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83
GATE Electrical 2014 Set 3 | Question: 26
Integration of the complex function $f(z)=\dfrac{z^2}{z^2-1}$ , in the counterclockwise direction, around $\mid z-1 \mid = 1$, is $-\pi i$ $0$ $\pi i$ $2 \pi i$
Integration of the complex function $f(z)=\dfrac{z^2}{z^2-1}$ , in the counterclockwise direction, around $\mid z-1 \mid = 1$, is$-\pi i$$0$$\pi i$$2 \pi i$
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85
GATE Electrical 2013 | Question: 50
The state variable formulation of a system is given as ... The system is controllable but not observable not controllable but observable both controllable and observable both not controllable and not observable
The state variable formulation of a system is given as$\begin{bmatrix} x^\cdot_1 \\ x^\cdot_2 \end{bmatrix}=\begin{bmatrix} -2 & 0\\ 0 & -1 \end{bmatrix}\begin{bmatrix} x...
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86
GATE Electrical 2015 Set 2 | Question: 26
The volume enclosed by the surface $f(x, y) = e^{x}$ over the triangle bounded by the lines $x = y; x = 0; y = 1$ in the $xy$ plane is ________.
The volume enclosed by the surface $f(x, y) = e^{x}$ over the triangle bounded by the lines $x = y; x = 0; y = 1$ in the $xy$ plane is ________.
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91
GATE Electrical 2013 | Question: 11
A continuous random variable $X$ has a probability density function $f(x)=e^{-x}, 0< x< \infty$. then $P\{X> 1\}$ $0.368$ $0.5$ $0.632$ $1.0$
A continuous random variable $X$ has a probability density function $f(x)=e^{-x}, 0< x< \infty$. then $P\{X 1\}$$0.368$$0.5$$0.632$$1.0$
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93
GATE Electrical 2014 Set 2 | Question: 28
The minimum value of the function $f(x)=x^3-3x^2-24x+100$ in the interval $[-3,3]$ is $20$ $28$ $16$ $32$
The minimum value of the function $f(x)=x^3-3x^2-24x+100$ in the interval $[-3,3]$ is$20$$28$$16$$32$
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94
GATE Electrical 2013 | Question: 24
Given a vector field $\textbf{F}=y^2x \textbf{a}_x-yz \textbf{a}_y-x^2 \textbf{a}_z$ the line integral $\int \textbf{F} \cdot d \textbf{l}$ evaluated along a segment on the $x$-axis from $x=1$ to $x=2$ is $-2.33$ $0$ $2.33$ $7$
Given a vector field $\textbf{F}=y^2x \textbf{a}_x-yz \textbf{a}_y-x^2 \textbf{a}_z$ the line integral $\int \textbf{F} \cdot d \textbf{l}$ evaluated along a segment on t...
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97
GATE Electrical 2014 Set 2 | Question: 3
Minimum of the real valued function $f(x)=(x-1)^{2/3}$ occurs at $x$ equal to $-\infty$ $0$ $1$ $\infty$
Minimum of the real valued function $f(x)=(x-1)^{2/3}$ occurs at $x$ equal to$-\infty$$0$$1$$\infty$
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101
GATE Electrical 2015 Set 2 | Question: 4
The Laplace transform of $f(t)= 2\sqrt{t/\pi}$ is $s^{-3/2}$. The Laplace transform of $g(t)=\sqrt{1/\pi t}$ is. $3s^{-5/2} /2$ $s^{-1/2}$ $s^{1/2}$ $s^{3/2}$
The Laplace transform of $f(t)= 2\sqrt{t/\pi}$ is $s^{-3/2}$. The Laplace transform of $g(t)=\sqrt{1/\pi t}$ is.$3s^{-5/2} /2$$s^{-1/2}$$s^{1/2}$$s^{3/2}$
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102
GATE Electrical 2013 | Question: 46
A function $y=5x^2+10x$ is defined over an open interval $x$ = $(1, 2)$ . At least at one point in this interval, $\dfrac{\mathrm{dy} }{\mathrm{d} x}$ is exactly $20$ $25$ $30$ $35$
A function $y=5x^2+10x$ is defined over an open interval $x$ = $(1, 2)$ . At least at one point in this interval, $\dfrac{\mathrm{dy} }{\mathrm{d} x}$ is exactly$20$$25$$...
