Register

Web Page

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

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

Filter

Previous GATE Questions in Calculus

31 votes
8 answers
42
GATE CSE 2010 | Question: 5
What is the value of $ \displaystyle\lim_{n \to \infty}\left(1 - \frac{1}{n}\right)^{2n}$ ? $0$ $e^{-2}$ $e^{-1/2}$ $1$
What is the value of $ \displaystyle\lim_{n \to \infty}\left(1 - \frac{1}{n}\right)^{2n}$ ?$0$$e^{-2}$$e^{-1/2}$$1$
User Avatar
24 votes
3 answers
43
GATE CSE 2009 | Question: 25
$\int^{\pi/4}_0 (1-\tan x)/(1+\tan x)\,dx $ $0$ $1$ $\ln 2$ $1/2 \ln 2$
$\int^{\pi/4}_0 (1-\tan x)/(1+\tan x)\,dx $$0$$1$ $\ln 2$$1/2 \ln 2$
User Avatar
35 votes
3 answers
44
GATE CSE 2000 | Question: 2.3
Let $S = \sum_{i=3}^{100} i \log_{2} i$, and $T = \int_{2}^{100} x \log_{2}x dx$. Which of the following statements is true? $S > T$ $S = T$ $S < T$ and $2S > T$ $2S ≤ T$
Let $S = \sum_{i=3}^{100} i \log_{2} i$, and $T = \int_{2}^{100} x \log_{2}x dx$.Which of the following statements is true?$S T$$S = T$$S < T$ and $2S T$$2S ≤ T$
User Avatar
0 votes
0 answers
45
GATE CSE 1993 | Question: 02.10
User Avatar
0 votes
0 answers
47
GATE CSE 1993 | Question: 02.8
Given $\vec v= x\cos ^2y \hat i + x^2e^z\hat j+ z\sin^2y\hat k$ and $S$ the surface of a unit cube with one corner at the origin and edges parallel to the coordinate axes, the value of integral $\int^1 \int_s \vec V. \hat n dS$ is __________.
Given $\vec v= x\cos ^2y \hat i + x^2e^z\hat j+ z\sin^2y\hat k$ and $S$ the surface of a unit cube with one corner at the origin and edges parallel to the coordinate axes...
User Avatar
4 votes
2 answers
48
GATE CSE 1993 | Question: 02.6
The value of the double integral $\int^{1}_{0} \int_{0}^{\frac{1}{x}} \frac {x}{1+y^2} dxdy$ is_________.
The value of the double integral $\int^{1}_{0} \int_{0}^{\frac{1}{x}} \frac {x}{1+y^2} dxdy$ is_________.
User Avatar
1 votes
0 answers
49
GATE CSE 1993 | Question: 02.2
The radius of convergence of the power series$\sum_{}^{\infty} \frac{(3m)!}{(m!)^3}x^{3m}$ is: _____________
The radius of convergence of the power series$$\sum_{}^{\infty} \frac{(3m)!}{(m!)^3}x^{3m}$$ is: _____________
User Avatar
15 votes
3 answers
50
GATE CSE 1993 | Question: 02.1
$\displaystyle \lim_{x \to 0} \frac{x(e^x - 1) + 2(\cos x -1)}{x(1 - \cos x)}$ is __________
$\displaystyle \lim_{x \to 0} \frac{x(e^x - 1) + 2(\cos x -1)}{x(1 - \cos x)}$ is __________
User Avatar
1 votes
1 answer
51
GATE CSE 1993 | Question: 01.7
The function $f\left(x,y\right) = x^2y - 3xy + 2y +x$ has no local extremum one local minimum but no local maximum one local maximum but no local minimum one local minimum and one local maximum
The function $f\left(x,y\right) = x^2y - 3xy + 2y +x$ hasno local extremumone local minimum but no local maximumone local maximum but no local minimumone local minimum an...
User Avatar
36 votes
2 answers
54
GATE CSE 2008 | Question: 25
A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve $3x^4-16x^3+24x^2+37$ is $0$ $1$ $2$ $3$
A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve $3x^4-16x^3+24x^2+37$ is$0$$1$$2$$3...
User Avatar
25 votes
9 answers
55
GATE CSE 2008 | Question: 1
$\displaystyle \lim_{x \to \infty}\frac{x-\sin x}{x+\cos x}$ equals $1$ $-1$ $\infty$ $-\infty$
$\displaystyle \lim_{x \to \infty}\frac{x-\sin x}{x+\cos x}$ equals$1$$-1$$\infty$$-\infty$
User Avatar
1 votes
1 answer
56
GATE CSE 1993 | Question: 01.5
Fourier series of the periodic function (period 2π) defined by ... $\frac{{\pi }^2 }{4}$ $\frac{{\pi }^2 }{6}$ $\frac{{\pi }^2 }{8}$ $\frac{{\pi }^2 }{12}$
Fourier series of the periodic function (period 2π) defined by$$f(x) = \begin{cases} 0, -p < x < 0\\x, 0 < x < p \end{cases} \text { is }\\ \frac{\pi}{4} + \sum \left [ ...
User Avatar
Page: