Recent questions and answers in Differential Equations - GO Electrical

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GATE2013-36
$\oint \frac{z^2-4}{z^2+4} dz$ evaluated anticlockwise around the circle $|z-i|=2$ , where $i=\sqrt{-1}$, is $-4\pi$ 0 $2+\pi$ $2+2i$

asked Feb 12, 2017 in Differential Equations by piyag476 (1.5k points)

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2

GATE2014-2-26
To evaluate the double integral $\int_{0}^{8}(\int_{(y/2)}^{y/2+1}(\frac{2x-y}{2})dx)dy$ , we make the substitution $u=(\frac{2x-y}{2})$ and $v=\frac{y}{2}$ The integral will reduce $\int_{0}^{4}(\int_{0}^{2}2udu) dv$ $\int_{0}^{4}(\int_{0}^{1}2udu) dv$ $\int_{0}^{4}(\int_{0}^{1}udu) dv$ $\int_{0}^{4}(\int_{0}^{2}udu) dv$

asked Feb 12, 2017 in Differential Equations by makhdoom ghaya (9.2k points)

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3

GATE2014-2-5
Consider the differential equation $x^2\frac{d^2y}{dx^2}+x\frac{dy}{dx}-y=0$ . Which of the following is a solution to this differential equation for$x>0$? $e^x$ $x^2$ $1/x$ $lnx$

asked Feb 12, 2017 in Differential Equations by makhdoom ghaya (9.2k points)

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4

GATE2014-1-17
In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of only one root at the origin Imaginary roots only positive real roots only negative real roots

asked Feb 12, 2017 in Differential Equations by makhdoom ghaya (9.2k points)

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5

GATE2014-1-3
The solution for the differential equation $\frac{d^2x}{dt^2}=-9x$ with initial conditions $x(0)=1$ and $\frac{dx}{dt}|_{t=0}=1$ , is $t^2+t+1$ $sin3t+\frac{1}{3}cos3t+\frac{2}{3}$ $\frac{1}{3}sin3t+cos3t$ $cos3t$+$t$

asked Feb 12, 2017 in Differential Equations by makhdoom ghaya (9.2k points)

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6

GATE2014-1-2
Let $f(x)=xe^{-x}$ . The maximum value of the function in the interval ($0,\infty$) is $e^{-1}$ $e$ $1$-$e^{-1}$ $1$+$e^{-1}$

asked Feb 12, 2017 in Differential Equations by makhdoom ghaya (9.2k points)

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7

GATE2014-1-GA-5
The roots of $ax^2+bx+c=0$ are real and positive. $a$, $b$ and $c$ are real. Then $ax^2+b|x|+c=0$ has no roots $2$ real roots $3$ real roots $4$ real roots

asked Feb 12, 2017 in Differential Equations by makhdoom ghaya (9.2k points)

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8

GATE2015-2-28
A differential equation $\frac{di}{dt}-0.2i=0$ is applicable over $−10 < t < 10$. If $i(4) = 10$, then $i(−5)$ is _________.

asked Feb 12, 2017 in Differential Equations by makhdoom ghaya (9.2k points)

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9

GATE2015-1-27
A solution of the ordinary differential equation $\frac{d^{2}y}{dt^{2}}+5\frac{dy}{dt}+6y=0$ is such that $y(0) = 2$ and $y(1)= -\frac{1-3e}{e^{3}}$. The value of $\frac{dy}{dt}(0)$ is _______.

asked Feb 12, 2017 in Differential Equations by makhdoom ghaya (9.2k points)

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10

GATE2016-2-30
Let $y(x)$ be the solution of the differential equation $\frac{d^{2}y}{dx^{2}}-4\frac{dy}{dx}+4y=0$ with initial conditions $y(0)=0$ and $\frac{dy}{dx}\mid _{x=0}=1$ Then the value of $y(1)$ is _________.

asked Jan 30, 2017 in Differential Equations by makhdoom ghaya (9.2k points)

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11

GATE2016-2-8
The solution of the differential equation, for $t > 0, y"(t)+2y'(t)+y(t)=0$ with initial conditions $y(0)=0$ and $y'(0)=1$, is ($u(t)$ denotes the unit step function), $te^{-t}u(t)$ $(e^{-t}-te^{-t})u(t)$ $(-e^{-t}+te^{-t})u(t)$ $e^{-t}u(t)$

asked Jan 30, 2017 in Differential Equations by makhdoom ghaya (9.2k points)

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12

GATE2016-2-4
Consider a causal $LTI$ system characterized by differential equation $\frac{dy(t)}{dt}+\frac{1}{6}y(t)=3x(t)$ The response of the system to the input $x(t)=3e^{-\frac{t}{3}}u(t)$, where $u(t)$ denotes the unit step function, is $9e^{-\frac{t}{3}}u(t)$ $9e^{-\frac{t}{6}}u(t)$ $9e^{-\frac{t}{3}}u(t)-6e^{-\frac{t}{6}}u(t)$ $54e^{-\frac{t}{6}}u(t)-54e^{-\frac{t}{3}}u(t)$

asked Jan 30, 2017 in Differential Equations by makhdoom ghaya (9.2k points)

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13

GATE2016-1-5
The value of the integral $\oint _{c}\frac{2z+5}{\left ( z-\frac{1}{2} \right ) \left (z^{2} -4z+5 \right )}dz$ over the contour $|z|=1$, taken in the anti-clockwise direction, would be $\frac{24 \pi i}{13}$ $\frac{48 \pi i}{13}$ $\frac{24}{13}$ $\frac{12}{13}$

asked Jan 30, 2017 in Differential Equations by makhdoom ghaya (9.2k points)

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14

GATE2016-1-4
A function $y(t)$, such that $y(0)=1$ and $y(1)=3e^{-1}$, is a solution of the differential equation $\frac{d^{2}y}{dt^{2}}+2\frac{dy}{dt}+y=0$. Then $y(2)$ is $5e^{-1}$ $5e^{-2}$ $7e^{-1}$ $7e^{-2}$

asked Jan 30, 2017 in Differential Equations by makhdoom ghaya (9.2k points)

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15

GATE2016-1-1
The maximum value attained by the function. $f(x) = x(x-1) (x-2)$ in the interval $[1, 2]$ is ___________.

asked Jan 30, 2017 in Differential Equations by makhdoom ghaya (9.2k points)

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