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Arjun asked Feb 24, 2017
GATE2015-1-27
Consider an ant crawling along the curve $(x-2)^2+y^2=4$ , where $x$ and $y$ are in meters. The ant starts at the point $(4, 0)$ and moves counter-clockwise with a speed of $1.57$ meters per second. The time taken by the ant to reach the point $(2, 2)$ is (in seconds) ____________
Consider an ant crawling along the curve $(x-2)^2+y^2=4$ , where $x$ and $y$ are in meters. The ant starts at the point $(4, 0)$ and moves counter-clockwise with a speed ...
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Arjun asked Feb 24, 2017
GATE2015-1-26
Consider a spatial curve in three-dimensional space given in parametric form by $x(t)= \cos t, \:y(t)=\sin t, z(t)=\dfrac{2}{\pi } t \: 0\leq t\leq \dfrac{\pi }{2}$ The length of the curve is _______
Consider a spatial curve in three-dimensional space given in parametric form by $$x(t)= \cos t, \:y(t)=\sin t, z(t)=\dfrac{2}{\pi } t \: 0\leq t\leq \dfrac{\pi }{2}$$ The...
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Arjun asked Feb 24, 2017
GATE2015-1-4
The value of $\displaystyle{} \lim_{x\rightarrow 0}\dfrac{1- \cos(x^2)}{2x^4}$ is $0 \\$ $\dfrac{1}{2} \\$ $\dfrac{1}{4} \\$ undefined
The value of $\displaystyle{} \lim_{x\rightarrow 0}\dfrac{1- \cos(x^2)}{2x^4}$ is$0 \\$$\dfrac{1}{2} \\$$\dfrac{1}{4} \\$undefined
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gatecse asked Feb 22, 2021
GATE Mechanical 2021 Set 1 | Question: 27
Let $\text{C}$ represent the unit circle centered at origin in the complex plane, and complex variable, $z=x+iy$. The value of the contour integral $\oint _{C}\dfrac{\cosh \:3z}{2z}\:dz$ (where integration is taken counter clockwise) is $0$ $2$ $\pi i$ $2 \pi i$
Let $\text{C}$ represent the unit circle centered at origin in the complex plane, and complex variable, $z=x+iy$. The value of the contour integral $\oint _{C}\dfrac{\cos...
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go_editor asked Feb 19, 2020
GATE2020-ME-1: 4
Which of the following function $f(z)$, of the complex variable $z,$ is NOT analytic at all the points of the complex plane? $f\left ( z \right )=z^{2}$ $f\left ( z \right )=e^{z}$ $f\left ( z \right )=\sin z$ $f\left ( z \right )=\log z$
Which of the following function $f(z)$, of the complex variable $z,$ is NOT analytic at all the points of the complex plane?$f\left ( z \right )=z^{2}$$f\left ( z \right ...
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