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

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

Recent questions in Calculus

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$\int x^7.e^{x^4}dx$How to do this?
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243
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244
Do read the comments from thebottom of the page :)
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245
https://gateoverflow.in/2608/gate1995-1-21IN THE GRAPH WHY TWO EQUATIONS ARE TAKEN MEANS HOW X=Y AND COSX TWO DIFFERENT THINGS ARE TAKEN TO GET INTERSECTION POINT.
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246
$\int_{0}^{1}\frac{x^{\alpha }-1}{logx}dx$ where $\alpha>0$
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247
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248
https://gateoverflow.in/610/gate1993-02-6what is the integration of xtan-1 (1/x) in this question.
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249
Find the limit of the given expression$\lim_{x\to\frac{\pi}{2}}\left ( \sec x-\frac{1}{1-\sin x} \right )$
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250
Please try to answer without using any standard result as i cant remember them.
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251
Answer is 1 but where it is going wrong the way I solved in following image.
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252
Can some one please how to solve above integral using mentioned property or any other way?
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253
https://gateoverflow.in/80571/gate1987-1-xxviA CAN BE ALSO ANSWER?
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254
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1 votes
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256
Which of following function is strictly bounded?
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257
how we can solve such type of question?
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258
$\int_{0}^{1}(x^2+1)^4dx$
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259