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

**Join the Group :**

CSIR-NET Exam Application form Released DateÂ **:** **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**Â

CSIR-NET Exam Result **: July – August 2023Â **

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

**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 :-Â **

**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 : –Â **

- CSIR-NET Exam will conducted Online Mode(CBT) .
- Duration ofÂ 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 : 120Â QuestionsÂ
- Total Marks : 200 Marks.

**CSIR-NET Exam Marking Pattern of the Paper :-**

The examination is ofÂ 3 hoursÂ duration , There are a totalÂ 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.
- InÂ all Parts , Questions not attempted will resulit in zero mark .

5.Â 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 | Â Â 20 | Â Â 40 | Â Â 60 | Â Â 120 |

Maximum questions to be attempted | Â Â 15 | Â Â 25 | Â Â 20 | Â Â 75 |

Marks for each correct answer | Â + 2 | Â + 3 | Â + 4.75 | Â Â – |

Maximum Marks | Â Â 30 | Â Â 75 | Â Â 95 | Â Â 200 |

Marks for each incorrect answer | Â – 0.5 | Â – 0.75 | Â Â 0 | Â Â – |

**Syllabus for Mathematical Science : –Â **

**Unit â€“ 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 â€“ 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 , Cauchyâ€™s theorem , Cauchyâ€™s integral formula , Liouvilleâ€™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 â€“ hole principle , inclusion â€“ exclusion principle , derangements .

Fundamental theorem of arithmetic , divisibility in Â , congruences , Chiness Remainder theorem , Eulerâ€™s Â function, primitive roots.

Groups , Subgroups , normal subgroups , quotient groups , homomorphism , cyclic groups , permutation groups, Cayleyâ€™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 â€“ 3**

**Ordinary Differential Equations (ODEâ€™s) : – **

Existence and uniqueness of solutions of initial value problems for first- order ordinary differential equations, singular solutions of first â€“ order ODEâ€™s , a system of first â€“ order ODEâ€™s.

General theory of homogenous and non â€“ homogeneous linear ODEâ€™s , variation of parameters , Sturm -Liouville boundary value problem , Greenâ€™s function.

**Partial Differential Equations (PDEâ€™s) : – **

Lagrange and Charpit methods for solving first â€“ order PDEâ€™s , Cauchy problem for first â€“ order PDEâ€™s.

Classification of second â€“ order PDEâ€™s , General solution of higher â€“ order PDEâ€™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 â€“ Raphson method , Rate of convergence , Solution of systems of linear algebraic equations using Gauss elimination and Gauss â€“ Seidel methods , Finite differences , Lagrange , Hermite and spline interpolation , Numerical differentiation and integration, Numerical solutions of ODEâ€™s using Picard , Euler , modified Euler and Runge â€“ Kutta methods.

**Calculus of Variations : –**

Variation of a functional , Euler â€“ 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 , Lagrangeâ€™s equations , Hamiltonâ€™s canonical equations , Hamiltonâ€™s principle and principle of least action , Two â€“ dimensional motion of rigid bodies , Eulerâ€™s dynamical equations for the motion of a rigid body about an axis , theory of small oscillations.

**Unit â€“ 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 â€“ 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 â€“ 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 â€“ 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 :-Â **

csirnet_2023_syllabus**CSIR-NET Exam Application Fees : –**

- General Category can apply for the examination fees
**Rs.1100 / –**only.Â - OBC Category can apply for the examination fees
**Rs.550 / –**only.Â - SC / ST Category can apply for the examination fees
**Rs.275 / –**only.Â - 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,Â
**csirnet.nta.nic.in** - On the Home Page, Search for the
**CSIR-NET Exam Result.** - Then click on theÂ
**Result link.** - Enter yourÂ
**Email ID**Â andÂ**Password.** - Then click on theÂ
**Submit Button.** - Check theÂ
**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.Â

**Join the CSIR NET Exam (Mathematics) CourseÂ :-Â **

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