GATE Mathematics (MA) Question Paper 2024 with answer keys will help students self-evaluate, adjust to the difficulty level of the GATE exam, identify key themes, and revise the fundamental concepts. The GATE Mathematics exam was held on Feb 4, 2024.

Candidates appearing for the GATE 2024 exam must practise the previous year question papers thoroughly to remain acquainted with the pattern and trend of questions asked in the entrance examination.

GATE Mathematics Question Papers with Answer Keys PDF 2024

GATE Mathematics question papers 2024 with answer keys and analysis is available. The GATE 2024 Mathematics question paper, answer key and paper analysis will help the students to guage their performance and estimate score.

Also Check: GATE Answer Key 2024

GATE Mathematics Previous Year Question Papers with Answer Keys PDF

The previous year question papers are always a treasure. They are a good resource for daily practice. They help the candidates understand the difficulty level of the questions and to perceive the trend of questions as well.

GATE Mathematics previous year question papers have been provided in the table below along with their corresponding official answer keys.

Also Check: GATE Response Sheet 2024

Top 10+ GATE Mathematics Questions with Answers

Shared below are the top 20+ GATE Mathematics (MA) questions that are important for the upcoming GATE 2024.

1. Let T ∶ R3 → R3 be a linear transformation satisfying

T(1, 0, 0) = (0, 1, 1), T(1, 1, 0) = (1, 0, 1) and T(1, 1, 1) = (1, 1, 2).

Then

(A) T is one-one but T is NOT onto

(B) T is one-one and onto

(C) T is NEITHER one-one NOR onto

(D) T is NOT one-one but T is onto

Ans: (C) T is NEITHER one-one NOR onto

2. Let N ⊆ R be a non-measurable set with respect to the Lebesgue measure on R.

Consider the following statements:

P: If M = { x ∈ N ∶ x is irrational }, then M is Lebesgue measurable.

Q: The boundary of N has positive Lebesgue outer measure.

Then

(A) both P and Q are TRUE

(B) P is FALSE and Q is TRUE

(C) P is TRUE and Q is FALSE

(D) both P and Q are FALSE

Ans: (B) P is FALSE and Q is TRUE

3. Let C[0, 1] = { f ∶ [0, 1] → R ∶ f is continuous}.

Consider the metric space (C[0,1], d_∞), where

                                     d_∞(f, g) = sup{ |f(x) − g(x)| ∶ x ∈ [0, 1] } for f, g ∈ C[0,1].

Let f0(x) = 0 for all x ∈ [0,1] and

                                      X = {f ∈ (C[0, 1], d_∞) ∶ d_∞(f0, f) ≥ 1/2}.

Let f₁, f₂ ∈ C[0, 1] be defined by f₁(x) = x and f₂(x) = 1 − x for all x ∈ [0,1]. 

Consider the following statements: 

P: f₁ is in the interior of X.

Q: f₂ is in the interior of X. 

Which of the following statements is correct? 

(A) P is TRUE and Q is FALSE

(B) P is FALSE and Q is TRUE

(C) Both P and Q are FALSE

(D) Both P and Q are TRUE 

Ans: (D) Both P and Q are TRUE

4. Let T ∶ R⁴ → R⁴ be a linear transformation and the null space of T be the subspace of R⁴ given by

{ (x₁, x₂, x₃, x₄) ∈ R⁴ ∶ 4x₁ + 3x₂ + 2x₃ + x₄ = 0}.

If Rank (T − 3I) = 3, where I is the identity map on R⁴, then the minimal polynomial of T is

(A) x(x − 3)

(B) x(x − 3)³

(C) x³(x − 3)

(D) x²(x − 3)²

Ans: (A) x(x − 3)

Also Read: Importance of GATE Mock Tests 2024 for Effective Preparation

5. Let C[0,1] denote the set of all real valued continuous functions defined on 

[0,1] and ‖f‖∞ = sup{|f(x)| ∶ x ∈ [0,1]} for all f ∈ C[0,1]. Let 

X = { f ∈ C[0,1] ∶ f(0) = f(1) = 0 }.

Define F ∶ (C[0,1], ‖⋅‖∞) → R by F(f) = ∫ f(t)dt 10 for all f ∈ C[0,1].

Denote S_X = {f ∈ X ∶ ‖f‖∞ = 1}.

Then the set {f ∈ X ∶ F(f) = ‖F‖} ∩ S_X has

(A) No element

(B) exactly one element

(C) exactly two elements

(D) an infinite number of elements

Ans: (A) No element

6. Consider the following Linear Programming Problem P:

Minimize 3x₁ + 4x₂

subject to x₁ − x₂ ≤ 1,

x₁ + x₂ ≥ 3,

x₁ ≥ 0, x₂ ≥ 0.

