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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 answered questions in Calculus

2 votes
2 answers
151
What does the following integral evaluate to?a) 5 π /16b) 5 π /8c) 0d) 5 π /32
0 votes
2 answers
154
what is the integration of this funcion? f(x)=1−|x| where −1≤x≤1
1 votes
2 answers
156
Consider the funciton $M$ defined as follows:$M(n) = \begin{cases} n-10 & \text{ if } n 100 \\ M(M(n+11)) & \text{ if } n \leq 100 \end{cases}$Compute the following$: M(...
2 votes
2 answers
157
Consider the funciton $M$ defined as follows:$M(n) = \begin{cases} n-10 & \text{ if } n 100 \\ M(M(n+11)) & \text{ if } n \leq 100 \end{cases}$Compute the following$: M(...
1 votes
2 answers
160
How to solve this?
2 votes
2 answers
161
How to slove this$\lim_{n\rightarrow \infty }\left ( 10^{n}+n^{20} \right )/n!$
3 votes
2 answers
162
what is the value of$\textstyle \lim_{x \to 2}\frac{x-2}{\log(x-1)}$
2 votes
2 answers
163
The expression $\lim_{a \to 0}\frac{x^{a}-1}{a}$ is equal to (A)$\log x$ (B)0 (c)$x\log x$ (D)$\infty$
3 votes
2 answers
164
Can anyone tell me range of f(x)=|sinx|+|cosx|
3 votes
2 answers
165
If f ' (x) =$\frac{8}{x^{}2+3x+4}$ and f(0) =1 then the lower and upper bounds of f(1) estimated by Langrange 's Mean Value Theorem are ___
3 votes
2 answers
166
A function y= 5x^2+ 10x is defined over an open interval x = (1,2). Atleast at one point in this interval, dy/dx is exactly(A) 20 (B) 25 (C) 30 (D) 35
0 votes
2 answers
168
The question is f(x) = | x-1 | + | x+1 | is differentiable at x=1 or not . Now , when x<1 , the first part becomes : -(x-1) , i.e 1-x and why should we not change the sig...
1 votes
2 answers
169
Given that &alpha; &ge; 0 and value of integral at &alpha; = 0 is 0. The value of$\int_{0}^{1}\frac{x^{\alpha }-1}{log x}dx$
0 votes
2 answers
170
how to solve it