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IIT JAM 2025 will be conducted by IIT Delhi on February 2, 2025. The IIT JAM Mathematics Syllabus 2025 includes a range of topics such as Set Theory, Real Analysis, Linear Algebra, Calculus, Probability, Complex Analysis, and Differential Equations.
In IIT JAM 2024, the highest score in the Mathematics paper was 98.67, while the cut-off for the General category was 33.5 marks, and for OBC-NCL, it was 30.1 marks. The total number of candidates who appeared for the Mathematics paper in 2024 was over 50,000, indicating the high competition.
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- What is the Syllabus of IIT JAM Maths 2025?
1.1 Brief Explanation of Key Topics
1.2 IIT JAM 2025 Mathematics Exam Pattern
1.3 Topic-wise Weightage for IIT JAM 2025 Mathematics
1.4 Which IIT Will Conduct IIT JAM 2025?
- How to Prepare for IIT JAM 2025: A Concise Guide
2.1 IIT JAM Mathematics: Previous Year Cut-off Analysis
What is the Syllabus of IIT JAM Maths 2025?
IIT JAM Mathematics Syllabus 2025 is designed to test your understanding of various mathematical concepts. and problem-solving skills at M.Sc. and other postgraduate programs in the field of mathematics This course covers the basics of various areas of mathematics. Including calculus, algebra, and real analysis. linear algebra, etc. It is important to understand each section of the syllabus in detail to help candidates prepare effectively.
IIT JAM Mathematics Syllabus 2025 Overview
| Section | Topics |
|---|---|
| Set Theory and Logic | Sets, relations, functions, binary operations, countable and uncountable sets, mathematical induction, propositional and first-order logic |
| Real Analysis | Limits, continuity, differentiation, Riemann-Stieltjes integration, sequences and series of functions, uniform convergence |
| Linear Algebra | Vector spaces, linear transformations, eigenvalues and eigenvectors, diagonalization, inner product spaces, Gram-Schmidt orthogonalization |
| Calculus | Differential and integral calculus, limits, continuity, differentiation, multiple integrals, Taylor’s theorem, applications |
| Differential Equations | First and second-order differential equations, linear differential equations, Laplace transform, series solutions of differential equations |
| Probability and Statistics | Probability theory, random variables, probability distributions, moment-generating functions, statistical inference, estimation, hypothesis testing |
| Complex Analysis | Complex functions, analytic functions, Cauchy-Riemann equations, Cauchy’s integral theorem, series expansions, residue theorem |
| Numerical Methods | Solutions of algebraic equations, numerical differentiation and integration, root-finding methods, interpolation techniques |
| Geometry | Coordinate geometry of two and three dimensions, conic sections, straight lines, and planes |
| Vectors and 3D Geometry | Scalar and vector products, equations of lines and planes in three dimensions, surface and volume integrals |
Brief Explanation of Key Topics
- Set Theory and Logic
Focuses on operations with sets, relations, functions, logical statements, and mathematical induction techniques.
| Topic | Sub-topics |
|---|---|
| Set Theory | Operations on sets, Venn diagrams, power sets, relations, functions, countability, set identities |
| Relations and Functions | Types of relations (reflexive, symmetric, transitive), binary operations, functions, inverse functions |
| Mathematical Induction | Principle of mathematical induction, applications of induction, pigeonhole principle |
| Logic | Propositional logic, logical connectives, truth tables, equivalences, quantifiers |
- Real Analysis
Involves limits, continuity of functions, differentiation, Riemann-Stieltjes integration, and convergence of sequences/series.
| Topic | Sub-topics |
|---|---|
| Limits and Continuity | Limits of functions, continuity of functions, types of discontinuities, properties of continuous functions |
| Differentiation | Differentiation rules, applications of differentiation, mean value theorem, Taylor’s theorem |
| Riemann-Stieltjes Integration | Concept of integration, properties of Riemann-Stieltjes integrals, applications |
| Sequences and Series | Convergence of sequences, series, tests for convergence (e.g., ratio test, comparison test), power series |
- Linear Algebra
Covers vector spaces, eigenvalues and eigenvectors, linear transformations, and inner product spaces, all of which are foundational for matrix theory and solving linear systems.
