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

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

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Highest voted questions in Calculus

18 votes
4 answers
31
GATE IT 2005 | Question: 35
What is the value of $\int_{0}^{2\pi}(x-\pi)^2 (\sin x) dx$ $-1$ $0$ $1$ $\pi$
What is the value of $\int_{0}^{2\pi}(x-\pi)^2 (\sin x) dx$$-1$$0$$1$$\pi$
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17 votes
4 answers
32
GATE CSE 2013 | Question: 22
Which one of the following functions is continuous at $x = 3?$ $f(x) = \begin{cases} 2,&\text{if $x = 3$ } \\ x-1& \text{if $x > 3$}\\ \frac{x+3}{3}&\text{if $x < 3$ } \end{cases}$ ... $} \end{cases}$ $f(x) = \begin{cases} \frac{1}{x^3-27}&\text{if $x \neq 3$ } \end{cases}$
Which one of the following functions is continuous at $x = 3?$$f(x) = \begin{cases} 2,&\text{if $x = 3$ } \\ x-1& \text{if $x 3$}\\ \frac{x+3}{3}&\text{if $x < 3$ } \end...
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15 votes
5 answers
36
GATE CSE 1987 | Question: 1-xxii
The equation $7x^{7}+14x^{6}+12x^{5}+3x^{4}+12x^{3}+10x^{2}+5x+7=0$ has All complex roots At least one real root Four pairs of imaginary roots None of the above
The equation $7x^{7}+14x^{6}+12x^{5}+3x^{4}+12x^{3}+10x^{2}+5x+7=0$ hasAll complex rootsAt least one real rootFour pairs of imaginary rootsNone of the above
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15 votes
6 answers
39
TIFR CSE 2010 | Part A | Question: 7
The limit of $\dfrac{10^{n}}{n!}$ as $n \to \infty$ is. $0$ $1$ $e$ $10$ $\infty$
The limit of $\dfrac{10^{n}}{n!}$ as $n \to \infty$ is.$0$$1$$e$$10$$\infty$
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15 votes
3 answers
40
GATE CSE 1993 | Question: 02.1
$\displaystyle \lim_{x \to 0} \frac{x(e^x - 1) + 2(\cos x -1)}{x(1 - \cos x)}$ is __________
$\displaystyle \lim_{x \to 0} \frac{x(e^x - 1) + 2(\cos x -1)}{x(1 - \cos x)}$ is __________
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14 votes
7 answers
41
GATE CSE 2019 | Question: 13
Compute $\displaystyle \lim_{x \rightarrow 3} \frac{x^4-81}{2x^2-5x-3}$ $1$ $53/12$ $108/7$ Limit does not exist
Compute $\displaystyle \lim_{x \rightarrow 3} \frac{x^4-81}{2x^2-5x-3}$$1$$53/12$$108/7$Limit does not exist
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13 votes
1 answer
42
GATE CSE 1995 | Question: 25a
Find the minimum value of $3-4x+2x^2$.
Find the minimum value of $3-4x+2x^2$.
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13 votes
1 answer
43
GATE CSE 1998 | Question: 8
Find the points of local maxima and minima, if any, of the following function defined in $0\leq x\leq 6$. $x^3-6x^2+9x+15$ Integrate $\int_{-\pi}^{\pi} x \cos x dx$
Find the points of local maxima and minima, if any, of the following function defined in $0\leq x\leq 6$. $$x^3-6x^2+9x+15$$Integrate $$\int_{-\pi}^{\pi} x \cos x dx$$
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12 votes
4 answers
44
GATE CSE 2022 | Question: 24
The value of the following limit is ________________. $\lim_{x \rightarrow 0^{+}} \frac{\sqrt{x}}{1-e^{2\sqrt{x}}}$
The value of the following limit is ________________.$$\lim_{x \rightarrow 0^{+}} \frac{\sqrt{x}}{1-e^{2\sqrt{x}}}$$
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12 votes
4 answers
45
TIFR CSE 2011 | Part A | Question: 14
The limit $\lim_{x \to 0} \frac{d}{dx}\,\frac{\sin^2 x}{x}$ is $0$ $2$ $1$ $\frac{1}{2}$ None of the above
The limit $$\lim_{x \to 0} \frac{d}{dx}\,\frac{\sin^2 x}{x}$$ is$0$$2$$1$$\frac{1}{2}$None of the above
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12 votes
6 answers
46
GATE CSE 1998 | Question: 1.4
Consider the function $y=|x|$ in the interval $[-1, 1]$. In this interval, the function is continuous and differentiable continuous but not differentiable differentiable but not continuous neither continuous nor differentiable
Consider the function $y=|x|$ in the interval $[-1, 1]$. In this interval, the function iscontinuous and differentiablecontinuous but not differentiabledifferentiable but...
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10 votes
1 answer
47
ISRO2016-3
$\displaystyle{}\lim_{x\rightarrow 0}\frac{\sqrt{1+x}-\sqrt{1-x}}{x}$ is given by $0$ $-1$ $1$ $\frac{1}{2}$
$\displaystyle{}\lim_{x\rightarrow 0}\frac{\sqrt{1+x}-\sqrt{1-x}}{x}$ is given by$0$$-1$$1$$\frac{1}{2}$
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10 votes
3 answers
48
TIFR CSE 2011 | Part A | Question: 11
$\int_{0}^{1} \log_e(x) dx=$ $1$ $-1$ $\infty $ $-\infty $ None of the above
$$\int_{0}^{1} \log_e(x) dx=$$$1$$-1$$\infty $$-\infty $None of the above
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10 votes
2 answers
49
TIFR CSE 2011 | Part A | Question: 4
Consider the problem of maximizing $x^{2}-2x+5$ such that $0< x< 2$. The value of $x$ at which the maximum is achieved is: $0.5$ $1$ $1.5$ $1.75$ None of the above
Consider the problem of maximizing $x^{2}-2x+5$ such that $0< x< 2$. The value of $x$ at which the maximum is achieved is:$0.5$$1$$1.5$$1.75$None of the above
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10 votes
4 answers
50
GATE CSE 1997 | Question: 4.1
What is the maximum value of the function $f(x) = 2x^2 - 2x + 6$ in the interval $\left[0,2 \right]$? 6 10 12 5.5
What is the maximum value of the function $f(x) = 2x^2 - 2x + 6$ in the interval $\left[0,2 \right]$?610125.5
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