# Calculus

 Question 1
The value of the definite integral $\int_{-3}^{3} \int_{-2}^{2} \int_{-1}^{1} (4x^2y-z^3)dzdydx$ is _____. (Rounded off to the nearest integer)
 A 0 B 1 C 2 D 3
GATE CSE 2023   Engineering Mathematics
Question 1 Explanation:
 Question 2
Let $f(x)=x^3+15x^2-33x-36$ 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.
GATE CSE 2023   Engineering Mathematics
Question 2 Explanation:

 Question 3
The value of the following limit is _____
$\lim_{x \to 0+} \frac{ \sqrt{x}}{1-e^{2 \sqrt{x}}}$
 A -0.5 B 0.5 C 0 D 1
GATE CSE 2022   Engineering Mathematics
Question 3 Explanation:
 Question 4
For two n-dimensional real vectors $P$ and $Q$, the operation $s(P,Q)$ is defined as follows:

$s(P,Q) = \displaystyle \sum_{i=1}^n (P[i] \cdot Q[i])$

Let $\mathcal{L}$ be a set of 10-dimensional non-zero real vectors such that for every pair of distinct vectors $P,Q \in \mathcal{L}, s(P,Q)=0$. What is the maximum cardinality possible for the set $\mathcal{L}$?
 A 9 B 10 C 11 D 100
GATE CSE 2021 SET-2   Engineering Mathematics
Question 4 Explanation:
 Question 5
Suppose that $f: \mathbb{R} \rightarrow \mathbb{R}$ is a continuous function on the interval [-3,3] and a differentiable function in the interval (-3,3) such that for every $x$ in the interval, $f'(x) \leq 2$. If $f(-3) =7$, then $f(3)$ is at most __________
 A 19 B 32 C 11 D 54
GATE CSE 2021 SET-2   Engineering Mathematics
Question 5 Explanation:

There are 5 questions to complete.

### 5 thoughts on “Calculus”

1. Question number 35 of calculas of CS option B is misprinted? Please check!!