# Calculus

 Question 1
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 1 Explanation:
 Question 2
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 2 Explanation:
 Question 3
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 3 Explanation:
 Question 4
Consider the following expression.
$\lim_{x\rightarrow-3}\frac{\sqrt{2x+22}-4}{x+3}$
The value of the above expression (rounded to 2 decimal places) is ___________.
 A 0.25 B 0.45 C 0.75 D 0.85
GATE CSE 2021 SET-1   Engineering Mathematics
Question 4 Explanation:
 Question 5
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 only C II and III only D I and III only
GATE CSE 2020   Engineering Mathematics
Question 5 Explanation:
 Question 6
Compute $\lim_{x \to 3}\frac{x^4-81}{2x^2-5x-3}$
 A 1 B 53/12 C 108/7 D Limit does not exist
GATE CSE 2019   Engineering Mathematics
Question 6 Explanation:
 Question 7
The domain of the function $\log (\log \sin (x))$ is:
 A $0\lt x \lt \pi$ B $2 n \pi \lt x \lt (2 n+1) \pi$, for n in N C Empty set D None of the above
ISRO CSE 2018   Engineering Mathematics
Question 7 Explanation:
 Question 8
The value of $\int_{0}^{\frac{\pi }{4}}x\cos (x^{2})dx$ correct to three decimal places (assuming that $\pi$ = 3.14 ) is
 A 0.3 B 0.2 C 0.25 D 0.4
GATE CSE 2018   Engineering Mathematics
Question 8 Explanation:
 Question 9
Which one of the following is a closed form expression for the generating function of the sequence $\left \{ a_{n} \right \}$, where $a_{n}=2n+3$ for all n = 0, 1, 2,...?
 A $\frac{3}{(1-x)^{2}}$ B $\frac{3x}{(1-x)^{2}}$ C $\frac{2-x}{(1-x)^{2}}$ D $\frac{3-x}{(1-x)^{2}}$
GATE CSE 2018   Engineering Mathematics
Question 9 Explanation:
 Question 10
If a random variable X has a Poisson distribution with mean 5, then the expectation $E[(X+2)^{2}]$ equals ______________.
 A 49 B 25 C 54 D 64
GATE CSE 2017 SET-2   Engineering Mathematics
Question 10 Explanation:
There are 10 questions to complete.

### 3 thoughts on “Calculus”

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

• 2. 