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 2023
Numerical
+1
-0.33

The value of the definite integral

$$\int\limits_{ - 3}^3 {\int\limits_{ - 2}^2 {\int\limits_{ - 1}^1 {(4{x^2}y - {z^3})dz\,dy\,dx} } }$$

is ___________. (Rounded off to the nearest integer)

3
GATE CSE 2022
Numerical
+1
-0.33

The value of the following limit is _____________.

$$\mathop {\lim }\limits_{x \to {0^ + }} {{\sqrt x } \over {1 - {e^{2\sqrt x }}}}$$

4
GATE CSE 2020
MCQ (Single Correct Answer)
+1
-0.33
Consider the functions

I. $${e^{ - x}}$$
II. $${x^2} - \sin x$$
III. $$\sqrt {{x^3} + 1}$$

Which of the above functions is/are increasing everywhere in [0,1]?
A
III only
B
II and III only
C
II only
D
I and III only
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