1
GATE CSE 2024 Set 1
MCQ (Single Correct Answer)
+1
-0.33

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

A

{-1, 1, 2}

B

{-2, -1, 1}

C

{0, 1}

D

{-1, 0, 1}

2
GATE CSE 2024 Set 1
MCQ (Single Correct Answer)
+1
-0.33

The product of all eigenvalues of the matrix $\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}$ is

A

-1

B

0

C

1

D

2

3
GATE CSE 2024 Set 1
MCQ (Single Correct Answer)
+1
-0.33

Consider a permutation sampled uniformly at random from the set of all permutations of {1, 2, 3, ..., n} for some n ≥ 4. Let X be the event that 1 occurs before 2 in the permutation, and Y the event that 3 occurs before 4. Which one of the following statements is TRUE?

A

The events X and Y are mutually exclusive

B

The events X and Y are independent

C

Either event X or Y must occur

D

Event X is more likely than event Y

4
GATE CSE 2024 Set 1
MCQ (More than One Correct Answer)
+1
-0

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

A

The two events A and B are independent.

B

$P(A \cup B) = 0.7$

C

$P(A \cap B^c) = 0.2$, where $B^c$ is the complement of the event B

D

$P(A^c \cap B^c) = 0.4$, where $A^c$ and $B^c$ are the complements of the events A and B respectively

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