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Syllabus: Limits, Continuity, and Differentiability, Maxima and minima, Mean value theorem, Integration.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 1 &1&1&1&1&1&0&1&1&1&0&0.9&1
\\\hline\textbf{2 Marks Count} & 0 &0&0&0&0&0&1&0&0&0&0&0.1&1
\\\hline\textbf{Total Marks} & 1 &1&1&1&1&1&2&1&1&1&\bf{1}&\bf{1.1}&\bf{2}\\\hline
\end{array}}}$$

Most answered questions in Calculus

1 votes
3 answers
42
23 votes
3 answers
43
Consider the functions $e^{-x}$$x^{2}-\sin x$$\sqrt{x^{3}+1}$Which of the above functions is/are increasing everywhere in $[ 0,1]$?Ⅲ onlyⅡ onlyⅡ and Ⅲ onlyⅠ a...
2 votes
3 answers
44
If $f(x) = \dfrac{\sqrt{3} \sin x}{2+\cos x}$, then the range of $f(x)$ isthe interval $[-1 , \sqrt{3}{/2}]$the interval $[-\sqrt{3}{/2}, 1]$the interval $[-1, 1]$none of...
2 votes
3 answers
45
$\underset{x \to 2}{\lim} \dfrac{1}{1+e^{\frac{1}{x-2}}}$ is$0$$1/2$$1$non-existent
1 votes
3 answers
46
The limit $\underset{n \to \infty}{\lim} \left( 1- \frac{1}{n^2} \right) ^n$ equals$e^{-1}$$e^{-1/2}$$e^{-2}$$1$
1 votes
3 answers
47
A determinant is chosen at random from the set of all determinants of order $2$ with elements $0$ or $1$ only. The probability of choosing a non-zero determinant is$\frac...
0 votes
3 answers
49
$\int \left ( \sin\theta \right )^{\frac{1}{2}}d\theta$
5 votes
3 answers
50
3 votes
3 answers
51
The domain of the function $\log (\log \sin(x))$ is:$0<x<$$\pi$$2n$$\pi$$<$$x$$<$$(2n+1)$$\pi$, for $n$ in $N$Empty setNone of the above
2 votes
3 answers
53
5 votes
3 answers
54
Let $X =\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+\ldots+\frac{1}{3001}$. Then$X< 1$$X>\frac{3}{2}$$1< X< \frac{3}{2}$none of the above
1 votes
3 answers
55
1 votes
3 answers
56
The value of $\lim _{x \rightarrow 8}\left(\frac{x^{1 / 3}-2}{x-8}\right)$ is$1/4$$1/8$$1/12$$1/16$
2 votes
3 answers
57
Solve the following $\int_{0}^{\infty}e^{-x^2}x^4dx$
2 votes
3 answers
58
What is value of $\lim_{x\rightarrow 0, Y\rightarrow 0}\frac{xY}{x^2+Y^2}$1 -10Does not exist
1 votes
3 answers
59
0 votes
3 answers
60
Can we calculate. $\textstyle \lim_{n \to \infty}\frac{2^{n}}{3^{n}}$ if yes then what is the value.