| Topic | Sub-topics |
|---|---|
| Vector Spaces | Definition of vector spaces, subspaces, linear independence, basis, and dimension |
| Linear Transformations | Definition of linear transformations, kernel and range, isomorphisms |
| Eigenvalues and Eigenvectors | Eigenvalue equation, diagonalization of matrices, characteristic equation, Cayley-Hamilton theorem |
| Inner Product Spaces | Inner product, no |
- Calculus
Includes differentiation, integration techniques (e.g., substitution, integration by parts), Taylor's theorem, and multiple integrals for higher-dimensional problems.
| Topic | Sub-topics |
|---|---|
| Differentiation | Basic differentiation techniques, implicit differentiation, applications in maxima/minima problems |
| Integration | Integration techniques (substitution, integration by parts), definite and indefinite integrals, integration of trigonometric functions |
| Multiple Integrals | Double and triple integrals, change of variables in multiple integrals, applications |
| Taylor's Theorem | Taylor and Maclaurin series, Lagrange’s remainder term, applications in approximation |
- Differential Equations
Encompasses solving first and second-order differential equations, methods for solving using Laplace transforms, and series solutions to complex equations.
| Topic | Sub-topics |
|---|---|
| First-order Differential Equations | Separable equations, exact equations, integrating factor, linear differential equations |
| Second-order Linear Differential Equations | Homogeneous and non-homogeneous equations, method of undetermined coefficients, variation of parameters |
| Laplace Transforms | Laplace transforms, inverse transforms, application to solving differential equations |
| Series Solutions | Solution of differential equations using power series, Frobenius method |
- Probability and Statistics
Focuses on probability theory (random variables, distributions), along with statistical inference including hypothesis testing, estimation, and moment-generating functions.
| Topic | Sub-topics |
|---|---|
| Probability Theory | Basic concepts (sample space, events, probability), conditional probability, Bayes’ theorem, random variables |
| Probability Distributions | Discrete and continuous distributions (Binomial, Poisson, Normal, Exponential, etc.), expectation, variance |
| Moment Generating Functions | Definition, properties, use in finding moments of distributions |
| Statistical Inference | Point estimation, maximum likelihood estimation, confidence intervals, hypothesis testing |
- Complex Analysis
Deals with complex functions, their properties, the Cauchy-Riemann equations for analyticity, and contour integration techniques to evaluate integrals in the complex plane.
| Topic | Sub-topics |
|---|---|
| Complex Functions | Real and imaginary parts, domain, range, and limits of complex functions |
| Analytic Functions | Cauchy-Riemann equations, conditions for differentiability, properties of analytic functions |
| Cauchy’s Integral Theorem | Statement of the theorem, applications to contour integration, Cauchy’s Integral Formula |
| Series Expansions | Power series, Laurent series, radius of convergence, singularities of complex functions |
| Residue Theorem | Definition of residues, calculation of integrals using residues |
- Numerical Methods
Includes methods for solving equations (e.g., Newton-Raphson), numerical differentiation/integration, and interpolation techniques to estimate values of functions.
| Topic | Sub-topics |
|---|---|
| Root-finding Methods | Bisection method, Newton-Raphson method, Secant method, false position method |
| Numerical Integration | Trapezoidal rule, Simpson’s rule, error estimation in numerical integration |
| Numerical Differentiation | Forward, backward, and central difference formulas, applications |
| Interpolation | Lagrange and Newton interpolation, spline interpolation, applications in curve fitting |
- Geometry and Vectors
Involves 2D and 3D coordinate geometry (conic sections, lines, planes) and vector operations such as dot/cross products and their geometric interpretations.
