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81

GATE Electrical 2024 | Question: 26
Consider a vector $\bar{u}=2 \hat{x}+\hat{y}+2 \hat{z}$, where $\hat{x}, \hat{y}, \hat{z}$ represent unit vectors along the coordinate axes $x, y, z$ respectively. The directional derivative of the function $f(x, y, z)=2 \ln (x y)+\ln (y z)+3 \ln (x z)$ at the point $(x, y, z)=(1,1,1)$ in the direction of $\bar{u}$ is $0$ $\frac{7}{5 \sqrt{2}}$ $7$ $21$

Consider a vector $\bar{u}=2 \hat{x}+\hat{y}+2 \hat{z}$, where $\hat{x}, \hat{y}, \hat{z}$ represent unit vectors along the coordinate axes $x, y, z$ respecti...

Arjun

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Arjun asked Feb 16

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82

GATE Electrical 2024 | Question: 9
The figure shows the single line diagram of a 4-bus power network. Branches $b_{1}$, $b_{2}, b_{3}$, and $b_{4}$ have impedances $4 z, z, 2 z$, and $4 z$ per-unit (pu), respectively, where $z=r+j x$, with $r>0$ and $x>0$. The ... $b_{1}$ $b_{2}$ $b_{3}$ $b_{4}$

The figure shows the single line diagram of a 4-bus power network. Branches $b_{1}$, $b_{2}, b_{3}$, and $b_{4}$ have impedances $4 z, z, 2 z$, and $4 z$ p...

Arjun

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Arjun asked Feb 16

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83

GATE Electrical 2024 | Question: 29
If the $Z$-transform of a finite-duration discrete-time signal $x[n]$ is $X(z)$, then the $Z$ transform of the signal $y[n]=x[2 n]$ is $Y(z)=X\left(z^{2}\right)$ ... $Y(z)=\frac{1}{2}\left[X\left(z^{2}\right)+X\left(-z^{2}\right)\right]$

If the $Z$-transform of a finite-duration discrete-time signal $x[n]$ is $X(z)$, then the $Z$ transform of the signal $y[n]=x[2 n]$ is$Y(z)=X\left(z^{2}\right)$$...

Arjun

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Arjun asked Feb 16

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84

GATE Electrical 2014 Set 3 | Question: 30
The power delivered by the current source, in the figure, is ________.

The power delivered by the current source, in the figure, is ________.

makhdoom ghaya

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makhdoom ghaya asked Feb 11, 2017

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85

GATE Electrical 2024 | Question: 28
Consider the discrete-time systems $T_{1}$ and $T_{2}$ defined as follows: \[ \begin{array}{c} \left\{T_{1} x\right\}[n]=x[0]+x[1]+\cdots+x[n] \\ \left\{T_{2} x\right\}[n]=x[0]+\frac{1}{2} x[1]+\cdots+\frac{1}{2^{n}} x[n] \ ... $T_{1}$ is BIBO stable but $T_{2}$ is not BIBO stable. $T_{1}$ is not BIBO stable but $T_{2}$ is BIBO stable.

Consider the discrete-time systems $T_{1}$ and $T_{2}$ defined as follows:\[\begin{array}{c}\left\{T_{1} x\right\}[n]=x[0]+x +\cdots+x[n] \\\left\{T_{2} x\right\...

Arjun

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Arjun asked Feb 16

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86

GATE Electrical 2024 | Question: 34
Consider the function $f(t)=(\max (0, t))^2$ for $-\infty<t<\infty$, where $\max (a, b)$ denotes the maximum of $a$ and $b$. Which of the following statements is/are true? $f(t)$ is not ... differentiable and its derivative is continuous. $f(t)$ is differentiable but its derivative is not continuous. $f(t)$ and its derivative are differentiable.

Consider the function $f(t)=(\max (0, t))^2$ for $-\infty<t<\infty$, where $\max (a, b)$ denotes the maximum of $a$ and $b$. Which of the following stateme...

Arjun

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Arjun asked Feb 16

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87

GATE Electrical 2023 | GA Question: 8
Which one of the options does NOT describe the passage below or follow from it? We tend to think of cancer as a 'modern' illness because its metaphors are so modern. It is a disease of overproduction, of sudden growth ... imagined as a machine. Modern cell biology never uses figurative language, such as metaphors, to describe or explain anything.

