The Ultimate Guide to IIT JAM Mathematics Syllabus and Exam Pattern – by Dr. Gajendra Purohit | Mathscare
| Mode of Exam | Computer Based Test (CBT) |
| Duration | 3 Hours |
| Language | English |
| Sections | Section A – Multiple-Choice Questions (30 Q)
Section B – Multiple Select Questions (10 Q) Section C – Numerical Answer Type (20 Q) |
| Marking Scheme | Section A – 1 or 2 Marks
Section B – 2 Marks Section C – 2 Marks |
| Negative Marking | Section A – ⅓ deducted for 1 Mark Questions & ⅔ deducted for 2 Mark Questions
Section B – No Negative Marking Section C – No Negative Marking |
| Number of Questions | 60 Questions |
| Total Marks | 100 Marks |
| Type of Questions | Subject Specific Questions |
IIT JAM Mathematics Syllabus comprises –
Real Analysis:
Sequences and Series of Real Numbers: convergence of sequences, bounded and monotone sequences, Cauchy sequences, Bolzano-Weierstrass theorem, absolute convergence, tests of convergence for series – comparison test, ratio test, root test; Power series (of one real variable), radius and interval of convergence, term-wise differentiation and integration of power series.
Functions of One Real Variable: limit, continuity, intermediate value property, differentiation, Rolle’s Theorem, mean value theorem, L’Hospital rule, Taylor’s theorem, Taylor’s series, maxima and minima, Riemann integration (definite integrals and their properties), fundamental theorem of calculus.
Multivariable Calculus and Differential Equations:
Functions of Two or Three Real Variables: limit, continuity, partial derivatives, total derivative, maxima and minima.
Integral 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: Bernoulli’s equation, exact differential equations, integrating factors, orthogonal trajectories, homogeneous differential equations, method of separation of variables, linear differential equations of second order with constant coefficients, method of variation of parameters, Cauchy-Euler equation.
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Linear Algebra and Algebra:
Matrices: systems of linear equations, rank, nullity, rank-nullity theorem, inverse, determinant, eigenvalues, eigenvectors.
Finite Dimensional Vector Spaces: linear independence of vectors, basis, dimension, linear transformations, matrix representation, range space, null space, rank-nullity theorem.
Groups: cyclic groups, abelian groups, non-abelian groups, permutation groups, normal subgroups, quotient groups, Lagrange’s theorem for finite groups, and group homomorphisms.
Here, in IIT JAM Exam, Real Analysis and Linear Algebra are two of the high-weightage topics which should be an aspirant’s priority topics. But most students try to focus on just these two topics during their preparation resulting in exam mishaps. If a student focuses on a lesser number of topics, he/ she must maintain an accuracy of 90% or above which gets completely uncertain in an examination.
So it is crucial to understand & focus on all the topics equally to crack an exam positively. Relying only upon high-weightage topics might turn into an exam-day misadventure!
Happy Studying & All the Best for your Preparation. Stay Tuned for more such Tips & Advice!
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