GATE Maths Questions

Practising previous years’ GATE Questions papers is the most widely used way to prepare for the GATE Exam. Candidates can practise, analyse and understand concepts while solving them. It helps students strengthen their time management skills. We have attempted to compile, here in this article, a collection of GATE Questions on Maths.

Candidates are urged to practise these Maths GATE previous year questions to get the best results. Maths is an important topic in the GATE question papers, and solving these questions will help the candidates to prepare more proficiently for the MA GATE exams. Meanwhile, candidates can find the GATE Questions for Maths here, in this article below, to solve and practise before the exams. They can also refer to the GATE previous year question papers and start preparing for the exams.

GATE Questions on Mathematics

1. For a balanced transportation problem with three sources and three destinations where costs, availability and demands are all finite and positive, which one of the following statements is FALSE?

(GATE 2019)

1. The transportation problem does not have unbounded solution
2. The number of non-basic variables of the transportation problem is 4
3. The dual variables of the transportation problem are unrestricted in sign
4. The transportation problem has at most 5 basic feasible solutions

Answer (d)

2. Let X and Y be normed linear spaces, and let T: X → Y be any bijective linear map with

closed graph. Then which one of the following statements is TRUE?

(GATE 2019)

1. The graph of T is equal to X×Y
2. T¹ is continuous
3. T is continuous
4. The graph of T¹ is closed

Answer (c)

3. Let X and Y be metric spaces, and let f : X → Y be a continuous map. For any subset S of X, which one of the following statements is true?

(GATE 2018)

1. If S is open, then f (S) is open
2. If S is connected, then f (S) is connected
3. If S is closed, then f (S) is closed
4. If S is bounded, then f (S) is bounded

Answer (b)

4. An urn contains four balls, each ball having equal probability of being white or black. Three black balls are added to the urn. The probability that five balls in the urn are black is

(GATE 2018)

1. 2/7
2. ⅜
3. ½
4. 5/7

Answer (b)

5. For a linear programming problem, which one of the following statements is FALSE?

(GATE 2018)

1. If a constraint is an equality, then the corresponding dual variable is unrestricted in sign
2. Both primal and its dual can be infeasible
3. If primal is unbounded, then its dual is infeasible
4. Even if both primal and dual are feasible, the optimal values of the primal and the dual can differ

Answer (d)

6. Consider the polynomial p(X) = X⁴ + 4 in the ring Q[X] of polynomials in the variable X with coefficients in the field Q of rational numbers. Then

(GATE 2018)

1. the set of zeros of p(X) in C forms a group under multiplication
2. p(X) is reducible in the ring Q[X]
3. the splitting field of p(X) has degree 3 over Q
4. the splitting field of p(X) has degree 4 over Q

Answer (b)

7. Which one of the following statements is true?

(GATE 2018)

1. Every group of order 12 has a non-trivial proper normal subgroup
2. Some group of order 12 does not have a non-trivial proper normal subgroup
3. Every group of order 12 has a subgroup of order 6
4. Every group of order 12 has an element of order 12

Answer (a)

8. Let f : X → Y be a continuous map from a Hausdorff topological space X to a metric space Y. Consider the following two statements:

P: f is a closed map and the inverse image f ⁻¹(y) = {x ∈ X : f (x) = y} is compact for each y ∈ Y.

Q: For every compact subset K ⊂ Y, the inverse image f ⁻¹(K) is a compact subset of X.

Which one of the following is true?

(GATE 2018)

1. Q implies P but P does NOT imply Q
2. P implies Q but Q does NOT imply P
3. P and Q are equivalent
4. neither P implies Q nor Q implies P

Answer (c)

9. Let X denote R² endowed with the usual topology. Let Y denote R endowed with the co-finite topology. If Z is the product topological space Y × Y, then

(GATE 2018)

1. the topology of X is the same as the topology of Z
2. the topology of X is strictly coarser (weaker) than that of Z
3. the topology of Z is strictly coarser (weaker) than that of X
4. the topology of X cannot be compared with that of Z

Answer (c)

10. Let M₂(R) be the vector space of all 2 × 2 real matrices over the field R. Define the linear transformation S : M₂(R) → M₂(R) by S(X) = 2X + X^T , where X^T denotes the transpose of the matrix X. Then the trace of S equals ________

(GATE 2018)

1. 10
2. 20
3. 15
4. 0

Answer (a)

11. Let X be the number of heads in 4 tosses of a fair coin by Person 1 and let Y be the number of heads in 4 tosses of a fair coin by Person 2. Assume that all the tosses are independent. Then the value of P(X = Y ) correct up to three decimal places is ________

(GATE 2018)

1. 0.272 to 0.274
2. 0.275 to 0.300
3. 0.300 to 0.305
4. None of the above

Answer (a)

12. Consider a real vector space V of dimension n and a non‐zero linear transformation T ∶ V → V. If dimension(T(V)) < n and T² = A T, for some A ∈ !R\ 0 , then which of the following statements is TRUE?

(GATE 2016)

1. determinant(T) = |A|ⁿ
2. There exists a non‐trivial subspace V₁ of V such that T(X) = 0 for all X ∈ V₁
3. T is invertible
4. A is the only eigenvalue of T

Answer (b)

13. Let S = [0, 1)⋃[2, 3] and f ∶ S → !R be a strictly increasing function such that f(S) is connected. Which of the following statements is TRUE?

(GATE 2016)

1. f has exactly one discontinuity
2. f has exactly two discontinuities
3. f has infinitely many discontinuities
4. f is continuous

Answer (d)

14. Let (!R, r) be a topological space with the cofinite topology. Every infinite subset of

!R is

(GATE 2016)

1. Compact but NOT connected
2. Both compact and connected
3. NOT compact but connected
4. Neither compact nor connected

Answer (b)

15. Let R,1 be the set of all n x n real matrices with the usual norm topology. Consider the following statements P and Q:

P: The set of all symmetric positive definite matrices in R,1 is connected.

Q: The set of all invertible matrices in R,1 is compact.

Which of the above statements hold TRUE?

(GATE 2016)

1. both P and Q
2. only P
3. only Q
4. Neither P nor Q

Answer (b)