Which one of the options does NOT describe the passage below or follow from it?We tend to think of cancer as a 'modern' illness because its metaphors are so modern. It is...

admin

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admin asked May 20, 2023

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88

GATE Electrical 2023 | GA Question: 3
Given a fair six-faced dice where the faces are labelled $\text{‘1’, ‘2’, ‘3’, ‘4’, ‘5’, } \text{and ‘6’,}$ what is the probability of getting a $\text{‘1’}$ on the first roll of the dice and a $\text{‘4'}$ on the second roll? $\frac{1}{36}$ $\frac{1}{6}$ $\frac{5}{6}$ $\frac{1}{3}$

Given a fair six-faced dice where the faces are labelled $\text{‘1’, ‘2’, ‘3’, ‘4’, ‘5’, } \text{and ‘6’,}$what is the probability of getting a $\...

admin

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admin asked May 20, 2023

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89

GATE Electrical 2024 | Question: 7
A three phase, $50 \mathrm{~Hz}, 6$ pole induction motor runs at $960 \mathrm{rpm}$. The stator copper loss, core loss, and the rotational loss of the motor can be neglected. The percentage efficiency of the motor is $92$ $94$ $96$ $98$

A three phase, $50 \mathrm{~Hz}, 6$ pole induction motor runs at $960 \mathrm{rpm}$. The stator copper loss, core loss, and the rotational loss of the moto...

Arjun

15.9k points

Arjun asked Feb 16

3 votes

2 answers

90

GATE Electrical 2021 | GA Question: 4
Which one of the following numbers is exactly divisible by $\left ( 11^{13} +1\right )$? $11^{26} +1$ $11^{33} +1$ $11^{39} -1$ $11^{52} -1$

Which one of the following numbers is exactly divisible by $\left ( 11^{13} +1\right )$?$11^{26} +1$$11^{33} +1$$11^{39} -1$$11^{52} -1$

Arjun

15.9k points

Arjun asked Feb 19, 2021

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91

GATE Electrical 2021 | Question: 48
The waveform shown in solid line is obtained by clipping a full-wave rectified sinusoid (shown dashed). The ratio of the $\text{RMS}$ value of the full-wave rectified waveform to the $\text{RMS}$ value of the clipped waveform is _______________. (Round off to $2$ decimal places.)

The waveform shown in solid line is obtained by clipping a full-wave rectified sinusoid (shown dashed). The ratio of the $\text{RMS}$ value of the full-wave rectified wav...

Arjun

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Arjun asked Feb 19, 2021

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92

GATE Electrical 2024 | Question: 14
Simplified form of the Boolean function \[ F(P, Q, R, S)=\bar{P} \bar{Q}+\bar{P} Q S+P \bar{Q} \bar{R} \bar{S}+P \bar{Q} R \bar{S} \] is $\bar{P} S+\bar{Q} \bar{S}$ $\bar{P} \bar{Q}+\bar{Q} \bar{S}$ $\bar{P} Q+R \bar{S}$ $P \bar{S}+Q \bar{R}$

Simplified form of the Boolean function\[F(P, Q, R, S)=\bar{P} \bar{Q}+\bar{P} Q S+P \bar{Q} \bar{R} \bar{S}+P \bar{Q} R \bar{S}\]is$\bar{P} S+\bar{Q} \bar{S}...

Arjun

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Arjun asked Feb 16

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93

GATE Electrical 2024 | Question: 22
The sum of the eigenvalues of the matrix $A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]^{2}$ is ____________(rounded off to the nearest integer).

The sum of the eigenvalues of the matrix $A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]^{2}$ is ____________(rounded off to the nearest integer).

Arjun

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Arjun asked Feb 16

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94

GATE Electrical 2024 | Question: 13
The table lists two instrument transformers and their features: \begin{array}{|l|l|} \hline \text{ Instrument Transformers } &\text{ Features } \\ \hline & \text{P}) \text{Primary is connected in parallel to the grid} \\ \hline \text{X}) \text{ ... $\mathrm{Q}$ and $\mathrm{S}$; $\mathrm{Y}$ matches with $\mathrm{P}$ and $\mathrm{R}$.

