IIT JAM Mathematics Question Paper 2025 With Solutions PDF: Download Math Paper Here

IIT JAM Mathematics Question Paper 2025: The IIT JAM exam date is scheduled for the Feb 2, 2025. Mathematics is one of the most important subjects of the IIT JAM Mathematics examination. Each year, thousands of students appear for the IIT JAM Mathematics examinations to pursue a postgraduate degree in the field of mathematics at various immensely popular and highly prestigious institutions such as the IITs, NITs, IISERs and so on. Needless to say, both the competition and the difficulty levels are extreme.

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This Story also Contains

1. IIT JAM Mathematics Question Paper 2025
2. IIT JAM Mathematics Syllabus and Exam Pattern
3. IIT JAM Mathematics Question Paper Analysis
4. IIT JAM Mathematics Question Paper Analysis 2024
5. IIT JAM Mathematics Question Paper 2024
6. IIT JAM Mathematics Official Mock Test

Proper and dedicated IIT JAM Mathematics preparation is necessary for clearing the IIT JAM exam with a good IIT JAM exam score and securing admissions to the top colleges of the country. But as soon as the IIT JAM Mathematics examination concludes, the candidates should also engage themselves in a comprehensive IIT JAM Mathematics question paper 2025 analysis to assess their performance and calculate their potential IIT JAM Mathematics score. The candidates are requested to revisit this article on the IIT JAM Mathematics exam day for more updates including the IIT JAM Mathematics question paper analysis and memory-based IIT jam questions.

IIT JAM Mathematics Question Paper 2025

All the memory-based questions of the IIT JAM 2025 Mathematics question paper will be published under this section. Do regularly visit us during the exam day for more regular updates.

IIT JAM Mathematics Syllabus and Exam Pattern

As the IIT JAM Mathematics exam date approaches faster, the candidates should revisit the syllabus prescribed by IIT Delhi for the IIT JAM Mathematics examination. They should ensure that they do not miss any topic prior to the examination because the IIT JAM Mathematics Syllabus is vast and there are chances that the candidate might miss a few topics. The entire IIT JAM Mathematics Syllabus for the 2025 examination is given below followed by the IIT JAM Mathematics exam pattern. The candidates should ensure that they have gone through the entire syllabus and properly understand the IIT JAM Mathematics Question Paper pattern.

IIT JAM Mathematics Question Paper Pattern

Also Read,

• JAM Answer Key 2025
• IIT JAM Cut off 2025

IIT JAM Mathematics Question Paper Analysis

The candidates can revisit this article as soon as the IIT JAM Mathematics exam is over. The comprehensive analysis of the IIT JAM Mathematics examination including the overall exam difficulty, sectionwise weightage and so on will be discussed here. Stay tuned.

IIT JAM Mathematics Question Paper Analysis 2024

Going through the analysis of the previous years is essential for any IIT JAM Mathematics aspirant because it helps to be prepared for the various possible surprises that may occur in the IIT JAM Mathematics 2025 question paper. Going through the analysis would help the candidates to prepare themselves for the IIT JAM Mathematics examination by understanding the most important IIT JAM Mathematics topics, IIT JAM Mathematics difficulty level, possible cutoff scores and so on.

• The overall difficulty of the IIT JAM Mathematics question paper 2024 was seen to be on the moderate side.

• The questions from the topics such as Group Theory and Integral Calculus were more lengthy.

• The topic Group Theory had the most weightage in the IIT JAM Mathematics question paper 2024.

• There were questions from differential equations in the IIT JAM Mathematics question paper 2024. These questions were of moderate level difficulty.

• There were also questions from topics such as linear transformation and linear algebra.

• The most difficult section of the test was Section C or the Numerical Answer Type (NAT) as per the responses of the candidates.

• The questions asked in the Multiple Select Questions (MSQs) section were doable in nature.

• The IIT JAM Mathematics question paper 2024 was more challenging than the IIT JAM Mathematics question paper 2023.

IIT JAM Mathematics Question Paper 2024

Given below are a few questions from each section of the IIT JAM Mathematics question paper 2024. By referring to these questions, the candidates will get to understand what they can expect from the actual IIT JAM 2025 Mathematics question papers.

Section A

Q.1 Let G be a group of order 39 such that it has exactly one subgroup of order 3 and exactly one subgroup of order 13. Then, which one of the following statements is TRUE?

(A) G is necessarily cyclic.
(B) G is abelian but need not be cyclic.
(C) G need not be abelian.
(D) G has 13 elements of order 13.

