CSIR-NET Exam , Syllabus , Application Form , Exam Date , Eligibility Criteria , Pattern

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CSIR-NET Exam Application form Released Date  : 10 March 2023

Last Date for submission of the application form : 10 April 2023

Admit Card Release : May 2023

CSIR-NET Exam Date : 06 – 08 June 2023

Conduct Agency : NTA (National Testing Agency )

CSIR-NET Exam Pattern : Online Mode 

CSIR-NET Exam Result : July – August 2023 

The Validity of CSIR-NET Exam Score Card : 2 Years ( Effective from the Date Mentioned in NET Certificate ) 

CSIR-NET Exam Eligibility Criteria : –

The condinates who qualify in CSIR-NET Exam shall have to fullfill the following Eligibility Requirement for Application form.

• M.sc / Equivalent Degree with 55 % Marks for General / OBC Candidates.
• For SC / ST and PH Candidates 50 % Marks .
• Intregrated Course and B.E / B.Tech / B.Pharma and MBBS Candidates are also Eligible for CSIR-NET Exam 2023.

CSIR-NET Exam Age Limit & Relaxation :- 

• For JRF (NET) : Maximum 28 years ( upper age limit may be relaxable up to 5 years in case of SC / ST / Persons with Disability (PWD) / female applicants and 03 years in case of OBC (Non – Creamy Layer) Applicants.
• For Lectureship ( NET ) : No upper Age limit.

CSIR-NET Exam Pattern : – 

• CSIR-NET Exam will conducted Online Mode(CBT) .
• Duration of  Exam will be 3 hours.
• The Paper will be asked in the English Language & Hindi Only .
• Section : 3 Sections ( Section – A , Section – B , Section – C ).
• Number of Questions : 120 Questions 
• Total Marks : 200 Marks.

CSIR-NET Exam Marking Pattern of the Paper :-

The examination is of  3 hours duration , There are a total 120 Questions carrying 200 Marks. The entire paper is divided into three Part- A , B and C . All sections are compulsory. Questions in each section are of different types.

• PART – A contains a Maximum of 20 Question of General Aptitude out of which only 15 Questions will be taken up for Evaluation. Each question carries 2 marks with negative marking of 0.5 marks.
• PART – B shall contain subject – related conventional MCQs. This part contains a maximum of 40 Questions out of which only 25 questions will be taken up for evalution. Each question carries 3 marks with negative marking of 0.75 marks.
• PART – C shall contain subject-related conventional MSQs. This part contains a maximum of 60 Questions out of which only 20 Questions will be taken up for Evaluation. Each question carries 4.75 marks with no negative marking.
• In all Parts , Questions not attempted will resulit in zero mark .

5. Only Virtual Scientific Calculator is allowed . Charts , Graph Sheets , Tables , Cellular Phone or Other Electronic Gadgets are NOT allowes in the examination hall.

Particulars	Part – A	Part – B	Part – C	Total
Total Questions	20	40	60	120
Maximum questions to be attempted	15	25	20	75
Marks for each correct answer	+ 2	+ 3	+ 4.75	–
Maximum Marks	30	75	95	200
Marks for each incorrect answer	– 0.5	– 0.75	0	–

Syllabus for Mathematical Science : – 

Unit – 1

Real Analysis : –

Elementary set theory , finite , countable and uncountable sets , Real number system as a complete ordered field , Archimedean property , supremum , infimum.

Sequence and series , convergence , limsup , liminf.

Bolzano Weierstrass theorem , Heine Borel theorem .

Continuity , uniform continuity , differentiability , mean value theorem .

Sequence 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 , Spaces of continuous functions as examples.

Linear Algebra :-

Vector spaces , subspaces , linear dependence , basis , dimension , algebra of linear transformations.

Algebra of matrices , rank and determinant of matrices, linear equations.

Eigen values and Eigen vectors , Cauchy- 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.

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.

Abstract Algebra : –

Permutations , combinations , pigeon – hole principle , inclusion – exclusion principle , derangements .

Fundamental theorem of arithmetic , divisibility in  , congruences , Chiness Remainder theorem , Euler’s  function, primitive roots.

Groups , Subgroups , normal subgroups , quotient groups , homomorphism , 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.

Topology :-

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

Unit – 3

Ordinary Differential Equations (ODE’s) : –

Existence and uniqueness of solutions of initial value problems for first- order ordinary differential equations, singular solutions of first – order ODE’s , a system of first – order ODE’s.

General theory of homogenous and non – homogeneous linear ODE’s , variation of parameters , Sturm -Liouville boundary value problem , Green’s function.

Partial Differential Equations (PDE’s) : –

Lagrange and Charpit methods for solving first – order PDE’s , Cauchy problem for first – order PDE’s.

Classification of second – order PDE’s , General solution of higher – order PDE’s 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 interpolation , Numerical differentiation and integration, Numerical solutions of ODE’s using Picard , Euler , modified Euler and Runge – Kutta methods.

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.

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 error and asymptotic distributions , distribution of order statistics and range.

Method 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 estimates , confidence intervals , tests for linear hypotheses . Analysis of variance and covariance. Fixed , random and mixed effects modes . Simple and multiple linear regression . Elementary regression diagnostics . Logistic regression.

Multivariate normal distribution , Wishart distribution and their properties . Distribution of quadratic form . 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 lock designs , BIBD . 2K factorial experiments : confounding and construction.

Hazard function and failure rates , censoring and life testing , series and parallel systems.

Linear programming problem , 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.

Syllabus Download :- 

csirnet_2023_syllabus

Download

CSIR-NET Exam Application Fees : –

• General Category can apply for the examination fees Rs.1100 / – only. 
• OBC Category can apply for the examination fees Rs.550 / – only. 
• SC / ST Category can apply for the examination fees Rs.275 / – only. 
• Pwd Category can apply for the examination fees zero .

Steps To Check CSIR-NET Exam Result :-

• Visit the Official Website of CSIR-NET Exam 2023 i.e,  csirnet.nta.nic.in
• On the Home Page, Search for the CSIR-NET Exam Result.
• Then click on the Result link.
• Enter your Email ID and Password.
• Then click on the Submit Button.
• Check the Result.
• Download and take the Printout of the Result.

Junior Research Fellowship Stipend :-

• The Stipend of JRF selected through CSIR-UGC National Eligibility Test (NET) will be Rs. 25000 / P.m. for the first two years.
• In addition , annual contingency grant Rs. 20000 /- per follow will be provided to the University / Institution. The Fellowship will be governed by terms and conditions of CSIR , UGC or Research Scheme , as Applicable.
• On Completion of two years as JRF and if the Fellow is registered for P.HD, the Fellowship will be upgraded to SRF asssessment of Fellows research progress / achievements through Interview by an Expert Committee consisting of the Guide . Head of the Department and External Member from outside the University Institution who is an Expert in the relevant field , not below the rank of Professor / Associate Professor. 

Join the CSIR NET Exam (Mathematics) Course  :- 

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