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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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Most viewed questions in Calculus

1 votes
1 answer
121
TIFR-2011-Maths-A-14
$\log x$ is uniformly continuous on $( \frac{1}{2}, \infty)$.
$\log x$ is uniformly continuous on $( \frac{1}{2}, \infty)$.
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4 votes
4 answers
122
ISI2014-DCG-3
$\underset{x \to \infty}{\lim} \left( \frac{3x-1}{3x+1} \right) ^{4x}$ equals $1$ $0$ $e^{-8/3}$ $e^{4/9}$
$\underset{x \to \infty}{\lim} \left( \frac{3x-1}{3x+1} \right) ^{4x}$ equals$1$$0$$e^{-8/3}$$e^{4/9}$
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0 votes
1 answer
123
bs grewal calculus question
please solve .?
please solve .?
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3 votes
0 answers
124
limit question find answer
$\lim_{x\rightarrow\infty}(\sqrt{x}-x)=?$
$\lim_{x\rightarrow\infty}(\sqrt{x}-x)=?$
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4 votes
1 answer
125
GATE CSE 1995 | Question: 7(B)
Compute without using power series expansion $\displaystyle \lim_{x \to 0} \frac{\sin x}{x}.$
Compute without using power series expansion $\displaystyle \lim_{x \to 0} \frac{\sin x}{x}.$
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5 votes
1 answer
126
ISI2004-MIII: 23
If $\textit{f}(x)=x^{2}$ and $g(x)=x \sin x +\cos x$ then $f$ and $g$ agree at no point $f$ and $g$ agree at exactly one point $f$ and $g$ agree at exactly two point $f$ and $g$ agree at more then two point
If $\textit{f}(x)=x^{2}$ and $g(x)=x \sin x +\cos x$ then$f$ and $g$ agree at no point$f$ and $g$ agree at exactly one point$f$ and $g$ agree at exactly two point$f$ and ...
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1 votes
1 answer
127
Mean Value Theorem
f(x) is a differentiable function that satisfies 5 ≤ f′(x) ≤ 14 for all x. Let a and b be the maximum and minimum values, respectively, that f(11)−f(3) can possibly have, then what is the value of a+b?
f(x) is a differentiable function that satisfies 5 ≤ f′(x) ≤ 14 for all x. Let a and b be the maximum and minimum values, respectively, that f(11)−f(3) can possib...
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8 votes
2 answers
128
TIFR CSE 2013 | Part A | Question: 16
The minimum of the function $f(x) = x \log_{e}(x)$ over the interval $[\frac{1}{2}, \infty )$ is $0$ $-e$ $\frac{-\log_{e}(2)}{2}$ $\frac{-1}{e}$ None of the above
The minimum of the function $f(x) = x \log_{e}(x)$ over the interval $[\frac{1}{2}, \infty )$ is$0$$-e$$\frac{-\log_{e}(2)}{2}$$\frac{-1}{e}$None of the above
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1 votes
1 answer
129
NIELIT2017 STA-set-c-119
The function $f(x)=\frac{x^2 -1}{x-1}$ at $x=1$ is: Continuous and Differentiable Continuous but not Differentiable Differentiable but not Continuous Neither Continuous nor Differentiable
The function $f(x)=\frac{x^2 -1}{x-1}$ at $x=1$ is:Continuous and Differentiable Continuous but not DifferentiableDifferentiable but not ContinuousNeither Continuous nor ...
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4 votes
4 answers
130
TIFR2010-Maths-A-8
Let $f(x)= |x|^{3/2}, x \in \mathbb{R}$. Then $f$ is uniformly continuous. $f$ is continuous, but not differentiable at $x=0$. $f$ is differentiable and $f ' $ is continuous. $f$ is differentiable, but $f ' $ is discontinuous at $x=0$.
Let $f(x)= |x|^{3/2}, x \in \mathbb{R}$. Then$f$ is uniformly continuous.$f$ is continuous, but not differentiable at $x=0$.$f$ is differentiable and $f ' $ is continuous...
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3 votes
2 answers
131
ISI2017-MMA-14
Let $(v_n)$ be a sequence defined by $v_1 = 1$ and $v_{n+1} = \sqrt{v_n^2 +\left(\dfrac{1}{5}\right)^n}$ for $n\geq1$. Then $\displaystyle{\lim_{n \rightarrow \infty}v_n}$ is $\sqrt{5/3}$ $\sqrt{5/4}$ $1$ $\text{non existent}$
Let $(v_n)$ be a sequence defined by $v_1 = 1$ and $v_{n+1} = \sqrt{v_n^2 +\left(\dfrac{1}{5}\right)^n}$ for $n\geq1$. Then $\displaystyle{\lim_{n \rightarrow \infty}v_n}...
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6 votes
1 answer
132
TIFR CSE 2011 | Part A | Question: 17
What is $\lim_{x \to 0} \frac{2^x-1}{x}$ $0$ $\log_2(e)$ $\log_e(2)$ $1$ None of the above
What is $$\lim_{x \to 0} \frac{2^x-1}{x}$$$0$$\log_2(e)$$\log_e(2)$$1$None of the above
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0 votes
1 answer
135
Maxima and Minima
Divide 75 into three parts such that their product is maximum.
Divide 75 into three parts such that their product is maximum.
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1 votes
1 answer
136
integration 10[IN]
http://gateforum.com/wp-content/uploads/2013/01/IN-2010.pdf Question 21 The integral $\int _{-\infty} ^{\infty}\delta (t-\frac{\pi}{6})6\sin(t)dt$ evaluates to (A).6 (B).3 (c).1.5 (D).0
http://gateforum.com/wp-content/uploads/2013/01/IN-2010.pdf Question 21The integral $\int _{-\infty} ^{\infty}\delta (t-\frac{\pi}{6})6\sin(t)dt$ evaluates to(A).6(B).3(c...
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0 votes
1 answer
137
ISRO 2013- Functions [EE]
The minimum point of the function ($x^3$ / $3$)- $x$ is at a) x= 1 b) x = -1 c) x = 0 d) x = 1/ √ 3
The minimum point of the function ($x^3$ / $3$)- $x$ is ata) x= 1b) x = -1c) x = 0d) x = 1/ √ 3
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1 votes
1 answer
138
ISI MMA-2015
Let, $a_{n} \;=\; \left ( 1-\frac{1}{\sqrt{2}} \right ) ... \left ( 1- \frac{1}{\sqrt{n+1}} \right )$ , $n \geq 1$. Then $\lim_{n\rightarrow \infty } a_{n}$ (A) equals $1$ (B) does not exist (C) equals $\frac{1}{\sqrt{\pi }}$ (D) equals $0$
Let, $a_{n} \;=\; \left ( 1-\frac{1}{\sqrt{2}} \right ) ... \left ( 1- \frac{1}{\sqrt{n+1}} \right )$ , $n \geq 1$. Then $\lim_{n\rightarrow \infty } a_{n}$(A) equals $1$...
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3 votes
1 answer
139
TIFR CSE 2018 | Part A | Question: 5
Which of the following is the derivative of $f(x)=x^{x}$ when $x>0$ ? $x^{x}$ $x^{x} \ln \;x$ $x^{x}+x^{x}\ln\;x$ $(x^{x}) (x^{x}\ln\;x)$ $\text{None of the above; function is not differentiable for }x>0$
Which of the following is the derivative of $f(x)=x^{x}$ when $x>0$ ?$x^{x}$$x^{x} \ln \;x$$x^{x}+x^{x}\ln\;x$$(x^{x}) (x^{x}\ln\;x)$$\text{None of the above; function is...
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