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

**Join the Group **

CSIR-NET Exam Application form Released Date **:** **01 May 2024**

Last Date for submission of the application form **:** **21 May 2024**

Admit Card Release **:** **Before the Exam **

CSIR-NET Exam Date **:** **25 – 27 June 2024**

Conduct Agency **:** **NTA **(National Testing Agency )

CSIR-NET Exam Pattern **:** **Online Mode**

CSIR-NET Exam Result **: Notified Soon **

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 Question to be Attempted | 15 | 25 | 20 | 75 |

Marks for each correct Answer | +2 | +3 | +4.75 | – |

Maximum Marks | 30 | 75 | 95 | 200 |

Negative Marking | -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 **

**CSIR-NET Exam Application Fees **

- General Category can apply for the examination fees
**Rs.1150 / –**only. - EWS / OBC Category can apply for the examination fees
**Rs.600 / –**only. - SC / ST / PH Category can apply for the examination fees
**Rs.325 / –**only.

**Steps To Check CSIR-NET Exam Result **

- Visit the Official Website of CSIR-NET Exam 2024 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.

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** **

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