# CSIR-UGC - JRF (NET)

#### CSIR UGC NET Maths Coaching in Chandigarh

*CSR Institute Of Mathematics:-*

*CSR Institute Of Mathematics:-*

#### At City Beautiful Chandigarh have been giving CSIR-NET/JRF Mathematics Coaching since 2008.*We have Specialization in Mathematical Sciences*.A large number of understudies have cleared Both NET as well as JRF Exam.

#### We provide the Best Coaching in Csir Net Mathematics.We Taking a Regular test to Enhance the performance level with the goal that they Qualify the Exams in Large Numbers.

## Model Question Paper For Csir Ugc Net Mathematics 2017 – CLICK HERE

CSIR UGC NET MATHS Coaching BY DR. KALER

## Minimum cut-off percentage –18th December 2016

##### Research Fellowship & Eligibility for Lectureship held on 18th December 2016

UNRESERVED – 59.50 %

OBC – 50.00 %

SC – 39.25 %

ST – 27.63 %

PWD – 26.00 %

UNRESERVED – 53.55 %

OBC – 45.00 %

SC – 35.33 %

ST – 25.00 %

PWD – 25.00 %

### **CSIR NET Qualified candidates for lecturer-ship.**

S. No. |
Category |
No. of Qualified Candidates |

1. |
UR (Un-Reserved) | 834 + 730 = 1564 |

2. |
OBC | 457 + 397 = 854 |

3. |
SC | 264 + 230 = 494 |

4. |
ST | 123 + 107 = 230 |

5. |
PWD | 45 + 36 = 81 |

Total |
1723 + 1500 = 3223 |

** CSIR NET/JRF December 2016 Result Declared, Check Here**

**CSIR NET/JRF December 2016 Result Declared, Check Here**

**Minimum cut-off percentage **

Award of fellowship/lectureship in different disciplines in the Joint CSIR-UGC test for Junior Research Fellowship & Eligibility for Lectureship held on 19th June 2016

** Mathematical Science**

Junior Research Fellowship (JRF)

UNRESERVED – 54.88 %

OBC -47.38 %

SC – 37.63 %

ST -25.00 %

PH/VH -25.75 %

Junior Research Fellowship (NET)

UNRESERVED – 49.39 %

OBC -42.64 %

SC- 33.87 %

ST -25.00 %

PH/VH -25.00 %

### CSIR UGC NET MATHS COACHING IN CHANDIGARH

### Eligibility Conditions for CSIR-UGC – JRF (NET)

### CSIR-UGC (NET) for Junior Research Fellowship and Lecturer-ship

CSIR UGC NET MATHEMATICS COACHING

About the CSIR-UGC (NET)

CSIR-NET Exam is mandatory for candidates aspiring to teach in various degree colleges/ universities in all over India.** CSIR-UGC conducts JRF/NET exam twice a year in the month of June and December. The exam will be conducted in different subjects like Mathematical Sciences, Physical Sciences & Life Sciences etc.**

**Recent changes in CSIR-UGC:**

- Observing that “the courts should not venture into the academic field, Delhi High Court has upheld the mandatory requirement of clearing the NET or SLET for appointment to the post of Lecturer.
- The University Grants Commission (UGC) framed the Rule & Regulations – 2009 in July. Which says that NET or SLET is mandatory for appointment of Lecturers.
- At least 55% marks or equivalent grade is required in master degree for NET qualification.
- At least one Professor in each Dept. in P.G. College is a requirement.
- The new regulations have also created an additional post senior professor. Accordingly, the new hierarchy in ascending order is an assistant professor, associate professor, professor and senior professor.
- One post of a professor in each department of the postgraduate college, and of 10% posts in an undergraduate college shall be of those from professors only.

# CSIR NET Maths December 2016: – Answer Keys

**Conditions of 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) Candidate enrolled for M.Sc. or having completed 10+2+3 years of the above qualifying examination 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.

B.Sc. (Hons) or equivalent degree holders or students enrolled in the integrated MS-Ph.D program with at least 55% marks for General & OBC candidates; 50% for SC/ST candidates, Physically and Visually handicapped candidates are also eligible to apply.

Candidates with bachelor’s degree, whether Science, engineering or any other discipline, will be eligible for fellowship only after getting registered/enrolled for Ph.D./integrated Ph.D. program within the validity period of two years.

The eligible for lectureship of NET qualified candidates will be subject to fulfilling the criteria laid down by UGC. Ph.D. degree holders who have passed Master’s degree prior to 19th September 1991 with at least 50% marks are eligible to apply for Lectureship only.

Age Limit & Relaxation:

For JRF (NET): Maximum 28 years (upper age limit may be relaxed up to 5 years in the case of candidates belonging to SC/ST/OBC (As per GOI central list), Physically handicapped/Visually handicapped and female applicants).

