GATE2018-1-3

Arjun asked Feb 17, 2018 • recategorized Mar 5, 2021 by Lakshman Bhaiya

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go_editor asked Sep 18, 2020

GATE2020-ME-2: 3
Let $I=\displaystyle \int_{x=0}^1 \int_{y=0}^{x^2} xy^2 dy \: dx$. Then, $I$ may also be expressed as $\displaystyle \int_{y=0}^1 \int_{x=0}^{\sqrt{y}} xy^2 dx \: dy$ $\displaystyle \int_{y=0}^1 \int_{x=\sqrt{y}}^1 yx^2 dx \: dy$ $\displaystyle \int_{y=0}^1 \int_{x=\sqrt{y}}^1 xy^2 dx \: dy$ $\displaystyle \int_{y=0}^1 \int_{x=0}^{\sqrt{y}} yx^2 dx \: dy$

Let $I=\displaystyle \int_{x=0}^1 \int_{y=0}^{x^2} xy^2 dy \: dx$. Then, $I$ may also be expressed as$\displaystyle \int_{y=0}^1 \int_{x=0}^{\sqrt{y}} xy^2 dx \: dy$$\dis...

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go_editor asked Sep 18, 2020

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Arjun asked Feb 17, 2018

GATE2018-1-27
The value of the integral over the closed surface $S$ bounding a volume $V$, where $\overrightarrow{r} = x \hat{i} + y \hat{j}+z \hat{k}$ is the position vector and $\overrightarrow{n}$ is the normal to the surface $S$, is $V$ $2V$ $3V$ $4V$

The value of the integralover the closed surface $S$ bounding a volume $V$, where $\overrightarrow{r} = x \hat{i} + y \hat{j}+z \hat{k}$ is the position vector and $\over...

Arjun

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Arjun asked Feb 17, 2018

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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...

Arjun

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Arjun asked Feb 17, 2018

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Arjun asked Feb 9, 2019

GATE2019 ME-1: 51
The value of the following definite integral is __________ (round off to three decimal places) $\int_1^e (x \: \ln \: x) dx$

The value of the following definite integral is __________ (round off to three decimal places)$$\int_1^e (x \: \ln \: x) dx$$

Arjun

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Arjun asked Feb 9, 2019

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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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