The optimal value of the problem P is _____________.

Ans: 10 to 10

7. Consider the Cauchy problem

x (∂u/∂x) + y (∂u/∂y) = u;

u = f(t) on the initial curve Γ = (t, t); t > 0.

Consider the following statements:

P: If f(t) = 2t + 1, then there exists a unique solution to the Cauchy problem in a neighbourhood of Γ.

Q: If f(t) = 2t − 1, then there exist infinitely many solutions to the Cauchy problem in a neighbourhood of Γ.

Then

(A) both P and Q are TRUE

(B) P is FALSE and Q is TRUE

(C) P is TRUE and Q is FALSE

(D) both P and Q are FALSE

Ans: (D) both P and Q are FALSE

8. Let φ and ψ be two linearly independent solutions of the ordinary differential equation

y′′ + (2 − cos x) y = 0, x ∈ R .

Let α, β ∈ R be such that α < β, φ(α) = φ(β) = 0 and φ(x) ≠ 0 for all

x ∈ (α, β).

Consider the following statements:

P: φ′(α)φ′(β) > 0.

Q: φ(x)ψ(x) ≠ 0 for all x ∈ (α, β).

Then

(A) P is TRUE and Q is FALSE

(B) P is FALSE and Q is TRUE

(C) both P and Q are FALSE

(D) both P and Q are TRUE

Ans: (C) both P and Q are FALSE

Also Read: GATE Subject Wise Weightage 2024: Chapter-wise Topic

9. Let (R, τ) be a topological space, where the topology τ is defined as

τ = {U ⊆ R ∶ U = ∅ or 1 ∈ U}.

Which of the following statements is/are correct?

(A) (R, τ) is first countable

(B) (R, τ) is Hausdorff

(C) (R, τ) is separable

(D) The closure of (1,5) is [1,5]

Ans: (A) (R, τ) is first countable ; (C) (R, τ) is separable

10. Let R = {p(x) ∈ Q[x] ∶ p(0) ∈ Z}, where Q denotes the set of rational numbers and Z denotes the set of integers. For a ∈ R, let ⟨a⟩ denote the ideal generated by a in R.

Which of the following statements is/are correct?

(A) If p(x) is an irreducible element in R, then ⟨p(x)⟩ is a prime ideal in R

(B) R is a unique factorization domain

(C) ⟨x⟩ is a prime ideal in R

(D) R is NOT a principal ideal domain

Ans: (A) If p(x) is an irreducible element in R, then ⟨p(x)⟩ is a prime ideal in R

11. Let x(t), y(t), t ∈ R, be two functions satisfying the following system of differential equations:

x′(t) = y(t), 

y′(t) = x(t),

and x(0) = α, y(0) = β, where α, β are real numbers.

Which of the following statements is/are correct?

(A) If α = 1, β = −1, then |x(t)| + |y(t)| → 0 as t → ∞

(B) If α = 1, β = 1, then |x(t)| + |y(t)| → 0 as t → ∞

(C) If α = 1.01, β = −1, then |x(t)| + |y(t)| → 0 as t → ∞

(D) If α = 1, β = 1.01, then |x(t)| + |y(t)| → 0 as t → ∞

Ans: (A) If α = 1, β = −1, then |x(t)| + |y(t)| → 0 as t → ∞

12. Let A be a 3 × 3 real matrix with det(A + i I) = 0, where i = √−1 and I is the 3 × 3 identity matrix. If det(A) = 3, then the trace of A2 is ________.

Ans: 7 to 7

13. Suppose that the characteristic equation of M ∈ C^3×3 is

λ³ + αλ² + βλ − 1 = 0,

where α, β ∈ C with α + β ̸= 0.

Which of the following statements is TRUE?

(A) M(I − βM) = M−1(M + αI)

(B) M(I + βM) = M−1(M − αI)

(C) M−1(M−1 + βI) = M − αI

(D) M−1(M−1 − βI) = M + αI

Ans: (D) M−1(M−1 − βI) = M + αI

Also Read: GATE 2024 Preparation Tips from Toppers & Experts

GATE Exam Pattern 2024

It is extremely important for the candidates to be aware of the GATE exam pattern 2024. The question paper will consist of 1-mark questions and 2-mark questions. GATE applies the negative marking scheme for the MCQs. However, no negative marking is done for wrong answers in the MSQ and NAT sections.

The GATE exam pattern 2024 can be found in the table below:

Also Read: GATE Qualifying Marks 2024: Passing Marks, Admission Cutoff