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GATE Mathematics(MA) Solutions (Topic-wise & Year-wise)

Handwritten Solution of GATE Mathematics for self preparation. We provide best quality notes for self preparation of GATE Mathematics for those who can not afford coaching. Best way to prepare for GATE 2022 is to do practice of problems from Previous Yr. Questions of GATE Mathematics. Start your preparation of GATE 2022 with P Kalika Notes and make a path to success.

Year-wise Solution

GATE Topic-wise Solution

Buy All PDF Study Materials & Solutions for GATE: Click Here

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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.

  1. Sol. of Linear algebra(Upto Nov-2020, Pages:205): Download PDF
  2. Sol. of Abstract algebra(Upto Nov-2020, Pages:107): Download PDF
  3. Sol. of Real Analysis(Upto Nov-2020, Pages:210): Download PDF
  4. Sol. of Complex Analysis(Upto June-2020, Pages:118): Download PDF
  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

  1. CSIR-NET 26 Nov 2020: Download Here
  2. CSIR-NET Dec-2019: Download Here
  3. CSIR-NET June-2019: Download PDF
  4. CSIR-NET Dec-2018: Download PDF
  5. CSIR-NET June-2018: Download PDF
  6. Combined Solutions of 2017D, 2018J, 2018D, 2019J, 2019D & 2020Nov Download Here
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GATE-2021 Mathematics(MA) Modified Syllabus (New)

Note: Syllabus of GATE-2021 have been revised. New Syllabus is presented here. (Check Old Syllabus of GATE-2020)

Calculus: Functions of two or more variables, continuity, directional derivatives, partial derivatives, total derivative, maxima and minima, saddle point, method of Lagrange’s multipliers; Double and Triple integrals and their applications to area, volume and surface area; Vector Calculus: gradient, divergence and curl, Line integrals and Surface integrals, Green’s theorem, Stokes’ theorem, and Gauss divergence theorem.

Abstract Algebra: Groups, subgroups, normal subgroups, quotient groups, homomorphisms, automorphisms; cyclic groups, permutation groups, Group action,Sylow’s theorems and their applications; Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domains, Principle ideal domains, Euclidean domains, polynomial rings, Eisenstein’s irreducibility criterion; Fields, finite fields, field extensions,algebraic extensions, algebraically closed fields.

Linear Algebra: Finite dimensional vector spaces over real or complex fields; Linear transformations and their matrix representations, rank and nullity; systems of linear equations, characteristic polynomial, eigenvalues and eigenvectors, diagonalization, minimal polynomial, Cayley-Hamilton Theorem, Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, symmetric, skew-symmetric, Hermitian, skew-Hermitian, normal, orthogonal and unitary matrices; diagonalization by a unitary matrix, Jordan canonical form; bilinear and quadratic forms.

Complex Analysis: Functions of a complex variable: continuity, differentiability, analytic functions, harmonic functions; Complex integration: Cauchy’s integral theorem and formula; Liouville’s theorem, maximum modulus principle, Morera’s theorem; zeros and singularities; Power series, radius of convergence, Taylor’s series and Laurent’s series; Residue theorem and applications for evaluating real integrals; Rouche’s theorem, Argument principle, Schwarz lemma; Conformal mappings, Mobius transformations.

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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

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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.
Quadratic forms, reduction and classification of quadratic forms

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.

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Free Maths Handwritten Study Materials (Donated)

To help students for their academics and competitive exams, we have started ‘Let’s Do’ Program in which anyone can take Notes FREELY and anyone can contribute*.

The following mathematical notes are contributed by students(mentioned below). These notes are available on FREE OF COST, You may download and share them.

We encourage you (BSc/MSc Students) to contribute your notes (Only scanned, Not hardcopy), your little contribution can help many people. Those who wish to contribute can send scanned notes on maths.whisperer@gmail.com.

