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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 viewed questions in Calculus

15 votes
5 answers
61
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
2 votes
2 answers
63
At $t=0$, the function $f(t)=\frac{\sin t}{t}$ has(A) a minimum(B) a discontinuity (C) a point of inflection(D) a maximum
2 votes
1 answer
64
7 votes
2 answers
65
Consider the integral$$\int^{1}_{0} \frac{x^{300}}{1+x^2+x^3} dx$$What is the value of this integral correct up to two decimal places?$0.00$$0.02$$0.10$$0.33$$1.00$
2 votes
1 answer
68
Find the limit of the given expression$\lim_{x\to\frac{\pi}{2}}\left ( \sec x-\frac{1}{1-\sin x} \right )$
1 votes
1 answer
69
Fourier series of the periodic function (period 2π) defined by$$f(x) = \begin{cases} 0, -p < x < 0\\x, 0 < x < p \end{cases} \text { is }\\ \frac{\pi}{4} + \sum \left [ ...
0 votes
4 answers
70
What is $\lim_{ x \to 0} (1-x)^{\frac{1}{x}}$ ? Also please explain the result?
19 votes
3 answers
72
0 votes
1 answer
73
Which of the following functions is not differentiable in the domain $[-1,1]$ ?(a) $f(x) = x^2$(b) $f(x) = x-1$(c) $f(x) = 2$(d) $f(x) = Maximum (x,-x)$
5 votes
3 answers
74
Let $X =\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+\ldots+\frac{1}{3001}$. Then$X< 1$$X>\frac{3}{2}$$1< X< \frac{3}{2}$none of the above
13 votes
1 answer
75
3 votes
1 answer
76
2 votes
2 answers
77
The expression $\lim_{a \to 0}\frac{x^{a}-1}{a}$ is equal to (A)$\log x$ (B)0 (c)$x\log x$ (D)$\infty$
4 votes
1 answer
78
Value of an Integral :I = $\frac{1}{\sqrt{2\Pi }} \int_{0}^{\infty } e^{\frac{-x^{2}}{8}}dx$Answer given is 1.
2 votes
1 answer
79
Differentiate with respect to x1)sin-1(sin x) x&isin;[0,2&pi;]2)cos-1(cos x) x&isin;[0,2&pi;]3)tan-1(tan x) x&isin;[0,&pi;]-{&pi;/2}Also find pts where function is no...
1 votes
1 answer
80
Which of following function is strictly bounded?