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Found 475 question(s)

Q126 MSQ GATE CS Medium 1 Mark 2024

EM → Calculus

Let f(x) = x^3 + 15x^2 - 33x - 36. Which of the following statements is/are TRUE?

Choose All Applicable:

A) f(x) does not have a local maximum.

B) f(x) has a local maximum.

C) f(x) does not have a local minimum.

D) f(x) has a local minimum.

Correct Answer:
Explanation:

Q127 MCQ GATE CS Medium 1 Mark 2024

EM → Calculus

Let f: R → R be a function such that f(x) = max{x, x^3}, x ∈ R, where R is the set of all real numbers. The set of all points where f(x) is NOT differentiable is

Choose One:

A) {-1, 1, 2}

B) {-2, -1, 1}

C) {0, 1}

D) {-1, 0, 1}

Correct Answer:
Explanation:

Q128 MSQ GATE CS Medium 2 Marks 2024

EM → Probability

Let A and B be two events in a probability space with P(A) = 0.3, P(B) = 0.5, and P(A ∩ B) = 0.1. Which of the following statements is/are TRUE?

Choose All Applicable:

A) The two events A and B are independent

B) P(A ∪ B) = 0.7

C) P(A ∩ B^c) = 0.2 where B^c is the complement of the event B

D) P(A^c ∩ B^c) = 0.4 where A^c and B^c are the complements of the events A and B

Correct Answer:
Explanation:

Q129 MCQ GATE CS Easy 1 Mark 2024

EM → Linear Algebra

Let A and B be 4x4 matrices where A has rows R1, R2, R3, R4 and B is formed by swapping row 1 and row 3 of A. Let det(A) and det(B) denote their determinants. Which one of the options given below is TRUE?

Choose One:

A) det(A) = det(B)

B) det(B) = -det(A)

C) det(A) = 0

D) det(AB) = det(A) + det(B)

Correct Answer:
Explanation:

Q130 NAT GATE CS Easy 1 Mark 2024

EM → Linear Algebra

Let A be the adjacency matrix of a simple graph with 5 vertices. Let λ1, λ2, λ3, λ4, and λ5 be the five eigenvalues of A. The value of λ1 + λ2 + λ3 + λ4 + λ5 =

Enter Numerical Answer:

Correct Answer:
Explanation:

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95