IIT JAM Mathematics is one of the best MSc exams in the country. Every year more than 14000 students appear for this exam for less than 500 seats. In this post, we will discuss complete guide of IIT JAM Mathematics paper including syllabus, the pattern of test paper, last 4 year papers of IIT JAM Mathematics, opening and closing rank, the number of seats in IITs for mathematics and at the end some useful tips and books to prepare for IIT JAM Mathematics.

IIT JAM Examination is conducted in six subjects, also referred to as Test Papers; Biotechnology (BT), Chemistry (CY), Geology (GG), Mathematics (MA), Mathematical Statistics (MS) and Physics (PH).

IIT JAM Mathematics comes with a bright future scope. Data scientist, data analyst, Researcher, teaching, software engineer are some of the jobs offered to Mathematics students from IITs. 


1. IIT JAM Syllabus for mathematics

2. The pattern of IIT JAM mathematics Test Papers

3. IIT JAM Mathematics previous year papers

4. Opening and Closing Ranks for IIT JAM 2020

5. IIT JAM Mathematics  Seats from IITs

6. Useful Tips for preparation of IIT JAM exam Mathematics

IIT JAM Syllabus for Mathematics:

Sequences and Series of Real Numbers: Sequence of real numbers, the convergence of sequences, bounded and monotone sequences, convergence criteria for sequences of real numbers, Cauchy sequences, subsequences, Bolzano-Weierstrass theorem. Series of real numbers, absolute 28 convergence, tests of convergence for series of positive terms – comparison test, ratio test, root test; Leibniz test for convergence of alternating series. Functions of One 

Real Variable: Limit, continuity, intermediate value property, differentiation, Rolle’s Theorem, mean value theorem, L'Hospital rule, Taylor's theorem, maxima, and minima. 

Functions of Two or Three Real Variables: Limit, continuity, partial derivatives, differentiability, maxima, and minima. Integral Calculus: Integration as the inverse process of differentiation, definite integrals, and their properties, fundamental theorem of calculus. Double and triple integrals, change of order of integration, calculating surface areas and volumes using double integrals, calculating volumes using triple integrals. 

Differential Equations: Ordinary differential equations of the first order of the form y'=f(x,y), Bernoulli’s equation, exact differential equations, integrating factor, orthogonal trajectories, homogeneous differential equations, variable separable equations, linear differential equations of second order with constant coefficients, Method of variation of parameters, Cauchy-Euler equation. 

Vector Calculus: Scalar and vector fields, gradient, divergence, curl, line integrals, surface integrals, Green, Stokes, and Gauss theorems. Group Theory: Groups, subgroups, Abelian groups, non-Abelian groups, cyclic groups, permutation groups, normal subgroups, Lagrange's Theorem for finite groups, group homomorphisms, and basic concepts of quotient groups.

Linear Algebra: Finite dimensional vector spaces, linear independence of vectors, basis, dimension, linear transformations, matrix representation, range space, null space, rank-nullity theorem. Rank and inverse of a matrix, determinant, solutions of systems of linear equations, consistency conditions, eigenvalues, and eigenvectors for matrices, Cayley-Hamilton theorem.

Real Analysis: Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets, completeness of R. Power series (of a real variable), Taylor’s series, radius and interval of convergence, term-wise differentiation and integration of power series.

IIT JAM Mathematics Topic-wise marks Distribution


Avg. Marks Distribution

Differential Calculus

23 Marks

Linear Algebra

13 Marks

Sequence and Series

12 Marks

Differential Equation

12 Marks

Integral Calculus

11 Marks

Group Theory

11 Marks

Vector Calculus

10 Marks

Real Analysis

8 Marks

The pattern of IIT JAM Mathematics Test Papers:

The JAM 2020 Examination for all the six test papers will be carried out as ONLINE Computer Based Test (CBT) where the candidates will be shown the questions in a random sequence on a computer screen. 

For all the six test papers, the duration of the examination will be 3 hours. The medium for all the test papers will be English only.

