# P Kalika

## A Site for Higher Mathematics ## CSIR-NET (Maths) Topic-wise & Year-wise Solutions

Handwritten Solutions of CSIR-NET Mathematics Prev. Yr. Que. Papers (Upto November-2020) is available here. Very very helpful in preparation of CSIR-NET, SET, GATE, PSC, …. and other equivalent exams. Self preparation materials(No need of any coaching).

Note: CSIR NET(JRF) Exam of June-2020 has been done in Nov-2020 and Exam for Dec-2020 and June-2021 still not held and also no any information out.

5. Sol. of NT, NA, LPP & DS (Upto 2021, Pages:118)Download PDF
6. Sol. of ODE, PDE, IE & COV(Upto Nov 2020, Pages:205): Download PDF
7. Combined Solutions (All above Sr. No. 1 – 6): Click Here

### CSIR-NET Year wise Complete Solution

6. Combined Solutions of 2017D, 2018J, 2018D, 2019J, 2019D & 2020Nov Download Here

## Free Test Series for CSIR-NET, SET, GATE, PSC

We have started providing topic-wise FREE test series for CSIR-NET, GATE, SET Aspirants. After the topic-wise test, we will start full tests. Test your knowledge here.

Note/Instruction:

1. The result will be released on 08:00 PM on respective days of tests. The result will be sent on your email id which you will enter in a test.
2. Related information will be shared on Telegram Channel: https://t.me/pkalika_mathematics
3. We welcome those who are interested in questions setting for a test, write to us on maths.whisperer@gmail.com.
4. Next Test: ODE+PDE+COV+IE Test-1 on 30/05/2020
5. Next Test: Abstract Algebra on 01/06/2020

CSIR-NET, SET & PhD Entrance Test(07/06/2020): Attend Test

Algebra(Abstract+Linear) Tests:-

Analysis(Real+Complex) Tests

• Complex Test-1(28/05/20): Attend Test-1
• Complex Test-2: – – – – – – – – – – –

Applied Part(ODE+PDE+LPP+NA) Tests

## Important Topics for CSIR NET

Comprehensive list of Topic-wise Marks distribution for CSIR-NET Exam. Important Topics of Complex Analysis for CSIR-NET & GATE

## CSIR-NET Mathematics Details Syllabus

CSIR-UGC National Eligibility Test (NET) for JRF & Lecturer-ship
Common Syllabus for PART ‘B’ AND ‘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, 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.

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.

UNIT – 2
Abstract Algebra: Permutations, combinations, pigeon-hole principle, inclusion-exclusion principle, derangements. Fundamental theorem of arithmetic, divisibility in Z, Number Theory: 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.

## CSIR NET Previous Yr. Que. Papers

FREE PDF Download Question Papers of CSIR-NET (Mathematical Science) year-wise upto 2020 (Latest).

12. June-2015 (Que. Paper+Key):

## Que. Papers of CSIR-NET, GATE, JAM, CUCET, BHU, JNU, IIT, NBHM, DU, …etc

Here, you will get the collection of Previous Year Que. Papers (Math & Stat.) for CSIR-NET(JRF), GATE, NBHM, TIFR, IITs, CUCET, …etc and many mores including MSc/PhD Entrance Que. Papers. Practice these questions for your entrance exams. It will be very very helpful and sufficient for qualifying.

Questions Paper of NET, GATE & Ph.D. Entrance

9. JNU PhD Mathematics Que. Papers(2018-2015):
15. Any others: On Demand

Questions Paper of  MSc Entrance exams

10. Others: On demand

Note:

• If you need any other Exam paper, write here.
• If you want to share any Que. Paper, then send it to help@pkalika.in

Related Posts:

## Probability and Statistics

Handwritten study materials of Probability, Probability Distribution & Statistics(Markov chain) for CSIR-NET, GATE(Stat.), NBHM-PhD, SET/SLET, PSC, …etc.

Practice Set

## Abstract/Modern Algebra

2. Abstract-2 (Ring Theory): (Buy Now

All Notes of Abstract Algebra (Available Now)

## Linear Algebra

1. Linear(Only Matrix Theory):

## Fast Revision Notes for CSIR-NET, GATE, JAM & SET exam

Followings FAST Revision notes are VERY VERY helpful for JAM, CSIR-NET, GATE, SET, NBHM, and PSC examinations.

2. Group Theory:
5. Numerical Analysis
6. Ordinary Differential Equations
8. Probability & Prob. Distribution(Sample PDF):
9. Linear Programming(LPP) with sol. Buy Now
10. Linear Algebra  Available Soon

## Real Analysis

Real Analysis handwritten study material for CSIR-NET, GATE, SET, JAM, NBHM, TIFR, PSC, PhD Interview, …etc

## Markov Chain (Statistics)

### Markov Chain (with solution)

Note: Every yr. 2~3 Questions came in CSIR-NET Exam, So it is important for NET (Marks: 03~12.50). Also easy to understand by putting a little effort. (Check Sample PDF)

No. of Pages: 61

Updated On: July 2021

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