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GATE2018-1-27

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go_editor asked Feb 19, 2020
GATE2020-ME-1: 27
A vector field is defined as ... shell formed by two concentric spheres with origin as the center, and internal and external radii of $1$ and $2$, respectively, is $0$ $2\pi$ $4\pi$ $8\pi$
A vector field is defined as $$\overrightarrow{f}\left ( x,y,z \right )=\dfrac{x}{\left [ x^{2}+y^{2}+z^{2} \right ]^{\frac{3}{2}}}\widehat{i}\:+\:\dfrac{y}{\left [ x^{2}...
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Arjun asked Feb 26, 2017
GATE2017 ME-1: 27
For the vector $\vec{V}=2yz\hat{i}+3xz \hat{j}+4xy \hat{k}$, the value of $\bigtriangledown$. $(\bigtriangledown \times \vec{V})$ is ________.
For the vector $\vec{V}=2yz\hat{i}+3xz \hat{j}+4xy \hat{k}$, the value of $\bigtriangledown$. $(\bigtriangledown \times \vec{V})$ is ________.
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Arjun asked Feb 17, 2018
GATE2018-1-4
$F(z)$ is a function of the complex variable $z=x+iy$ given by $F(z)+ i \: z + k \: Re(z) + i \: Im(z)$. For what value of $k$ will $F(z)$ satisfy the Cauchy-Riemann equations? $0$ $1$ $-1$ $y$
$F(z)$ is a function of the complex variable $z=x+iy$ given by $F(z)+ i \: z + k \: Re(z) + i \: Im(z)$. For what value of $k$ will $F(z)$ satisfy the Cauchy-Riemann equa...
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Arjun asked Feb 17, 2018
GATE2018-1-3
According to the Mean Value Theorem, for a continuous function $f(x)$ in the interval $[a,b]$, there exists a value $\xi$ in this interval such that $\int_a^b f(x) dx = $ $f(\xi)(b-a)$ $f(b)(\xi-a)$ $f(a)(b-\xi)$ $0$
According to the Mean Value Theorem, for a continuous function $f(x)$ in the interval $[a,b]$, there exists a value $\xi$ in this interval such that $\int_a^b f(x) dx = $...
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