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103
GATE Electrical 2014 Set 1 | Question: 2
Let $f(x)=xe^{-x}$ . The maximum value of the function in the interval $(0,\infty)$ is $e^{-1}$ $e$ $1-e^{-1}$ $1+e^{-1}$
Let $f(x)=xe^{-x}$ . The maximum value of the function in the interval $(0,\infty)$ is$e^{-1}$$e$$1-e^{-1}$$1+e^{-1}$
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105
GATE Electrical 2015 Set 2 | Question: 3
Match the following. ... $P-4; Q-1; R-3; S-2$ $P-4; Q-3; R-1; S-2$ $P-3; Q-4; R-2; S-1$
Match the following.$\begin{array}{|l|l|l|l|} \hline P. & \text{Stokes’s Theorem} & 1. & ∯ D.ds = Q \\ \hline Q. & \text{Gauss’s Theorem} & 2. & \oint f(z) dz =0 \\...
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107
GATE Electrical 2014 Set 3 | Question: 3
Let $\nabla .(fv)=x^2y+y^2z+z^2x$ , where $f$ and $v$ are scalar and vector fields respectively. If $v=yi+zj+xk$ then $v.\Delta f$ is $x^2y+y^2z+z^2x$ $2xy+2yz+2zx$ $x+y+z$ $0$
Let $\nabla .(fv)=x^2y+y^2z+z^2x$ , where $f$ and $v$ are scalar and vector fields respectively. If $v=yi+zj+xk$ then $v.\Delta f$ is$x^2y+y^2z+z^2x$$2xy+2yz+2zx$$x+y+z$...
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108
GATE Electrical 2015 Set 1 | Question: 3
If the sum of the diagonal elements of a $2 \times 2$ matrix is $-6$, then the maximum possible value of determinant of the matrix is ________
If the sum of the diagonal elements of a $2 \times 2$ matrix is $-6$, then the maximum possible value of determinant of the matrix is ________
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109
GATE Electrical 2013 | Question: 36
$\displaystyle{}\int \frac{z^2-4}{z^2+4}\: dz$ evaluated anticlockwise around the circle $\mid z-i \mid=2$ , where $i=\sqrt{-1}$, is $-4\pi$ $0$ $2+\pi$ $2+2i$
$\displaystyle{}\int \frac{z^2-4}{z^2+4}\: dz$ evaluated anticlockwise around the circle $\mid z-i \mid=2$ , where $i=\sqrt{-1}$, is$-4\pi$$0$$2+\pi$$2+2i$
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110
GATE Electrical 2014 Set 3 | Question: 28
The function $f(x)=e^x-1$ is to be solved using Newton-Raphson method. If the initial value of $x_0$ is taken as $1.0$, then the absolute error observed at $2^{nd}$ iteration is _______.
The function $f(x)=e^x-1$ is to be solved using Newton-Raphson method. If the initial value of $x_0$ is taken as $1.0$, then the absolute error observed at $2^{nd}$ iter...
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112
GATE Electrical 2015 Set 1 | Question: 2
If a continuous function $f(x)$ does not have a root in the interval $[a, b]$, then which one of the following statements is TRUE? $f(a) . f(b)=0$ $f(a) . f(b) < 0$ $f(a) . f(b) > 0$ $f(a) / f(b) \leq 0$
If a continuous function $f(x)$ does not have a root in the interval $[a, b]$, then which one of the following statements is TRUE?$f(a) . f(b)=0$$f(a) . f(b) < 0$$f(a) . ...
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113
GATE Electrical 2015 Set 2 | Question: 28
A differential equation $\dfrac{di}{dt}-0.2i=0$ is applicable over $−10 < t < 10$. If $i(4) = 10$, then $i(−5)$ is _________.
A differential equation $\dfrac{di}{dt}-0.2i=0$ is applicable over $−10 < t < 10$. If $i(4) = 10$, then $i(−5)$ is _________.
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114
GATE Electrical 2014 Set 2 | Question: 5
Consider the differential equation $x^2\dfrac{d^2y}{dx^2}+x\dfrac{dy}{dx}-y=0$. Which of the following is a solution to this differential equation for $x>0$? $e^x$ $x^2$ $1/x$ $\ln x$
Consider the differential equation $x^2\dfrac{d^2y}{dx^2}+x\dfrac{dy}{dx}-y=0$. Which of the following is a solution to this differential equation for $x>0$?$e^x$$x^2$$1/...
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117
GATE Electrical 2016 Set 1 | Question: 33
Given the following polynomial equation $s^{3}+5.5 s^{2}+8.5s+3=0$ the number of roots of the polynomial, which have real parts strictly less than $−1$, is ________.
Given the following polynomial equation $s^{3}+5.5 s^{2}+8.5s+3=0$ the number of roots of the polynomial, which have real parts strictly less than $−1$, is ________.
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