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Recent activity in Calculus

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GATE2019 IN: 1
$\overrightarrow{a}$,$\overrightarrow{b}$,$\overrightarrow{c}$ are three orthogonal vectors. Given that $\overrightarrow{a}$ = ${\widehat{i}}$ + 2${\widehat{j}}$ + 5${\wi...
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GATE2019 IN: 2
The vector function $\overrightarrow{A}$ is given by $\overrightarrow{A}$ = $\overrightarrow{\bigtriangledown}$u , where u(x, y) is a scalar function. Then |$\overrightar...
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1 1 answer
GATE2019 IN: 26
The curve y = f(x) is such that the tangent to the curve at every point (x,y) has a y-axis intercept c, given by c = -y. Then,f(x) is proportional tox$^{-1}$x$^{2}$x$^{3}...
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GATE IN 2026 | Question: 2
Which one among the following statements is true for the function $f(x)=x\mid x \mid $?$f(x)$ is discontinuous but not differentiable at $x=0$.$f(x)$ is discontinuous and...
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GATE IN 2021 | Question: 23
Consider the function $f\left ( x \right )=-x^{2}+10x+100$. The minimum value of the function in interval $[5,10]$ is ___________.
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GATE IN 2023 | Question: 47
Consider the real-valued function $g(x)=\max \left\{(x-2)^2,-2 x+7\right\}$, where $x \in(-\infty, \infty)$. The minimum value attained by $g(x)$ is_____________(rounded ...
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GATE IN 2025 | Question: 28
The value of the integral $\int_{-\pi}^{\pi}\left(\cos ^{6} x+\cos ^{4} x\right) \mathrm{d} x$ is$\frac{\pi}{2}$$\frac{5 \pi}{8}$$\frac{11 \pi}{8}$$\frac{9 \pi}{8}$
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GATE IN 2025 | Question: 26
The value of the surface integral $\iint_{S}(2 x+z) \mathrm{d} y \mathrm{~d} z+(2 x+z) \mathrm{d} x \mathrm{~d} z+(2 z+y) \mathrm{d} x \mathrm{~d} y$ over the sphere $S: ...
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GATE IN 2025 | GA | Question: 3
If $P e^{x}=Q e^{-x}$ for all real values of $x$, which one of the following statements is true?$P=Q=0$$P=Q=1$$P=1 ; Q=-1$$\frac{P}{Q}=0$
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GATE IN 2022 | Question: 18
The global minimum of $x^{3} e^{-|x|}$ for $x \in (-\infty, \infty)$ occurs at $x = $ _________ (round off to one decimal place)
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GATE IN 2023 | Question: 13
What is $\lim _{x \rightarrow 0} f(x)$, where $f(x)=x \sin \frac{1}{x} ?$$0$$1$$\infty$Limit does not exist
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GATE IN 2021 | Question: 2
Consider the sequence $x_{n}=0.5x_{n-1}+1,n=1,2, \dots \:\dots$ with $x_0=0$ . Then $\displaystyle \lim_{n\rightarrow \infty} x_n$ is$0$$1$$2$$\infty$
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GATE2020 IN: 28
A straight line drawn on an x-y plane intercepts the x-axis at -0.5 and the y-axis at 1.The equation that describes this line is __________.$\text{y=-0.5x+1}$$\text{y=x-0...
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GATE2020 IN: 31
Consider the function $f(x,y)=x^2+y^2.$ The minimum value the function attains on the line $x+y=1$ (rounded off to one decimal place) is __________.
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GATE2020: 1
The unit vectors along the mutually perpendicular x,y and z axes are $\hat{i},\;\hat{j}\; and \;\hat{k}$ respectively. Consider the plane $z=0$ and two vectors $\overrigh...
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GATE2018IN: 26
Given $\overrightarrow{F}$ = (x$^2$ – 2y) $\overrightarrow{i}$ – 4xz$\overrightarrow{j}$ + 4xz$^2$$\overrightarrow{k}$, the value of the linear integral $\int_c$$\overrig...
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GATE2018IN: 4
Consider two functions f(x) = (x – 2)$^2$ and g(x) = 2x – 1, where x is real. The smallest value of x for which f(x) = g(x) is $\_\_\_\_\_\_$
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GATE IN 2017 | Question: 27
The angle between two vectors $X_1=\begin{bmatrix}2 & 6 & 14\end{bmatrix}^T$ and $X_2=\begin{bmatrix}-12 & 8 & 16\end{bmatrix}^T$ in radian is __________.
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GATE 2016 - 1
A straight line of the form $y=mx+c$ passes through the origin and the point $(x,y)$ =$(2,6)$. The value of $m$ is _____.
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GATE2016-2
$\underset{n\rightarrow \infty }{\lim}\:\left(\sqrt{n^2+n}-\sqrt{n^2+1}\right)$ is __________.
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GATE2016-4
The vector that is $NOT$ perpendicular to the vectors $(i+j+k)$ and $(i+2j+3k)$ is ______.$(i-2j+k)$ $(-i+2j-k)$$(0i+0j+0k)$$(4i+3j+5k)$
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GATE2016-26
Let $f: [-1,1]\rightarrow \mathbb{R}$, where $f(x)=2x^3-x^4-10$. The minimum value of $f(x)$ is $\_\_\_\_\_\_\_.$
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GATE2015-13
The double integral $\int_0^a \int_0^y f(x,y) dx\;dy$ is equivalent to$\int_0^x\int_0^y f(x,y) dx\;dy$$\int_0^a \int_x^y f(x,y) dx\;dy$$\int_0^a \int_x^a f(x,y) dy\;dx$$\...
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GATE2015-14
The magnitude of the directional derivative of the function $f(x,y)=x^2+3y^2$ in a direction normal to the circle $x^2+y^2=2,$ at the point $(1,1),$ is$4\sqrt{2}$$5\sqrt{...
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GATE2015-57
The fundamental period of the signal $x(t)=2\cos(\frac{2\pi t}{3})+\cos(\pi t)$, in seconds, is ________________ s.
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GATE2014-4
A vector is defined as $$f=y\hat{i}+x\hat{j}+z\hat{k}$$where $\hat{i},\hat{j},\hat{k}$ are unit vectors in Cartesian $(x,y,z)$ coordinate system.The surface integral $f....
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GATE IN 2013 | Question: 5
For a vector $E$, which one of the following statements is $\text{NOT TRUE}$?If $\Delta.E=0,\;E$ is called solenoidalIf $\Delta \times E=0,\;E$ is called conservativeIf $...
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GATE IN 2012 | Question: 29
The maximum value of $f(x)=x^3-9x^2+24x+5$ in the interval $[1, 6]$ is $21$$25$$41$$46$
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GATE IN 2012 | Question: 28
The direction of vector $\text{A}$ is radially outward from the origin, with $|A|=kr^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of $n$ for which $\nabla....
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GATE IN 2012 | Question: 1
If $x=\sqrt{-1},$ then the value of $x^x$ is $e^{-\pi/2}$$e^{\pi/2}$$x$$1$
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