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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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Hot questions in Calculus

5 votes
1 answer
4
GATE CSE 2024 | Set 2 | Question: 6
​​​​​Let $f(x)$ be a continuous function from $\mathbb{R}$ to $\mathbb{R}$ such that \[ f(x)=1-f(2-x) \] Which one of the following options is the CORRECT value of $\int_{0}^{2} f(x) d x$ ? $0$ $1$ $2$ $-1$
​​​​​Let $f(x)$ be a continuous function from $\mathbb{R}$ to $\mathbb{R}$ such that\[f(x)=1-f(2-x)\]Which one of the following options is the CORRECT value of ...
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14 votes
7 answers
5
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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1 votes
2 answers
6
GATE DS&AI 2024 | Question: 50
Evaluate the following limit: \[ \lim _{x \rightarrow 0} \frac{\ln \left(\left(x^{2}+1\right) \cos x\right)}{x^{2}}= \]
Evaluate the following limit:\[\lim _{x \rightarrow 0} \frac{\ln \left(\left(x^{2}+1\right) \cos x\right)}{x^{2}}= \]
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5 votes
2 answers
7
GATE CSE 2023 | Question: 21
The value of the definite integral \[ \int_{-3}^{3} \int_{-2}^{2} \int_{-1}^{1}\left(4 x^{2} y-z^{3}\right) \mathrm{d} z \mathrm{~d} y \mathrm{~d} x \] is _________. (Rounded off to the nearest integer)
The value of the definite integral \[\int_{-3}^{3} \int_{-2}^{2} \int_{-1}^{1}\left(4 x^{2} y-z^{3}\right) \mathrm{d} z \mathrm{~d} y \mathrm{~d} x\]is _________. (Rounde...
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8 votes
2 answers
8
GATE CSE 2023 | Question: 18
Let $\qquad f(x)=x^{3}+15 x^{2}-33 x-36$ be a real-valued function. Which of the following statements is/are $\text{TRUE}?$ $f(x)$ does not have a local maximum. $f(x)$ has a local maximum. $f(x)$ does not have a local minimum. $f(x)$ has a local minimum.
Let $$\qquad f(x)=x^{3}+15 x^{2}-33 x-36$$be a real-valued function.Which of the following statements is/are $\text{TRUE}?$$f(x)$ does not have a local maximum.$f(x)$ has...
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36 votes
2 answers
9
GATE CSE 2008 | Question: 25
A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve $3x^4-16x^3+24x^2+37$ is $0$ $1$ $2$ $3$
A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve $3x^4-16x^3+24x^2+37$ is$0$$1$$2$$3...
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1 votes
2 answers
11
Memory Based GATE DA 2024 | Question: 3
Evaluate the limit: \[ \lim_{{x \to 0}} \frac{\ln \left(\left(x^2+1\right) \cos x\right)}{x^2} \]
Evaluate the limit:\[\lim_{{x \to 0}} \frac{\ln \left(\left(x^2+1\right) \cos x\right)}{x^2}\]
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26 votes
6 answers
12
GATE CSE 2015 Set 1 | Question: 4
$\displaystyle \lim_{x\rightarrow \infty } x^{ \tfrac{1}{x}}$ is $\infty $ $0$ $1$ Not defined
$\displaystyle \lim_{x\rightarrow \infty } x^{ \tfrac{1}{x}}$ is$\infty $$0$$1$Not defined
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25 votes
9 answers
15
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$
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0 votes
1 answer
18
Memory Based GATE DA 2024 | Question: 7
Consider the function \(f(x) = \frac{1}{1+e^{-x}}\). Determine the derivative \(f^{\prime}(x)\) when \(f(x) = 0.4\).
Consider the function \(f(x) = \frac{1}{1+e^{-x}}\). Determine the derivative \(f^{\prime}(x)\) when \(f(x) = 0.4\).
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