The table lists two instrument transformers and their features:\begin{array}{|l|l|}\hline \text{ Instrument Transformers } &\text{ Features } \\\hline & \text{P}) ...

Arjun

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Arjun asked Feb 16

1 votes

2 answers

95

GATE Electrical 2021 | GA Question: 3
For a regular polygon having $10$ sides, the interior angle between the sides of the polygon, in degrees, is: $396$ $324$ $216$ $144$

For a regular polygon having $10$ sides, the interior angle between the sides of the polygon, in degrees, is:$396$$324$$216$$144$

Arjun

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Arjun asked Feb 19, 2021

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96

GATE Electrical 2024 | Question: 32
A $\text{BJT}$ biasing circuit is shown in the figure, where $V_{B E}=0.7 \mathrm{~V}$ and $\beta=100$. The Quiescent Point values of $V_{C E}$ and $I_{C}$ are respectively $4.6 \mathrm{~V}$ and $2.46 \mathrm{~mA}$ $3.5 \mathrm{~V}$ and $2.46 \mathrm{~mA}$ $2.61 \mathrm{~V}$ and $3.13 \mathrm{~mA}$ $4.6 \mathrm{~V}$ and $3.13 \mathrm{~mA}$

A $\text{BJT}$ biasing circuit is shown in the figure, where $V_{B E}=0.7 \mathrm{~V}$ and $\beta=100$. The Quiescent Point values of $V_{C E}$ and $I_{...

Arjun

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Arjun asked Feb 16

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97

GATE Electrical 2024 | Question: 43
If the energy of a continuous-time signal $x(t)$ is $\text{E}$ and the energy of the signal $2 x(2 t-1)$ is $c E$, then $c$ is ___________ (rounded off to $1$ decimal place).

If the energy of a continuous-time signal $x(t)$ is $\text{E}$ and the energy of the signal $2 x(2 t-1)$ is $c E$, then $c$ is ___________ (rounded off to $1$ decimal pla...

Arjun

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Arjun asked Feb 16

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98

GATE Electrical 2013 | Question: 8
A single-phase load is supplied by a single-phase voltage source. If the current flowing from the load to the source is $10\angle -150^0\: A$ and if the voltage at the load terminals is $100\angle 60^0\: V$, ... absorbs real power and absorbs reactive power. Load delivers real power and delivers reactive power. Load delivers real power and absorbs reactive power.

A single-phase load is supplied by a single-phase voltage source. If the current flowing from the load to the source is $10\angle -150^0\: A$ and if the voltage at the lo...

piyag476

1.6k points

piyag476 asked Feb 11, 2017

1 votes

1 answer

99

GATE Electrical 2023 | GA Question: 5
How many triangles are present in the given figure? $12$ $16$ $20$ $24$

How many triangles are present in the given figure?$12$ $16$$20$$24$

admin

1.7k points

admin asked May 20, 2023

1 votes

1 answer

100

GATE Electrical 2021 | GA Question: 10
Seven cars $\text{P, Q. R, S, T, U and V}$ are parked in a row not necessarily in that order. The cars $T$ and $U$ should be parked next to each other. The cars $S$ and $V$ also should be parked next to each other, whereas $P$ and $Q$ ... and $R$ are not parked together. $V$ is the only car parked in between $S$ and $R$. Car $P$ is parked at the extreme end.

Seven cars $\text{P, Q. R, S, T, U and V}$ are parked in a row not necessarily in that order. The cars $T$ and $U$ should be parked next to each other. The cars $S$ and $...

Arjun

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Arjun asked Feb 19, 2021

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101

GATE Electrical 2021 | Question: 4
For the network shown, the equivalent Thevenin voltage and Thevenin impedance as seen across terminals ‘$\text{ab}$’ is $\text{10 V}$ in series with $12\:\Omega$ $\text{65 V}$ in series with $15\:\Omega$ $\text{50 V}$ in series with $2\:\Omega$ $\text{35 V}$ in series with $2\:\Omega$

For the network shown, the equivalent Thevenin voltage and Thevenin impedance as seen across terminals ‘$\text{ab}$’ is$\text{10 V}$ in series with $12\:\Omega$$\text...

