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
- 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?
- The transportation problem does not have unbounded solution
- The number of non-basic variables of the transportation problem is 4
- The dual variables of the transportation problem are unrestricted in sign
- The transportation problem has at most 5 basic feasible solutions
- Let X and Y be normed linear spaces, and let T: X → Y be any bijective linear map with
- The graph of T is equal to X×Y
- T1 is continuous
- T is continuous
- The graph of T1 is closed
- 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?
- If S is open, then f (S) is open
- If S is connected, then f (S) is connected
- If S is closed, then f (S) is closed
- If S is bounded, then f (S) is bounded
- 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
- 2/7
- ⅜
- ½
- 5/7
- For a linear programming problem, which one of the following statements is FALSE?
- If a constraint is an equality, then the corresponding dual variable is unrestricted in sign
- Both primal and its dual can be infeasible
- If primal is unbounded, then its dual is infeasible
- Even if both primal and dual are feasible, the optimal values of the primal and the dual can differ
- 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
- the set of zeros of p(X) in C forms a group under multiplication
- p(X) is reducible in the ring Q[X]
- the splitting field of p(X) has degree 3 over Q
- the splitting field of p(X) has degree 4 over Q
- Which one of the following statements is true?
- Every group of order 12 has a non-trivial proper normal subgroup
- Some group of order 12 does not have a non-trivial proper normal subgroup
- Every group of order 12 has a subgroup of order 6
- Every group of order 12 has an element of order 12
- Let f : X → Y be a continuous map from a Hausdorff topological space X to a metric space Y. Consider the following two statements:
- Q implies P but P does NOT imply Q
- P implies Q but Q does NOT imply P
- P and Q are equivalent
- neither P implies Q nor Q implies P
- 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
- the topology of X is the same as the topology of Z
- the topology of X is strictly coarser (weaker) than that of Z
- the topology of Z is strictly coarser (weaker) than that of X
- the topology of X cannot be compared with that of Z
- 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 + XT , where XT denotes the transpose of the matrix X. Then the trace of S equals ________
- 10
- 20
- 15
- 0
- 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 ________
- 0.272 to 0.274
- 0.275 to 0.300
- 0.300 to 0.305
- None of the above
- 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?
- determinant(T) = |A|n
- There exists a non‐trivial subspace V1 of V such that T(X) = 0 for all X ∈ V1
- T is invertible
- A is the only eigenvalue of T
- 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?
- f has exactly one discontinuity
- f has exactly two discontinuities
- f has infinitely many discontinuities
- f is continuous
- Let (!R, r) be a topological space with the cofinite topology. Every infinite subset of
- Compact but NOT connected
- Both compact and connected
- NOT compact but connected
- Neither compact nor connected
- 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:
- both P and Q
- only P
- only Q
- Neither P nor Q
(GATE 2019)
Answer (d)
closed graph. Then which one of the following statements is TRUE?
(GATE 2019)
Answer (c)
(GATE 2018)
Answer (b)
(GATE 2018)
Answer (b)
(GATE 2018)
Answer (d)
(GATE 2018)
Answer (b)
(GATE 2018)
Answer (a)
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)
Answer (c)
(GATE 2018)
Answer (c)
(GATE 2018)
Answer (a)
(GATE 2018)
Answer (a)
(GATE 2016)
Answer (b)
(GATE 2016)
Answer (d)
!R is
(GATE 2016)
Answer (b)
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)
Answer (b)
Comments