| Topic | Sub-topics |
|---|---|
| Coordinate Geometry | Cartesian coordinates, equations of straight lines, circles, conic sections (parabola, ellipse, hyperbola) |
| 3D Geometry | Vector representation of points and lines in space, equations of planes and lines, distances between points/lines/planes |
| Vector Products | Scalar product, vector product, triple scalar product, applications in geometry |
IIT JAM 2025 Mathematics Exam Pattern
The IIT JAM Mathematics exam follows a multiple-choice and numerical answer type pattern, with questions from various mathematical topics. Here is an overview of the exam pattern:
| Section | Number of Questions | Type of Questions | Marks per Question | Negative Marking |
|---|---|---|---|---|
| Section A | 30 questions | Multiple Choice Questions (MCQs) | 2 marks per question | -1 mark for each incorrect answer |
| Section B | 10 questions | Multiple Select Questions (MSQs) | 2 marks per question | No negative marking for MSQs |
| Section C | 20 questions | Numerical Answer Type (NAT) | 2 marks per question | No negative marking |
| Total | 60 questions | Mixed types (MCQs, MSQs, NATs) | 120 marks total | -1 mark for incorrect MCQs |
- Section A (MCQs): Multiple-choice questions, each with four options, only one of which is correct. Negative marking of −1 mark for each incorrect answer.
- Section B (MSQs): Multiple Select Questions, where more than one option may be correct. No negative markings for wrong answers.
- Section C (NAT): Numerical Answer Type questions with no options. No negative markings for incorrect or unanswered questions.
Topic-wise Weightage for IIT JAM 2025 Mathematics
The following table provides an approximate weightage for each topic in the IIT JAM Mathematics exam. The weightage is based on previous trends and is subject to minor changes each year.
| Topic | Sub-topics | Approximate Weightage |
|---|---|---|
| Set Theory and Logic | Set operations, relations, functions, induction, propositional logic | 6–8% |
| Real Analysis | Limits, continuity, differentiation, Riemann-Stieltjes integration, sequences and series | 15–18% |
| Linear Algebra | Vector spaces, linear transformations, eigenvalues, matrices, inner product spaces | 15–18% |
| Calculus | Differentiation, integration techniques, Taylor's theorem, multiple integrals | 18–20% |
| Differential Equations | First and second-order differential equations, Laplace transform, series solutions | 12–14% |
| Probability and Statistics | Probability theory, random variables, probability distributions, statistical inference | 8–10% |
| Complex Analysis | Complex functions, analytic functions, Cauchy’s integral theorem, residues | 8–10% |
| Numerical Methods | Root-finding methods, numerical integration, interpolation | 6–8% |
| Geometry and Vectors | Coordinate geometry, conic sections, and vectors in 3D | 6–8% |
Which IIT Will Conduct IIT JAM 2025?
The Indian Institute of Technology (IIT) Delhi will be responsible for conducting the IIT JAM 2025 exam. Every year there will be one Master of Science (JAM). For the year 2025, IIT Delhi will be responsible for the exam. Including all application procedures Conducting the exam and Announcement of Results, IIT Delhi is famous for its rigorous academic standards and technological innovations. This ensures that the examination process is well-organized and fair.
How to Prepare for IIT JAM 2025: A Concise Guide
The IIT JAM 2025 exam will be conducted on February 2, 2025. With less than two months left, effective preparation is crucial for success. Here’s a focused, concise preparation strategy.
Create a Short-Term Timetable (2 Months)
| Time Frame | Focus Areas | Goals |
|---|---|---|
| Now - Mid-January | Core Topics (Calculus, Linear Algebra, Real Analysis) | Build conceptual clarity and solve basic problems |
| Mid-January - February 1st Week | Advanced Topics (Differential Equations, Complex Analysis) | Solve higher-level problems and review core topics |
| Last Week | Mock Tests, Previous Year Papers | Simulate exam conditions, improve speed and accuracy |
Practice with Mock Tests & Previous Year Papers
| Activity | Frequency | Purpose |
|---|---|---|
| Mock Tests | Every 3-4 days | Build exam stamina, analyze time management |
| Previous Year Papers | 2-3 papers each week | Understand trends, improve problem-solving speed |
Check the Previous year's question paper with the answer key
- IIT JAM 2024 Question Paper with Answer Key
- IIT JAM 2023 Question Paper with Answer Key
- IIT JAM 2022 Question Paper with Answer Key
- IIT JAM 2021 Question Paper with Answer Key
IIT JAM Mathematics: Previous Year Cut-off Analysis
For candidates preparing for IIT JAM Mathematics 2025, understanding the cut-off trends is crucial. The cut-off marks represent the minimum score required to qualify for the exam and secure admission into postgraduate programs offered by IITs and IISc. These cut-offs depend on factors like the difficulty level of the paper, the number of candidates, and the total seats available.
