GATE2016-1-27

The figure below represents a triangle $PQR$ with initial coordinates of the vertices as $P(1,3)$, $Q(4,5)$ and $R(5,3.5)$. The triangle is rotated in the $X$-$Y$ plane a...

Arjun

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Arjun asked Feb 24, 2017

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Arjun asked Feb 24, 2017

GATE2016-1-28
The value of the integral $\displaystyle{\int_{-\infty }^{\infty }\frac{\sin x}{x^2+2x+2}}dx$ evaluated using contour integration and the residue theorem is $\displaystyle{\frac{-\pi \sin(1)}{e}}\\$ $\displaystyle{\frac{-\pi \cos (1)}{e}} \\$ $\displaystyle{\frac{\sin (1)}{e}} \\$ $\displaystyle{\frac{\cos (1)}{e}}$

The value of the integral $$\displaystyle{\int_{-\infty }^{\infty }\frac{\sin x}{x^2+2x+2}}dx$$ evaluated using contour integration and the residue theorem is$\displaysty...

Arjun

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Arjun asked Feb 24, 2017

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Arjun asked Feb 24, 2017

GATE2016-1-3
$f(z)=u(x,y)+iv(x,y)$ is an analytic function of complex variable $z=x+iy$ where $i=\sqrt{-1}$. If $u(x,y)$=$2xy$ , then $v(x,y)$ may be expressed as $-x^2 + y^2 + $ constant $x^2 – y^2 +$ constant $x^2 + y^2 +$ constant $-(x^2 + y^2) +$ constant

$f(z)=u(x,y)+iv(x,y)$ is an analytic function of complex variable $z=x+iy$ where $i=\sqrt{-1}$. If $u(x,y)$=$2xy$ , then $v(x,y)$ may be expressed as$-x^2 + y^2 + $ const...

Arjun

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GATE2016-3-27
The value of the line integral $\oint_{c}^{ }\overline{F}.{\overline{r}}'ds$ ,where $C$ is a circle of radius $\dfrac{4}{\sqrt{\pi }}$ units is ________ Here, $\overline{F}(x,y)=y\hat{i}+2x\hat{j}$ ... $x-y$ Cartesian reference. In evaluating the line integral, the curve has to be traversed in the counter-clockwise direction.

The value of the line integral $\oint_{c}^{ }\overline{F}.{\overline{r}}'ds$ ,where $C$ is a circle of radius $\dfrac{4}{\sqrt{\pi }}$ units is ________Here, $\overline{F...

Arjun

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Arjun asked Feb 24, 2017

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