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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

4 votes
1 answer
81
integration
Please solve the following integration problem $\int_{0}^{\infty}{ y^{\frac{1}{2} }}e^{-y^3}dx$ I want full explanation. please help me ?
Please solve the following integration problem$\int_{0}^{\infty}{ y^{\frac{1}{2} }}e^{-y^3}dx$I want full explanation. please help me ?
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10 votes
3 answers
82
TIFR CSE 2011 | Part A | Question: 11
$\int_{0}^{1} \log_e(x) dx=$ $1$ $-1$ $\infty $ $-\infty $ None of the above
$$\int_{0}^{1} \log_e(x) dx=$$$1$$-1$$\infty $$-\infty $None of the above
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2 votes
1 answer
83
area
Find Volume under surface z(x,y)=x+y and above the triangle defined in x-y plane by 0<=y<=x and 0<=x<=12
Find Volume under surface z(x,y)=x+y and above the triangle defined in x-y plane by 0<=y<=x and 0<=x<=12
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12 votes
4 answers
84
TIFR CSE 2011 | Part A | Question: 14
The limit $\lim_{x \to 0} \frac{d}{dx}\,\frac{\sin^2 x}{x}$ is $0$ $2$ $1$ $\frac{1}{2}$ None of the above
The limit $$\lim_{x \to 0} \frac{d}{dx}\,\frac{\sin^2 x}{x}$$ is$0$$2$$1$$\frac{1}{2}$None of the above
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1 votes
2 answers
85
Integration- CE 2013
Find the value of the integral $\int_{0}^{\pi/6}cos^43\theta\ sin^36\theta\ d\theta$ Please show the steps.(upload a pic of your solution) a) 0 b) 1/15 c) 8/3 d) 1
Find the value of the integral $$\int_{0}^{\pi/6}cos^43\theta\ sin^36\theta\ d\theta$$Please show the steps.(upload a pic of your solution)a) 0b) 1/15c) 8/3d) 1
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5 votes
1 answer
86
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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2 votes
3 answers
87
VALUE OF LIMIT
What is value of $\lim_{x\rightarrow 0, Y\rightarrow 0}\frac{xY}{x^2+Y^2}$ 1 -1 0 Does not exist
What is value of $\lim_{x\rightarrow 0, Y\rightarrow 0}\frac{xY}{x^2+Y^2}$1 -10Does not exist
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1 votes
2 answers
88
Integration in Sinx and Cosx
My answer is coming 0. Please explain.
My answer is coming 0. Please explain.
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3 votes
2 answers
89
A function is defined over an open interval atleast at one point in this interval, dy/dx is exactly?GATE_2013-EC,EE,IN
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
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5 votes
1 answer
91
ISRO2009-49
$x=a \cos(t), y=b \sin(t)$ is the parametric form of Ellipse Hyperbola Circle Parabola
$x=a \cos(t), y=b \sin(t)$ is the parametric form ofEllipseHyperbolaCircleParabola
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1 votes
1 answer
92
ISI2019-MMA-28
Consider the functions $f,g:[0,1] \rightarrow [0,1]$ given by $f(x)=\frac{1}{2}x(x+1) \text{ and } g(x)=\frac{1}{2}x^2(x+1).$ Then the area enclosed between the graphs of $f^{-1}$ and $g^{-1}$ is $1/4$ $1/6$ $1/8$ $1/24$
Consider the functions $f,g:[0,1] \rightarrow [0,1]$ given by$$f(x)=\frac{1}{2}x(x+1) \text{ and } g(x)=\frac{1}{2}x^2(x+1).$$Then the area enclosed between the graphs of...
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5 votes
1 answer
94
ISRO2011-59
$n$-th derivative of $x^n$ is $nx^{n-1}$ $n^n.n!$ $nx^n!$ $n!$
$n$-th derivative of $x^n$ is$nx^{n-1}$$n^n.n!$$nx^n!$$n!$
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7 votes
3 answers
100
TIFR CSE 2010 | Part A | Question: 3
The function $f (x) = 2.5 \log_e \left( 2 + \exp \left( x^2 - 4x + 5 \right)\right)$ attains a minimum at $x = $? $0$ $1$ $2$ $3$ $4$
The function $f (x) = 2.5 \log_e \left( 2 + \exp \left( x^2 - 4x + 5 \right)\right)$ attains a minimum at $x = $?$0$$1$$2$$3$$4$
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