualification

BS-4 years program/BE/B. Tech/B. Pharma/MBBS/Integrated BS-MS/M.Sc. or Equivalent degree with at least 55% marks for General & OBC (50% for SC/ST candidates, Physically and Visually handicapped candidates).

Age Limit & Relaxation:

The age limit for admission to the Test is as under:

For JRF (NET): -Maximum 28 years

The reservation for reserved category is as per the govt rules.

Syllabus of exam

UNIT – 1:
Analysis: Elementary set theory, finite, countable and uncountable sets, Real number system as a complete ordered field, Archimedean property, supremum, infimum.Sequences and series, convergence, limsup, liminf.

Linear Algebra: Vector spaces, subspaces, lineardependence, BAsis, dimension, algebra of linear transformations.Algebra of matrices, rank and determinant of matrices, linear equations. Eigenvalues and eigenvectors, Cayley-Hamilton theorem.Matrix representationof linear transformations. Change of BAsis, canonical forms, diagonal forms, triangular forms, Jordan forms.Inner product spaces, orthonormal BAsis.Quadratic forms, reduction and classification of quadratic forms.

UNIT – 2:

Complex Analysis: Algebra of complex numbers, the complex plane, polynomials, Power series, transcendental functions such as exponential, trigonometric and hyperbolic functions. Analytic functions.

Algebra: Permutations, combinations, pigeon-hole principle, inclusion-exclusion principle, derangements.Fundamental theorem of arithmetic, divisibility in Z,congruences, Chinese Remainder Theorem, Euler’s Ø- function, primitive roots. Groups, subgroups.

UNIT – 3:
Ordinary Differential Equations (ODEs):
Existence and Uniqueness of solutions of initial value problems for first order ordinary differential equations, singular solutions of first order ODEs.

Partial Differential Equations (PDEs):
Lagrange and Charpit methods for solving first order PDEs, Cauchy problem for first order PDEs. Classification of second order PDEs, General solution of higher order PDEs with constant coefficients, Method of separation of variables for Laplace, Heat and Wave equations.

Numerical Analysis :
Numerical solutions of algebraic equations, Method of iteration and Newton-Raphson method, Rate of convergence, Solution of systems of linear algebraic equations using Gauss elimination and Gauss-Seidel methods, Finite differences, Lagrange, Hermite and spline.

Calculus of Variations:
Variation of a functional, Euler-Lagrange equation, Necessary and sufficient conditions for extrema. Variational methods for boundary value problems in ordinary and partial differential equations.

Linear Integral Equations:
Linear integral equation of the first and second kind of Fredholm and Volterra type, Solutions with separable kernels. Characteristic numbers and eigenfunctions, resolvent kernel.


Classical Mechanics:
Generalized coordinates, Lagrange’s equations, Hamilton’s canonical equations, Hamilton’s principle and principle of least action, Two-dimensional motion of rigid bodies, Euler’s dynamical equations for the motion of a rigid body about an axis, theory of small oscillations.

UNIT – 4:
Descriptive statistics, exploratory data analysis.

Sample space, discrete proBAbility, independent events, BAyes theorem, Random variables and distribution functions (univariate and multivariate); expectation and moments, Independent random variables, marginal and conditional distributions. Characteristic functions.

Markov chains with finite and countable state space, classification of states, limiting behaviour of n-step transition proBAbilities, stationary distribution.

Methods of estimation. Properties of estimators. Confidence intervals. Tests of hypotheses: most powerful and uniformly most powerful tests, Likelihood ratio tests. Analysis of discrete data and chi-square test of goodness of fit. Large sample tests.

Syllabus of Part - C

Mathematics: This section shall carry questions from Unit I, II and III.

Statistics: Apart from Unit IV, this section shall also carry questions from the following areas. Sequences and series, convergence, continuity, uniform continuty, differentibility. Remann integeral, improper integerals, algebra of matrices, rank and determinant of matrices, linear equations, eigenvalues and eigenvectors, quadratic froms.

Previous year question of mathematical science of NET JRF





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Previous year question of mathematical science of NET JRF.pdf (1.26 MB, 61 views)

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