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 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 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 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 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 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 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 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 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 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
There are 10 questions to complete.

3 thoughts on “Calculus”

  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

    Reply

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