(Notes are arranged in Alphabetical order(A-Z) )

  1. Classical Mechanics (New): Download PDF
    • (by  Rakhee Kumari, MSc, CUJ)
  2. Linear Algebra: Download PDF
    • (by  M. Sarojini, MSc, CUJ)
  3. Metric Space: Download PDF
    • (by  M. Sarojini, MSc, CUJ)
  4. Number Theory: Download PDF
    • (by  M. Sarojini, MSc, CUJ)
  5. Probability & Statistics: Download PDF
    • (by  M. Sarojini, MSc, CUJ)
  6. Real Analysis
    • Sequence(by Laxmi, MSc, Ranchi Univ.): Download PDF
    • Sequence, Series & Uniform Continuity(Rahul Anand, MSc, NIT Jalandhar): Download PDF
    • Point set Topology(Rahul Anand, MSc, NIT Jalandhar): Download PDF
  7. Ring Theory(Rahul Anand, MSc, NIT Jalandhar)Download PDF
  8. Free Study Materials(by P Kalika): Download Here

*Term & conditions for Contribution

  1. Notes will be Scanned in PDF Format
  2. Writing Should be Clear/Clean
  3. No Copyright Materials
  4. Only Notes Related to Mathematics
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CSIR NET Previous Yr. Que. Papers

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

  1. Nov-2020 (Que.+Ans, 26 Nov): Download PDF
  2. Dec-2019 (Que. Paper+Key): Download PDF
  3. Dec-2019(Assam)(Que. Paper+Key): Download PDF 
  4. June-2019 (Que. Paper+Key): Download PDF
  5. Dec-2018 (Que. Paper+Key): Download PDF
  6. June-2018 (Que. Paper+Key): Download PDF
  7.  Dec-2017 (Que. Paper+Key): Download PDF
  8. June-2017 (Que. Paper+Key): Download PDF
  9. Dec-2016 (Que. Paper+Key): Download PDF
  10. June-2016 (Que. Paper+Key): Download PDF
  11. Dec-2015 (Que. Paper+Key): Download PDF
  12. June-2015 (Que. Paper+Key): Download PDF
  13. Dec-2014 (Que. Paper): Download PDF
  14. June-2014 (Que. Paper+Key): Uploading Soon
  15. Dec-2013 (Que. Paper): Download PDF
  16. June-2013 (Que. Paper+Key): Download PDF
  17. Dec-2012(Que. Paper+Key): Download PDF
  18. June-2012 (Que. Paper+Key): Download PDF
  19. CSIR-NET June-2011: Download PDF
  20. CSIR-NET Dec-2011: Download PDF
  21. CSIR-NET 2008:  Download Paper-1 and Download Paper-2

CSIR NET Mathematical Science Syllabus: Download Syllabus

CSIR-NET Solutions(Upto 2020 June): Click Here

GATE Maths Solution(Upto 2021): Click Here

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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

  1. CSIR-NET Mathematics Que. Paper+Ans (2019-2011): Download Here
  2. CUCET PhD Mathematics Que. Paper+Ans (2020-2016): Download PDF
  3. Delhi University PhD Entrance Test(2015-2019): Download PDF
  4. GATE Mathematics Que Paper+Ans (2020-2010): Download PDF
  5. IIT Bombay PhD Screening Test(Dec 2015-May 2019): Download PDF
  6. IIT Kanpur PhD Screening Test(Dec 2015-May 2019): Uploading Soon
  7. IISc Banglore Int. PhD Test(178Pages): Uploading Soon
  8. ISI PhD Entrance Test(2015-2019): Uploading Soon
  9. JNU PhD Mathematics Que. Papers(2018-2015): Download PDF
  10. NBHM PhD Que Paper+Ans (2020-2005): Download PDF
  11. SAU PhD Admission Que. Paper(115 Pages): Download PDF
  12. TIFR Mathematics Que Paper(2020-2010): Download PDF
  13. BHU RET Que Paper(Math & Statistics): Uploading Soon
  14. P Kalika Practices Sets(52Pages): Download Practice Sets
  15. Any others: On Demand

Questions Paper of  MSc Entrance exams

  1. BHU PET Que Paper(Mathematics): Download PDF
  2. BHU PET Que Paper(Statistics): Download PDF
  3. CMI PG Entrance Papers(2010-2019): Uploading Soon
  4. CUCET MSc Maths Que. Paper(2019-2016+Sample): Download PDF
  5. JAM Mathematics(2020-2007): PDF Download
  6. NBHM MSc Que Paper(2019-2008): Uploading Soon
  7. TIFR Mathematics Que Paper(2019-2010): Download PDF
  8. University of Delhi(Central University): Uploading Soon
  9. University of Hyderabad(Central University): Download PDF
  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

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Youtube Videos on CSIR-NET/GATE

Video Lectures and Video Series for CSIR-NET/GATE on Important Topics, Marks Distribution, Cut off Set up, Preparation Strategy, Fast Revision, …etc.