Previous Year Cut-off for IIT JAM Mathematics
| Year | General Category Cut-off | OBC-NCL/EWS Cut-off | SC/ST/PWD Cut-off |
|---|---|---|---|
| 2024 | 33.5 | 30.1 | 16.7 |
| 2023 | 31 | 27.9 | 15.5 |
| 2022 | 36 | 32.5 | 18 |
| 2021 | 24.7 | 22.2 | 12.3 |
The IIT JAM Mathematics exam 2025 is the gateway to prestigious postgraduate courses at top IITs and IISc. With an expected score of 32–35 for the general category, applicants should focus on subjects with heavy weightage, e.g. Calculus and linear algebra Past trends show that the cut-off for reserved categories is much lower. This creates more opportunities for a diverse range of applicants. to succeed Aim to score above the cutoff by practicing mock tests. Review key ideas and maintain a consistent effort.
Download the Other Subjects syllabus of IIT JAM 2025
IIT JAM Syllabus 2024 for Mathematics
The candidate will have to cover all the topics from each section of the syllabus to compete and get a high score in the entrance examination easily. The detailed Mathematics syllabus of IIT JAM is mentioned below in a table.
| Topic | Subtopic |
|---|---|
| Sequences and Series of Real Numbers | All the areas covered in this topic are Sequence of real numbers, the convergence of sequences, bounded and monotone sequences, convergence criteria for sequences of real numbers. Apart from that, there are Cauchy sequences and sub-sequences, Bolzano-Weierstrass theorem. Also, there are Series of real numbers, absolute convergence, tests of convergence for series of positive terms that includes comparison test, ratio test, root test and also Leibniz test for convergence of alternating series, etc. |
| Differential Equations | Under this section all the areas are 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. There are also includes variable separable equations along with linear differential equations that are only for second order with constant coefficients. And also, the Method of variation of parameters, Cauchy-Euler equation is there. |
| Integral Calculus | This section includes details on Integration that defines as the inverse process of differentiation along with definite integrals, and all the properties with the fundamental theorem of calculus. Besides that, there are Double and triple integrals, details on change of order of integration, the process to calculate surface areas and volumes with the help of double integrals and also includes calculating volumes with the help of triple integrals. |
| Linear Algebra | All the areas that falls in this section are Finite dimensional vector spaces along with linear independence of vectors, its basis and dimension, linear transformations, details on matrix representation and also range space with null space, concepts on rank-nullity theorem. It also covers Rank and inverse of a matrix, determinant and all the solutions of linear equation’s systems. On the contrary there are consistency conditions along with eigenvalues, and also eigenvectors for matrices, Cayley-Hamilton theorem, etc in this section. |
IIT JAM 2024 Mathematics Exam Pattern
IIT JAM 2024 exam pattern for Mathematics is given below.
