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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

5 votes
1 answer
81
GO Classes Test Series 2023 | Calculus | Test 1 | Question: 4
The function $f(x)=\cos x-x$ is an even function is an odd function is neither an even nor an odd function None of these
The function $f(x)=\cos x-x$is an even functionis an odd functionis neither an even nor an odd functionNone of these
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5 votes
3 answers
82
ISI2017-MMA-1
The area lying in the first quadrant and bounded by the circle $x^{2}+y^{2}=4$ and the lines $x= 0$ and $x=1$ is given by $\frac{\pi}{3}+\frac{\sqrt{3}}{2}$ $\frac{\pi}{6}+\frac{\sqrt{3}}{4}$ $\frac{\pi}{3}-\frac{\sqrt{3}}{2}$ $\frac{\pi}{6}+\frac{\sqrt{3}}{2}$
The area lying in the first quadrant and bounded by the circle $x^{2}+y^{2}=4$ and the lines $x= 0$ and $x=1$ is given by$\frac{\pi}{3}+\frac{\sqrt{3}}{2}$$\frac{\pi}{6}+...
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5 votes
0 answers
83
Maxima-Minima: EC GATE 2014
$The\ maximum\ value\ of\\f(x)\ =\ 2x^3-9x^2+12x-3\ in\ the\ interval\ 0<=x<=3\ is\ $ _____________________
$The\ maximum\ value\ of\\f(x)\ =\ 2x^3-9x^2+12x-3\ in\ the\ interval\ 0<=x<=3\ is\ $_____________________
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5 votes
1 answer
84
Limit and Continuity
Evaluate the given limit : $lim_{x\rightarrow0} \ {\Large \frac{(1+x)^{\frac{1}{x}}-e}{x}}$ options : $ \\ a) \frac{e}{8} \\ b) -\frac{e}{2} \\ c)- \frac{e}{4} \\ d) 1$
Evaluate the given limit :$lim_{x\rightarrow0} \ {\Large \frac{(1+x)^{\frac{1}{x}}-e}{x}}$options :$ \\ a) \frac{e}{8} \\ b) -\frac{e}{2} \\ c)- \frac{e}{4} \\ d) 1$
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5 votes
1 answer
85
Integration
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5 votes
1 answer
86
ISI2004-MIII: 23
If $\textit{f}(x)=x^{2}$ and $g(x)=x \sin x +\cos x$ then $f$ and $g$ agree at no point $f$ and $g$ agree at exactly one point $f$ and $g$ agree at exactly two point $f$ and $g$ agree at more then two point
If $\textit{f}(x)=x^{2}$ and $g(x)=x \sin x +\cos x$ then$f$ and $g$ agree at no point$f$ and $g$ agree at exactly one point$f$ and $g$ agree at exactly two point$f$ and ...
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5 votes
3 answers
87
ISI2004-MIII: 13
Let $X =\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+\ldots+\frac{1}{3001}$. Then $X< 1$ $X>\frac{3}{2}$ $1< X< \frac{3}{2}$ none of the above
Let $X =\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+\ldots+\frac{1}{3001}$. Then$X< 1$$X>\frac{3}{2}$$1< X< \frac{3}{2}$none of the above
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5 votes
1 answer
88
ISRO2011-59
$n$-th derivative of $x^n$ is $nx^{n-1}$ $n^n.n!$ $nx^n!$ $n!$
$n$-th derivative of $x^n$ is$nx^{n-1}$$n^n.n!$$nx^n!$$n!$
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5 votes
1 answer
89
ISRO2009-49
$x=a \cos(t), y=b \sin(t)$ is the parametric form of Ellipse Hyperbola Circle Parabola
$x=a \cos(t), y=b \sin(t)$ is the parametric form ofEllipseHyperbolaCircleParabola
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5 votes
3 answers
90
ISRO-2013-49
What is the least value of the function $f(x) = 2x^{2}-8x-3$ in the interval $[0, 5]$? $-15$ $7$ $-11$ $-3$
What is the least value of the function $f(x) = 2x^{2}-8x-3$ in the interval $[0, 5]$?$-15$$7$$-11$$-3$
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4 votes
1 answer
95
GATE CSE 1995 | Question: 7(B)
Compute without using power series expansion $\displaystyle \lim_{x \to 0} \frac{\sin x}{x}.$
Compute without using power series expansion $\displaystyle \lim_{x \to 0} \frac{\sin x}{x}.$
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4 votes
2 answers
96
GATE CSE 2021 Set 1 | Question: 20
Consider the following expression.$\displaystyle \lim_{x\rightarrow-3}\frac{\sqrt{2x+22}-4}{x+3}$The value of the above expression (rounded to 2 decimal places) is ___________.
Consider the following expression.$$\displaystyle \lim_{x\rightarrow-3}\frac{\sqrt{2x+22}-4}{x+3}$$The value of the above expression (rounded to 2 decimal places) is ____...
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4 votes
4 answers
97
ISI2014-DCG-3
$\underset{x \to \infty}{\lim} \left( \frac{3x-1}{3x+1} \right) ^{4x}$ equals $1$ $0$ $e^{-8/3}$ $e^{4/9}$
$\underset{x \to \infty}{\lim} \left( \frac{3x-1}{3x+1} \right) ^{4x}$ equals$1$$0$$e^{-8/3}$$e^{4/9}$
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4 votes
0 answers
100
Limits
What is the value of $\displaystyle \lim_{x\to \infty} \left(\frac{x}{2+x}\right)^{2x}?$
What is the value of $\displaystyle \lim_{x\to \infty} \left(\frac{x}{2+x}\right)^{2x}?$
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