# 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!!

• Thank You Praful Sambhaji Rane,
We have updated the options.

2. All questions are quite jumbled up and there are questions from probability, algorithms and numerical methods too when it’s supposed to be only Calculus, please update everything accordingl y

3. • 