1
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)

2
GATE CSE 2022
Numerical
+1
-0.33

The value of the following limit is _____________.

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

3
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
4
GATE CSE 2019
MCQ (Single Correct Answer)
+1
-0.33
Compute $$\mathop {\lim }\limits_{x \to 3} {{{x^4} - 81} \over {2{x^2} - 5x - 3}}$$
A
1
B
Limit does not exits
C
$${{53} \over {12}}$$
D
$${{108} \over {7}}$$
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