1
GATE CSE 2023
MCQ (More than One Correct Answer)
+1
-0.33

Let $$f(x) = {x^3} + 15{x^2} - 33x - 36$$ be a real-valued function. Which of the following statements is/are TRUE?

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.
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
+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
GATE CSE Subjects
EXAM MAP
Medical
NEET