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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

2 votes
1 answer
241
Numerical Aptitude
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2 votes
2 answers
242
Limits
How to slove this $\lim_{n\rightarrow \infty }\left ( 10^{n}+n^{20} \right )/n!$
How to slove this$\lim_{n\rightarrow \infty }\left ( 10^{n}+n^{20} \right )/n!$
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2 votes
1 answer
243
Limit
Calculate the limit $\lim_{x \rightarrow 1-} \sqrt[3]{x+1} \: ln \: (x+1)$ 1 0 2 Does not exist
Calculate the limit$\lim_{x \rightarrow 1-} \sqrt[3]{x+1} \: ln \: (x+1)$102Does not exist
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2 votes
2 answers
244
Gate 2014 CE Set 2
The expression $\lim_{a \to 0}\frac{x^{a}-1}{a}$ is equal to (A)$\log x$ (B)0 (c)$x\log x$ (D)$\infty$
The expression $\lim_{a \to 0}\frac{x^{a}-1}{a}$ is equal to (A)$\log x$ (B)0 (c)$x\log x$ (D)$\infty$
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2 votes
1 answer
245
calculus
$\lim_{x \to \infty}\left (\frac{1}{1-x^{2}} + \frac{2}{1-x^{2}}+\dots+\frac{x}{1-x^{2}}\right )$ is equal to (a) $0$ (b) $-1/2$ (c) $1/2$ (d) None of the above
$\lim_{x \to \infty}\left (\frac{1}{1-x^{2}} + \frac{2}{1-x^{2}}+\dots+\frac{x}{1-x^{2}}\right )$ is equal to(a) $0$(b) $-1/2$(c) $1/2$(d) None of the above
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2 votes
2 answers
248
limits
Find the value of: $\lim_{\theta \to \pi/2} \left ( 1 - 5 \cot\theta \right )^{\tan\theta}$ $e^{5}$ $e^{-5}$ $e^{1/5}$ $e^{-1/5}$
Find the value of: $$\lim_{\theta \to \pi/2} \left ( 1 - 5 \cot\theta \right )^{\tan\theta}$$$e^{5}$ $e^{-5}$ $e^{1/5}$ $e^{-1/5}$
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2 votes
1 answer
249
Find the integral
$\int_{-5}^{5} \mid x+1 \mid dx$ is ____ Solution Given : 26 My Solution : 25 Splitting the integral from -5 to 0 and 0 to 5 Please correct my mistake.
$\int_{-5}^{5} \mid x+1 \mid dx$ is ____Solution Given : 26My Solution : 25Splitting the integral from -5 to 0 and 0 to 5Please correct my mistake.
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2 votes
1 answer
250
limit
Value of $\lim_{x \to 0} \frac{x^2 \sin \left(\frac{1}{x}\right)} {\sin x}$ is
Value of $\lim_{x \to 0} \frac{x^2 \sin \left(\frac{1}{x}\right)} {\sin x}$ is
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2 votes
1 answer
251
area
Find Volume under surface z(x,y)=x+y and above the triangle defined in x-y plane by 0<=y<=x and 0<=x<=12
Find Volume under surface z(x,y)=x+y and above the triangle defined in x-y plane by 0<=y<=x and 0<=x<=12
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2 votes
2 answers
252
The value of a and b such that
$\lim_{x \to 0} \frac{ a sin ^2x + b log ( cos x) }{ x^4} = \frac{1}{2}$ a) - 1, -2 b) 1, 2 c) -1,2 d) 1,-2
$\lim_{x \to 0} \frac{ a sin ^2x + b log ( cos x) }{ x^4} = \frac{1}{2}$a) - 1, -2 b) 1, 2c) -1,2 d) 1,-2
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2 votes
2 answers
253
Solve
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
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
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2 votes
2 answers
254
Solve : calculate the limit
Calculate the limit $\lim_{x\rightarrow 1^- } \sqrt[3]{x+1}\: ln(x+1)$ (A) $1$ (B) $0$ (C) $2$ (D) Does not exist
Calculate the limit $$\lim_{x\rightarrow 1^- } \sqrt[3]{x+1}\: ln(x+1)$$(A) $1$(B) $0$(C) $2$(D) Does not exist
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2 votes
1 answer
257
TIFR-2014-Maths-A-3
Let $f: \mathbb{R} \to \mathbb{R}$ be a differentiable function such that $\displaystyle \lim_{x \to +\infty} f'(x)=1$, then $f$ is bounded $f$ is increasing $f$ is unbounded $f'$ is bounded
Let $f: \mathbb{R} \to \mathbb{R}$ be a differentiable function such that $\displaystyle \lim_{x \to +\infty} f'(x)=1$, then$f$ is bounded $f$ is increasing $f$ is unboun...
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2 votes
1 answer
258
TIFR-2011-Maths-A-5
The differential equation $\frac{dy}{dx}= y^{1/3}, y(0)=0$ has A unique solution No nontrivial solution Finite number of solutions Infinite number of solutions
The differential equation$\frac{dy}{dx}= y^{1/3}, y(0)=0$ hasA unique solutionNo nontrivial solution Finite number of solutionsInfinite number of solutions
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2 votes
0 answers
259
bijection, surjection please confirm the ans
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2 votes
1 answer
260
Algorithm
A polynomial p(x) is such that p(0)=5 ,p(1)=4 ,p(2)=9 and p(3)=20 The minimum degree it can have is..
A polynomial p(x) is such that p(0)=5 ,p(1)=4 ,p(2)=9 and p(3)=20 The minimum degree it can have is..
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