There will be a total of 60 questions carrying 100 marks. The entire paper will be divided into three sections, A, B, and C. All sections are compulsory. Questions in each section will be of different types as given below:

Section–A contains a total of 30 Multiple Choice Questions (MCQs) involving 10 questions of one mark each and 20 questions of two marks each.

Each MCQ has four choices out of which only one choice is the correct answer. Candidates can mark the answer by clicking the choice.

Section–B contains a total of 10 Multiple Select Questions (MSQs) carrying two marks each. Each MSQ is similar to MCQ but with the difference that MSQ may have one or more than one correct choice(s) out of the four given choices. 

The candidate gets full credit only if he/she selects all the correct answer(s) only and no wrong answers. Candidates can mark the answer(s) by clicking the choice(s).

Section–C contains a total of 20 Numerical Answer Type (NAT) questions involving 10 questions of one mark each and 10 questions of two marks each. 

For these NAT type questions, the answer is a signed real number, which needs to be entered using the virtual numeric keypad on the monitor. No choices will be shown for NAT questions.

In all sections, questions not attempted will result in zero marks. 

In Section-A (MCQ), the wrong answer will result in negative marks. For each wrong answer to 1 mark questions, 1/3 mark will be deducted and similarly, for each wrong answer to 2 marks questions, 2/3 mark will be deducted.

In Section-B (MSQ), there are no negative and no partial marking provisions. There is no negative marking in Section-C (NAT) as well.

There is a provision of using the online virtual calculator. The candidates, therefore, should not bring any calculator with them.

Mobile phones or any other electronic devices are strictly prohibited inside the examination hall. Charts, graph sheets, and tables are also NOT allowed inside the examination hall.

A scribble pad will be provided for rough work and this has to be returned back at the end of the examination.

The candidates are required to select the answer for MCQ and MSQ type questions using the mouse. The answer for NAT questions can be entered using a virtual numeric keypad (the keyboard of the computer will be disabled).

At the end of the 3 hours, the computer will automatically end the examination.

IIT JAM Mathematical Mathematics previous year papers:

1. IIT JAM Mathematics Question Paper year 2017

2. IIT JAM Mathematics Question Paper year 2018

3. IIT JAM Mathematics Question Paper year 2019

4. IIT JAM Mathematics Question Paper year 2020 (answer key)

IIT JAM Mathematics Seats from IITs

The competition is very high for IIT JAM Mathematics as  there are limited seats in IITs for mathematics and there are 14000+ candidates who apply for the IIT JAM Mathematics every year for over 450+ seats

Opening and Closing Ranks for IIT JAM 2020:

1. JAM 2019 Round 1 (First) Opening and Closing Ranks

2. JAM 2019 Round 2 (Second) Opening and Closing Ranks

3. JAM 2019 Round 3 (Final) Opening and Closing Ranks

Useful Posts for preparation of IIT JAM exam:

10 Tips and tricks to prepare for entrance exams

Pomodoro Technique: How to study more in less time?

6 ways to boost your performance in the exam

Useful Books for IIT JAM Mathematics papers:

Some topic wise IIT JAM Mathematics Reference Books that will help you to prepare better. These are the books referred by toppers of IIT JAM mathematics. 

 Integral Calculus: F. Ayres (Schaum’s), Gorakh Prasad

 Vector Calculus: Murray R. Spiegel (Schaum’s), A.R.Vasishtha

 Linear Algebra: Seymour Lipschitz (Schaum’s), H. Anton, A.R.Vasishtha.

 Ordinary Differential Equation: Peter J. Collins, G.F. Simmons, M.D. Raisinghania.

 Principle of Real Analysis: S. C. Malik.

 Real Analysis: Book by H. L. Royden, Book by Shanti Narayan

 Modern Algebra: A. R. Vasishtha, University Algebra by N. S. Gopalakrishnan.

More about IIT JAM 2021: IIT JAM 2021 Exam Dates, Syllabus, Application Form, Result

All the best for your IIT JAM Exam 2021.

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