| Particulars | Details |
|---|---|
| Duration of the Exam | 3 hrs |
| Number of Questions | 60 Questions |
| Total Sections | 3 (Section A, B and C) |
| Types of Questions |
|
| Negative Marking | Only for Section A |
| Total Marks | 100 |
Section Wise Break up of Marks and Questions
| Section | No. of Questions | Marks per Question | Total Marks | Negative Marking |
|---|---|---|---|---|
| Section A | 10 | 1 | 10 | ⅓ |
| 20 | 2 | 40 | ⅔ | |
| Section B | 10 | 2 | 20 | Not Applicable |
| Section C | 10 | 1 | 10 | Not Applicable |
| 10 | 2 | 20 | ||
| 60 | 100 |
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Weightage of IIT JAM Mathematics Topics
Based on the paper analysis of previous years the important topics, with their weightage are tabulated below:
| Topic | Weightage |
|---|---|
| Real Analysis | 21% |
| Calculus of Single Variable | 18% |
| Linear Algebra | 14% |
| Calculus of Two Variables | 14% |
| Vector Calculus | 12% |
| Differential Equation | 11% |
| Abstract Algebra | 10% |
IIT JAM Mathematics Books for 2024 Preparation
Here we bring a list of books for IIT JAM 2024 Mathematics paper. These books will guide the candidates to prepare better for this section.
| Topic | Author |
|---|---|
| Ordinary Differential Equation | Peter J. Collins, G.F. Simmons, M.D. Raisinghania. |
| Real Analysis | H. L. Royden. |
| Principles of Real Analysis | S. C. Malik. |
| Linear Algebra | Seymour Lipschitz (Schaum’s), H. Anton, A.R.Vasishtha. |
| Modern Algebra | A. R. Vasishtha 8. University Algebra: N. S. Gopalakrishan. |
| Integral Calculus | F. Ayres (Schaum’s), Gorakh Prasad |
| Vector Calculus | Murray R. Spiegel (Schaum’s), A.R.Vasishtha |
What are Some Tips to Prepare IIT JAM Syllabus for Mathematics?
To start preparation for IIT JAM Syllabus for Mathematics, the candidate needs to take an effective way and also follow some tips to score higher than the average marks. As per the survey, Mathematics in IIT JAM is one of the most scoring subjects. Below are some tips for the subject of Mathematics.
- Candidate should make a list of all the topics and point out the specific section in which they are weak and also need to concentrate on those topics.
- Candidate need to solve all the questions from at least two chapters per day
- It is required for all the candidates to make a timetable to complete all the sections from IIT JAM Syllabus for Mathematics and must follow this on regular basis.
- To enhance the speed and boost up confidence, the candidate should solve all the questions from the previous year
- Giving mock tests as many times as possible per week will help the candidate to know their ability or understand where they can stand and that will lead to improvement.
- Last but not least, practice is the best way to ace the examination and helps to get maximum score especially in Mathematics.
Read More IIT JAM Preparation Tips
IIT JAM Syllabus for Mathematics 2024 FAQs
Ques. What books can I follow to practice Vector Calculus from IIT JAM Syllabus for Mathematics?
Ans. Some books to practice Vector Calculus from IIT JAM Syllabus for Mathematics are as follows.
- Geometry & Vectors written by Vasishtha
- Calculus written by Thomas & Finny
Ques. What are the areas that I need to practice from Group Theory under IIT JAM Syllabus for Mathematics?
Ans. From the section Group Theory, you can practice Abelian as well as non-abelian groups, details on permutation groups and also Lagrange's Theorem only for finite groups, must have a primary idea on quotient groups, etc.
Ques. Do I need to concentrate only on the important topics from IIT JAM Syllabus for Mathematics?
Ans. It is good to practice all the sections from the syllabus for high marks, and so, you need to concentrate on all the topics in Mathematics as this is the scoring subject.
Ques. Shall I need to cover Real Analysis from IIT JAM Syllabus for Mathematics?
Ans. Yes, you will have to cover this section from the syllabus. Many topics that can come in the entrance examination are interior points and limit points, different kinds of sets, R. Power series that contains a real variable, Apart from that, Taylor’s series, radius and interval of convergence, integration of power series, etc.
Ques. How much time do I need to invest in the syllabus of Mathematics in IIT JAM?
Ans. As this is the scoring subject, so, you need to give a large amount of time to solve and practice all the topics from this syllabus.
*The article might have information for the previous academic years, which will be updated soon subject to the notification issued by the University/College.
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