CSIR UGC NET MATHEMATICS COACHING

**MATHEMATICAL SCIENCES**

**EXAM SCHEME**

**TIME: 3 HOURS
MAXIMUM MARKS: 200**

From June 2011 CSIR-UGC (NET) Exam for Award of Junior Research Fellowship and Eligibility for Lectureship shall be a Single Paper Test having Multiple Choice Question (MCQs). The question paper shall be divided into three parts.

Part ‘A’

This part shall carry 20 questions pertaining to General Aptitude with emphasis on logical reasoning, graphical analysis, analytical and numerical ability, quantitative comparison, series formation, puzzle etc. The candidates shall be required to answer any 15 questions. Each question shall be of two marks. The total marks allocated to this section shall be 30 out of 200.

Part ‘B’

This part shall contain 40 Multiple Choice Questions (MCQs) generally covering the topics given in the syllabus. A candidate shall be required to answer any 25 questions. Each question shall be of three marks. The total marks allocated to this section shall be 75 out of 200.

Part ‘C’

This part shall contain 60 questions that are designed to test a 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. The questions in this part shall have multiple correct options. Credit in a question shall be given only on identification of all the correct options. No credit shall be allowed in a question if any incorrect option is marked as correct answer. No partial credit is allowed. A candidate shall be required to answer any 20 questions. Each question shall be of 4.75 marks. The total marks allocated to this section shall be 95 out of 200.

- For Part ‘A’ and ‘B’ there will be Negative marking @25% for each wrong answer. No Negative marking for Part ‘C’.
- To enable the candidates to go through the questions, the question paper booklet shall be distributed 15 minutes before the scheduled time of the exam.
- On completion of the exam i.e. at the scheduled closing time of the exam, the candidates shall be allowed to carry the question Paper Booklet. No candidate is allowed to carry the Question Paper Booklet in case he/she chooses to leave the test before the scheduled closing time.
- Best csir ugc net mathematics coaching in north India.

CSIR UGC NET MATHEMATICS COACHING

**CSIR-UGC (NET)**

CSIR-UGC holds a national eligibility test twice a year in the month of June and December for JRF and Lectureship (LS). Approximately 12000 students appear from Maths stream and among them, approximately two hundred students awarded eligibility certificate from CSIR/UGC, which make them eligible for teaching in various degree institutions all over India.

**Recent changes in CSIR-UGC:**

Observing that “the courts should not venture into an academic arena which is best suited for the academic arena which is best suited for academician and experts”, Delhi High Court has upheld the mandatory requirement of clearing the NET or SLET for appointment to the post of lecturer.

- The University Grants Commission had framed this rule called Regulations-2009 in July last year.
- NET or SLET mandatory for appointment of lecturers
- Good academic record, 55% marks (or equivalent grade) in master’s and NET qualification
- One of the professors in each department of a postgraduate college
- The new regulations have also created an additional post – senior professor. Accordingly, the new hierarchy in ascending order is an assistant professor, associate professor, professor and senior professor.
- One post of professor in each department of a postgraduate college, 10% posts in an undergraduate college shall be those of professors.

** SYLLABUS FOR CSIR UGC NET MATHEMATICAL SCIENCES**

General Aptitude (GA): Common to All Papers of Part A (CSIR UGC NET MATHEMATICS COACHING)

**Logical reasoning, graphical analysis, analytical and numerical ability, quantitative comparison, series formation, puzzle etc.**

(Common Syllabus for Part ‘B & C’)

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, limbs up, 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. Metric spaces, compactness, connectedness. Normed Linear 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. 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.

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.

**Algebra:** Permutations, combinations, pigeon-hole principle, inclusion-exclusion principle, derangements. The fundamental theorem of arithmetic, divisibility in

Permutations, combinations, pigeon-hole principle, inclusion-exclusion principle, derangements. The fundamental theorem of arithmetic, divisibility in Z, class equation congruences, Chinese Remainder Theorem, Euler’s Ø- function, primitive roots. Groups, subgroups, normal subgroups, quotient groups, homomorphisms, cyclic groups, permutation groups, Clay class equation, 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.

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, a system of first order ODEs.The general theory of homogeneous and non-homogeneous linear ODEs, a variation of parameters, Sturm-Liouville boundary value problem, Green’s function.

**Partial Differential Equations (PDEs)**Lagrange and Charpit methods for solving first order PDEs, the 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 interpolation, Numerical differentiation and integration, Numerical solutions of ODEs 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**A 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 the principle of least action, the Two-dimensional motion of rigid bodies, Euler’s dynamical equations for the motion of a rigid body about an axis, the 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 behavior of n-step transition probabilities, stationary distribution.
- 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, tests for linear hypotheses and confidence intervals. 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: Principal 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 blocks, and Latin-square designs.

Connectedness, and orthogonal block designs, BIBD. 2^{K}factorial experiments: confounding and construction.

Series and parallel systems, hazard function and failure rates, censoring and life testing. - 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 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 continuity, differentiability. Riemann integral, improper integrals, algebra of matrices, rank, and determinant of matrices, linear equations, eigenvalues and eigenvectors, quadratic forms.