Q.2 For a positive integer n, let U(n) = {r ∈ ℤₙ : gcd(r, n) = 1} be the group under multiplication modulo n. Then, which one of the following statements is TRUE?

(A) U(5) is isomorphic to U(8).
(B) U(10) is isomorphic to U(12).
(C) U(8) is isomorphic to U(10).
(D) U(8) is isomorphic to U(12).

Q.3 Let y(x) be the solution of the differential equation

dy/dx = 1 + y sec x, for x ∈ (-π/2, π/2)

that satisfies y(0) = 0. Then, the value of y(π/6) equals:

(A) √3 log (3/2)
(B) (√3/2) log (3/2)
(C) (√3/2) log 3
(D) √3 log 3

Q.4 Let g: R → R be a continuous function. Which one of the following is the solution of the differential equation

d²y/dx² + y = g(x), for x ∈ R,

satisfying the conditions y(0) = 0, y'(0) = 1?

(A) y(x) = sin(x) - ∫₀ˣ sin(x - t) g(t) dt
(B) y(x) = sin(x) + ∫₀ˣ sin(x - t) g(t) dt
(C) y(x) = sin(x) - ∫₀ˣ cos(x - t) g(t) dt
(D) y(x) = sin(x) + ∫₀ˣ cos(x - t) g(t) dt

Section B

Q.1 Which of the following statements is/are TRUE?

(A) The additive group of real numbers is isomorphic to the multiplicative group of positive real numbers.
(B) The multiplicative group of nonzero real numbers is isomorphic to the multiplicative group of nonzero complex numbers.
(C) The additive group of real numbers is isomorphic to the multiplicative group of nonzero complex numbers.
(D) The additive group of real numbers is isomorphic to the additive group of rational numbers.

Q.2 The center Z(G) of a group G is defined as

Z(G) = {x ∈ G : xg = gx for all g ∈ G}.

Let |G| denote the order of G. Then, which of the following statements is/are TRUE for any group G?

(A) If G is non-abelian and Z(G) contains more than one element, then the center of the quotient group G/Z(G) contains only one element.

(B) If |G| ≥ 2, then there exists a non-trivial homomorphism from Z to G.

(C) If |G| ≥ 2 and G is non-abelian, then there exists a non-identity isomorphism from G to itself.

(D) If |G| = p³, where p is a prime number, then G is necessarily abelian.

Q.3 For a matrix M, let Rowspace(M) denote the linear span of the rows of M and Colspace(M) denote the linear span of the columns of M. Which of the following hold(s) for all A, B, C ∈ M₁₀(R) satisfying A = BC?

(A) Rowspace(A) ⊆ Rowspace(B)
(B) Rowspace(A) ⊆ Rowspace(C)
(C) Colspace(A) ⊆ Colspace(B)
(D) Colspace(A) ⊆ Colspace(C)

Q.4 Let
S = {(x, y, z) ∈ R³ : x² + y² + z² = 4, (x − 1)² + y² ≤ 1, z ≥ 0}.

Then, the surface area of S equals _______ (rounded off to two decimal places).

Section C

Q.1 For α ∈ (−2π, 0), consider the differential equation

x²(d²y/dx²) + αx(dy/dx) + y = 0 for x > 0.

Let D be the set of all α ∈ (−2π, 0) for which all corresponding real solutions to the above differential equation approach zero as x → 0⁺. Then, the number of elements in D ∩ Z equals _______.

Q.2 For n ∈ N, if

aₙ = (1 / (n³ + 1)) + (2² / (n³ + 2)) + ... + (n² / (n³ + n))

then the sequence {aₙ} (n=1 to ∞) converges to _______ (rounded off to two decimal places).

Q.3 For k ∈ N, let 0 = t₀ < t₁ < ⋯ < tₖ < tₖ₊₁ = 1. A function f : [0,1] → R is said to be piecewise linear with nodes t₁, ⋯, tₖ if for each j = 1, 2, ⋯, k + 1, there exist aⱼ ∈ R and bⱼ ∈ R such that

f(t) = aⱼ + bⱼt for tⱼ₋₁ < t < tⱼ.

Let V be the real vector space of all real-valued continuous piecewise linear functions on [0,1] with nodes 1/4, 1/2, and 3/4. Then, the dimension of V equals _______.

IIT JAM Mathematics Official Mock Test

The candidates can attempt the official IIT JAM Mathematics mock test designed by IIT Delhi using the link given below.