## P. G. ENTRANCE EXAMS

#### CSIR NET/JRF

These are the entrance exams of POST GRADUATE COURSES (P.G.)

## Introduction

The main objective of this test will be to determine the eligibility of the Indian National candidates for the award of Junior Research Fellowships (JRF)/NET (National Eligibility Test) and also to determine their eligibility for appointment of Lecturers (NET) in subjects that fall under the faculty of Science & Technology.

CSIR-UGC NET Exam fir Science stream is conducted by CSIR in the following areas :-

## Infrastructure

- Chemical Sciences
- Earth, Atmospheric, Ocean and Planetary Sciences
- Life Sciences
- Mathematical Sciences
- Physical Sciences

## EDUCATIONAL QUALIFICATION

M. Sc or equivalent degree/ Integrated BS-MS/BS-4 years/BE/BTech/BPharma/MBBS with at least 55% marks for general and OBC-Non Creamy layer candidates (Central list only as provided in National Commission for Backward Classes website www.ncbc.nic.in) and 50% for SC/ST, Persons with disability (PwD) candidates.

Candidates enrolled for M.Sc or having completed 10+2+3 years of the above qualifying examination as on 01 March of every year, are also eligible to apply in the above subject under the Result Awaited (RA) category on the condition that they complete the qualifying degree with requisite percentage of marks within the validity period of two years to avail the fellowship from the effective date of award.

Such candidates will have to submit the attestation format (Given at the reverse of the application form) duly certified by the Head of the Department/Institute from where the candidate is appearing or has appeared.

BSc (Hons) or equivalent degree holders or students enrolled in Integrated MS-PhD program with at least 55% marks for general and OBC (Non Creamy layer) candidates; 50% marks for SC/ST, Persons with disability (PwD) candidates are also eligible to apply. Candidates with bachelor's degree will be eligible for CSIR fellowship only after getting registered/enrolled for PhD/Integrated PhD program within the validity period of two years.

The eligibility for lectureship of NET qualified candidates will be subject to fulfilling the criteria laid down by UGC. PhD degree holders who have passed Master's degree, with at least 50% marks are eligible to apply for Lectureship only.

The candidates with the above qualification are advised to fill up their degree with percentage of marks in column No. 18 to 21, as applicable.

## EXAMINATION CENTERS

The test will be held at 27 Centres spread all over India, as specified below:

**Bangalore, Bhavnagar, Bhopal, Bhubaneshwar, Chandigarh, Chennai, Cochin, Delhi, Guntur, Guwahati, Hyderabad, Imphal, Jammu, Jamshedpur, Jorhat, Karaikudi, Kolkata, Lucknow, Nagpur, Pilani, Pune, Raipur, Roorkee, Srinagar, Thiruvananthapuram, Udaipur and Varanasi.**

A candidate may opt for any of the above centres. No request for change of centre would ordinarily be granted. However, a request in writing for change of Centre may be entertained on merits. If sufficient number of candidates do not opt for any of the above Centres, that particular Centre may stand deleted from the above list OR otherwise also, the concerned candidates may be allotted another Centre nearest to their place of residence, at the discretion of CSIR. No TA/DA will be admissible to any candidate for attending the test, in any circumstances.

## AGE LIMIT

Exam Name | Age Limit |
---|---|

JRF (NET) | Maximum 28 years as on 01-01-2017 (upper age limit may be relaxed up to 5 years in case of candidates belonging to SC/ST/OBC(non creamy layer)/ Persons with disability (PwD) and female applicants). |

LS (NET) | No Upper Age Limit |

## EXAMINATION STRUCTURE

Exam paper consist of three Sections:

**The question paper shall be divided into three parts, (A, B & C) as per syllabus & Scheme of Exam**

**Part A:** Part 'A' shall be common to all subjects. This part shall contain questions pertaining to General Aptitude with emphasis on logical reasoning, graphical analysis, analytical and numerical ability, quantitative comparison, series formation, puzzles etc.

**Part B:** Part 'B' shall contain subject-related conventional Multiple Choice questions (MCQs), generally covering the topics given in the syllabus.

**Part C:** Part 'C' shall contain higher value questions that may test the candidate's knowledge of scientific concepts and/or application of the scientific concepts. The questions shall be of analytical nature where a candidate is expected to apply the scientific knowledge to arrive at the solution to the given scientific problem.

**Note:** The Exam Scheme for Chemical Sciences has been revised from June, 2017 CSIR-UGC (NET) Exam onwards. The revised exam scheme and model Question paper may be seen at CSIR HRDG website www.csirhrdg.res.in

## MARKING SCHEME

Negative marking for wrong answers, wherever required, shall be applicable as per subject wise scheme of Exam. If a question for any reason found wrong, the benefit of marks will be given to only those candidates who attempt the question. No grievances/representation with regard to Answer Key(s) after declaration of result will be entertained.

## Syllabus/Books

### 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 of real numbers and their convergence. limsup, liminf. Bolzano Weierstrass theorem, Heine Borel theorem. Continuity, uniform continuity, differentiability, mean value theorem. Sequences and series of functions, uniform convergence. Riemann sums and Riemann integral, Improper Integrals. Monotonic functions, types of discontinuity, functions of bounded variation, Lebesgue measure, Lebesgue integral. Functions of several variables, directional derivative, partial derivative, derivative as a linear transformation, inverse and implicit function theorems. Metric spaces, compactness, connectedness. Normed linear Spaces. Spaces of continuous functions as examples.