Free Lectures Watch Here: https://www.youtube.com/playlist?list=PLDu0JgProGz55UHLDu7Y1xLd-uWSGxSPQ

Online Classes Started Now, Check here:

Numerical Analysis Free Crash Course for NET, GATE & SET.


Number Theory Crash Course for NET, GATE & SET.


(Fast and Complete Revision of Dynamical System)

(List of Important Topics and their weightage in CSIR-NET exam )

(Where & how Download PDF Que. Papers of  CSIR-NET, GATE, BHU, …etc)

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CSIR-NET, GATE, MSc/PhD Exams Notes Center (Handwritten Notes)

I. CSIR-NET, GATE, JAM, SET Study Materials

Group  Ring Theory  Calculus for GATE JAM, SET 85Pages(Kalika)_1  Complex  Real Complete_1   Power Series   Linear Algebra_1  Number Theory 76Pages(Kalika)_1  Numerical with sol 61Pages  PDE full Part-1 77Pages Sample 25_1  Integral   Topology 92pages by Kalika_1  LPP   COV (Kalika) 58pages   Functional Analysis by 58pages(Kalika)_1   Prob  Prob Dist        

II. Quick Revision Notes for NET, GATE, SET, NBHM

Group Theory Quick Revision 112Pages_1   Ring Theory Quick Revision 40Pages_1  Quick revision Real_1  Complex Short notes 28pages_1  Quick revision PDE_1    Quick revision ODE_1  

III. CSIR-NET Sol. (Year-wise & Topic Wise)

2019J Sol  2018Dec sol  2018J Sol  NET Solution 2019J-2017D 297Pages(Kalika)_1   Real Sol    Linear Sol  Complex Sol  CSIR Abstract Sol Upto June2019 71Pages_1  Applied Sol  NT, NA, LPP, DS Solutions 79Pages 35_1   GATE 2019 35Pages_1  GATE 2019-2018 (Kalika)94Pages_1

Note: For  ALL-IN-ONE Package/Multiple Notes, Study Material write us on maths.whisperer@gmail.com.

Feedbacks on Our Notes: https://pkalika.in/feedback-on-notes/


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CSIR-NET Exam Tricks for Qualifying

Exam Tips:
Try to solve all previous year questions of CSIR-NET and GATE exam. By doing this, you will get an idea about the important and scoring topics of CSIR-NET. Also during the Study of any study materials, prepare your own short/quick revision notes(of 3 or 4pages) on each topic, So that at the time of examination you may do a quick revision.

Now, stop reading books and start solving problems of previous year CSIR-NET exams. Also, analyze yourself that in which topics you can gain marks easily, and make them stronger.

Not only read theory & solve problems but also make a strategy for the exam a/c to your strong points & preparation.

Keep in mind that, it is not necessary to solve all problems in an exam, your guessing power should also be strong which comes by solving a lot of problems. So that you can easily discard the wrong options and can identify correct options.Tips for NETGate

Numerical Analysis, Dynamical System & Markov Chain:  These are easy and scoring topics for NET. So complete them first. You may practice and solve all problems of NET from these topics within about 1 day.

Note: All the above mentioned topics may be practiced and solved in a maximum of 2 or 3 days.

Important Topics and Marks weightage for Upcoming CSIR NET Exam

NET Marks wt_1

Also, during study/practice make a chart of important key points for quick revision in the last days of preparation. Here is a sample (Sample PDF download).MarksDistribution

CSIR-NET Cut off analysis and setting up the target for You

Important links:  Quick revision Notes for CSIR-NET, GATE & SET exam and Study Materials for NET/GATE/SET/ JAM/PhD