ISI Mathematics Exam: Last 5 Years Question Papers

The Indian Statistical Institute (ISI) is renowned for its rigorous selection process for its prestigious Mathematics program. Aspiring mathematicians and statisticians eagerly await the chance to prove their mettle through the ISI Mathematics exam. This exam not only tests the depth of your mathematical knowledge but also your analytical and problem-solving skills. To help you prepare effectively, we have compiled the last 5 years of ISI Mathematics Previous Year Questions (PYQs).

Download ISI Mathematics PYQs (Last 5 Years)

To aid your preparation for ISI Entrance Exam, we have provided downloadable PDFs of the last 5 years of ISI Mathematics PYQs. These papers are a valuable resource for understanding the exam pattern, practicing various types of questions, and improving your problem-solving skills.

Year & Exam	Question Paper Link
ISI Mathematics Question Paper 2022	ISI Question Paper 2022 Set : A Download PDF
	ISI Question Paper 2022 Set : B Download PDF
ISI Mathematics Question Paper 2021	ISI Question Paper 2021 Set : A Download PDF
	ISI Question Paper 2021 Set : B Download PDF
ISI Mathematics Question Paper 2020	ISI Question Paper 2020 Set : A Download PDF
	ISI Question Paper 2020 Set :B Download PDF
ISI Mathematics Question Paper 2019	ISI Question Paper 2019 Set : A Download PDF
	ISI Question Paper 2019 Set : B Download PDF
ISI Mathematics Question Paper 2018	ISI Question Paper 2018 Set : A Download PDF
	ISI Question Paper 2018 Set : B Download PDF

Why Practice ISI Mathematics PYQs?

Practicing previous year questions is crucial for several reasons:

1. Understanding Exam Pattern: PYQs provide insights into the types of questions asked, the level of difficulty, and the marking scheme.
2. Time Management: Regular practice helps in managing time effectively during the actual exam.
3. Identifying Important Topics: Certain topics are frequently tested. PYQs help in identifying these key areas.
4. Self-Assessment: Solving PYQs enables you to assess your preparation level and identify areas that need improvement.

About the ISI Mathematics Exam

The ISI Mathematics JRF Math exam is conducted by the Indian Statistical Institute for admission to its many graduation and post graduation as well as PhD programs. The exam is known for its high level of difficulty and is highly competitive. Here’s a detailed overview for ISI Mathematics JRF Exam :

Exam Structure and Paper Pattern

The ISI Mathematics exam typically consists of two parts: Part 1 (Subjective) and Part 2 (Subjective).

Part 1: Subjective Type

• Number of Questions: 8-10 Subjective Questions
• Duration: 2 hours.
• Topics: Topics for MTA (Forenoon examination): Real Analysis, Measure and Integration, Complex Analysis, Ordinary Differential Equations, Functional Analysis.

Part 2: Subjective Type

• Number of Questions: Around 8 to 10 descriptive questions.
• Duration: 2 hours.
• Topics: Algebra, Linear Algebra, General Topology, Elementary Number Theory and Combinatorics.

Syllabus of ISI JRF Math Exam

The ISI Mathematics exam covers a wide range of topics. The complete syllabus is : Download PDF

1. Real analysis: Sequence and series of real numbers and functions, continuity and differentiability
   of real valued functions of one variable and applications, uniform convergence, Riemann integration,
   improper integrals, continuity and differentiability of real valued functions of several variables, partial
   derivatives and mixed partial derivatives, total derivative.
2. Lebesgue integration: Lebesgue measure on Rⁿ, measurable functions, Lebesgue integral, convergence almost everywhere, monotone and dominated convergence theorems, Fubini’s theorem.
3. Complex analysis: Analytic functions, Cauchy’s theorem and Cauchy integral formula, maximum modulus principle, Laurent series, singularities, theory of residues, contour integration.
4. Ordinary differential equations: First order ODE and their solutions, singular solutions, initial value problems for first order ODE, general theory of homogeneous and nonhomogeneous linear differential equations, second order ODE and their solutions.
5. Functional analysis: Normed linear spaces, Banach spaces, Hilbert spaces, compact operators. Knowledge of some standard examples like C[0, 1], L_p[0, 1]. Continuous linear maps (bounded linear operators). Hahn-Banach theorem, open mapping theorem, closed graph theorem, uniform boundedness principle.
6. Abstract algebra: Groups, homomorphisms, normal subgroups and quotients, isomorphism theorems, finite groups, symmetric and alternating groups, direct product, structure of finite Abelian groups, Sylow theorems. Rings and ideals, quotients, homomorphism and isomorphism theorems, maximal ideals, prime ideals, integral domains, field of fractions, Euclidean rings, principal ideal domains, unique factorization domains, polynomial rings. Fields, characteristic of a field, algebraic extensions, roots of polynomials, separable and normal extensions, finite fields.
7. Linear algebra: Vector spaces, linear transformations, characteristic roots and characteristic vectors, systems of linear equations, inner product spaces, diagonalization of symmetric and Hermitian matrices, quadratic forms.
8. General topology: Topological spaces, continuous functions, connectedness, compactness, separation axioms, product spaces, complete metric spaces, uniform continuity, Baire category theorem.
9. Elementary number theory and combinatorics: Divisibility, congruences, standard arithmetic functions, permutations and combinations, combinatorial probability.

Tips for Preparing for the ISI Mathematics Exam

1. Regular Practice: Consistent practice of PYQs and mock tests.
2. Conceptual Clarity: Focus on understanding fundamental concepts rather than rote learning.
3. Time Management: Practice solving questions within the stipulated time.
4. Revision: Regularly revise important topics and formulas.
5. Seek Help: Join study groups or seek help from mentors if needed.

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Frequently Asked Questions (FAQs) for ISI JRF Mathematics Exam

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Conclusion

The ISI JRF Mathematics Exam is a gateway to a prestigious research fellowship at the Indian Statistical Institute. By understanding the exam pattern, practicing PYQs, and preparing strategically, you can enhance your chances of success. Utilize the provided resources and FAQs to guide your preparation journey. Good luck!