- Play with Graphs (arihant Publication). (Amit M Agarwal)
- Calculus – Monty J. Strauss
- Principle of Mathematical Analysis -S.L.Gupta, N.R. Gupta (Pearson Publication)
- Introduction to Real Analysis - William F.Trench (Pearson Publication)
- Real Analysis – Robert G Bartle (Wiley Publication)

## LINEAR ALGEBRA

Vector spaces, subspaces, linear dependence, basis, dimension, algebra of linear transformations. Algebra of matrices, rank and determinant of matrices, linear equations. Eigenvalues and eigenvectors, Cayley-Hamilton theorem. Matrix representation of 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.

- Linear Algebra Schaum's Series -(Tata McGraw-Hill Publication)
- Linear Algebra and its applications -Gilbert Strang
- Linear Algebra -Vivek Sahai, Vikas Bist(Narosa Publication)
- Linear Algebra and its ApplicationsDavid C. Lay

## 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, Cauchy-Riemann equations. Contour integral, Cauchy's theorem, Cauchy's integral formula, Liouville's theorem, Maximum modulus principle, Schwarz lemma, Open mapping theorem. Taylor series, Laurent series, calculus of residues. Conformal mappings, Mobius transformations.

- Complex Analysis - Dennis G. Zill
- Complex Variables - H.S. Kasana
- Complex Analysis - S Ponnusamy
- Complex Analysis -R.V. Churchill

## 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, normal subgroups, quotient groups, homomorphisms, cyclic groups, permutation groups, Cayley's theorem, class equations, Sylow theorems. Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domain, principal ideal domain, Euclidean domain. Polynomial rings and irreducibility criteria. Fields, finite fields, field extensions, Galois Theory.

- A First Course In Abstract Algebra -John B. Fraleigh
- Contemporary Abstract Algebra -Joseph A. Gallian
- Modren Algebra - Surjeet Singh and Qazi Zameeruddin (Vikas Publication)
- Abstract Algebra - David S. Dummit, Richard M. Foote (Wiley Publication)

## TOPOLOGY

Basis, Dense sets, subspace and product topology, separation axioms, connectedness and compactness.

- Introduction to topology and modern analysis - G.F. Simmons
- Metric Spaces –Pawan K. Jain, Khalil Ahmad (Pearson Publication).
- Topology of Metric Spaces - S.Kumaresan
- Topology - K. D. Joshi

## UNIT – 3

### ORDINARY DIFFERENTIAL EQUATIONS (ODE)

Existence and uniqueness of solutions of initial value problems for first order ordinary differential equations, singular solutions of first order ODE , system of first order ODE. General theory of homogenous and non-homogeneous linear ODEs, variation of parameters, Sturm-Liouville boundary value problem, Green's function.

- Differential Equations - Earl Codington (PHI Publication )
- Differential Equations -Shepley L. Ross

## PARTIAL DIFFERENTIAL EQUATIONS (PDE)

Lagrange and Charpit methods for solving first order PDE, Cauchy problem for first order PDE. Classification of second order PDE, General solution of higher order PDE with constant coefficients, Method of separation of variables for Laplace, Heat and Wave equations.

- Partial Differential Equations -T. Amaranath
- Introduction To Partial Differential Equations -K. Sankara Rao

## 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 interpolation, Numerical differentiation and integration, Numerical solutions of ODEs using Picard, Euler, modified Euler and Runge-Kutta methods.

- Numerical Analysis -R.K. Jain, S.R.K. Iyengar(New Age Publication )

## 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.

- Calculus of Variations - A. S. GUPTA

## 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.

- Linear Integral Equations - M D Raisinghania

## 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.

- Classical Mechanics - J. C. Upadhyaya

## 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. Probability inequalities (Tchebyshef, Markov, Jensen). Modes of convergence, weak and strong laws of large numbers, Central Limit theorems (i.i.d. case). Markov chains with finite and countable state space, classification of states, limiting behaviour of n-step transition probabilities, stationary distribution, Poisson and birth-and-death processes. Standard discrete and continuous univariate distributions. sampling distributions, standard errors and asymptotic distributions, distribution of order statistics and range.

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.Simple nonparametric tests for one and two sample problems, rank correlation and test for independence. Elementary Bayesian inference. Gauss-Markov models, estimability of parameters, best linear unbiased estimators, confidence intervals, tests for linear hypotheses. Analysis of variance and covariance. Fixed, random and mixed effects models.

Simple and multiple linear regression. Elementary regression diagnostics. Logistic regression. Multivariate normal distribution, Wishart distribution and their properties. Distribution of quadratic forms. Inference for parameters, partial and multiple correlation coefficients and related tests data reduction techniques: Principle component analysis, Discriminant analysis, Cluster analysis, Canonical correlation.

Simple random sampling, stratified sampling and systematic sampling. Probability proportional to size sampling. Ratio and regression methods. Completely randomized designs,randomized block designs and Latin-square designs. Connectedness and orthogonality of block designs, BIBD. 2K factorial experiments: confounding and construction. Hazard function and failure rates, censoring and life testing, series and parallel systems.

- Probablity and statistics - S. C. Gupta and V. K. Kapoor (S.Chand Publication)

## LINEAR PROGRAMMING PROBLEM AND OPERATIONS RESEARCH

Simplex methods, duality. Elementary queuing and inventory models. Steady-state solutions of Markovian queuing models: M/M/1, M/M/1 with limited waiting space, M/M/C, M/M/C with limited waiting space, M/G/1.

- Operations Research – Hamdy A. Taha