Arjun

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Arjun asked Feb 19, 2021

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102

GATE Electrical 2022 | Question: 28
The open loop transfer function of a unity gain negative feedback system is given as $G \left ( s \right ) = \dfrac{1}{s\left ( s+1 \right )}$ The Nyquist contour in the $s$ -plane encloses the entire right half plane and a small neighbourhood around the ... $G(s)$, corresponding to the Nyquist contour, is denoted as $N$. Then $N$ equals to $0$ $1$ $2$ $3$

The open loop transfer function of a unity gain negative feedback system is given as $$G \left ( s \right ) = \dfrac{1}{s\left ( s+1 \right )}$$The Nyquist contour in the...

Arjun

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Arjun asked Feb 15, 2022

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1 answer

103

GATE Electrical 2020 | Question: 1
$ax^{3}+bx^{2}+cx+d$ is a polynomial on real $\text{x}$ over real coefficients $\text{a, b, c, d}$ wherein $a\neq 0.$ Which of the following statements is true? $\text{d}$ can be chosen to ensure that $\text{x = 0}$ is a root for any ... $\text{a, b, c, d}$ can be chosen to ensure that all roots are complex. $\text{c}$ alone cannot ensure that all roots are real.

$ax^{3}+bx^{2}+cx+d$ is a polynomial on real $\text{x}$ over real coefficients $\text{a, b, c, d}$ wherein $a\neq 0.$ Which of the following statements is true?$\text{d}$...

go_editor

1.9k points

go_editor asked Feb 28, 2020

1 votes

1 answer

104

GATE Electrical 2020 | GA Question: 2
People were prohibited_____their vehicles near the entrance of the main administrative building. to park from parking parking to have parked

People were prohibited_____their vehicles near the entrance of the main administrative building.to parkfrom parkingparkingto have parked

go_editor

1.9k points

go_editor asked Feb 28, 2020

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105

GATE Electrical 2015 Set 1 | Question: 55
The open loop poles of a third order unity feedback system are at $0, −1, −2$. Let the frequency corresponding to the point where the root locus of the system transits to unstable region be $K$. Now suppose we introduce a zero in ... a frequency less than $K$ It corresponds to a frequency $K$ Root locus of modified system never transits to unstable region

The open loop poles of a third order unity feedback system are at $0, −1, −2$. Let the frequency corresponding to the point where the root locus of the system transit...

makhdoom ghaya

9.4k points

makhdoom ghaya asked Feb 11, 2017

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106

GATE Electrical 2014 Set 1 | Question: 14
The undesirable property of an electrical insulating material is high dielectric strength High relative permittivity high thermal conductivity High insulation resistivity

The undesirable property of an electrical insulating material ishigh dielectric strengthHigh relative permittivityhigh thermal conductivityHigh insulation resistivity

makhdoom ghaya

9.4k points

makhdoom ghaya asked Feb 11, 2017

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0 answers

107

GATE Electrical 2024 | Question: 30
A $3$-phase, $11 \mathrm{kV}, 10 \mathrm{MVA}$ synchronous generator is connected to an inductive load of power factor $(\sqrt{3} / 2)$ via a lossless line with a per-phase inductive reactance of $5 \Omega$. The per-phase synchronous reactance ... power factor at the terminal of the generator is $0.63$ lagging. $0.87$ lagging. $0.63$ leading. $0.87$ leading.

A $3$-phase, $11 \mathrm{kV}, 10 \mathrm{MVA}$ synchronous generator is connected to an inductive load of power factor $(\sqrt{3} / 2)$ via a lossless line wi...

Arjun

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Arjun asked Feb 16

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108

GATE Electrical 2022 | Question: 2
For an ideal $\text{MOSFET}$ biased in saturation, the magnitude of the small signal current gain for a common drain amplifier is $0$ $1$ $100$ infinite

For an ideal $\text{MOSFET}$ biased in saturation, the magnitude of the small signal current gain for a common drain amplifier is$0$$1$$100$infinite

Arjun

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Arjun asked Feb 15, 2022

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109

GATE Electrical 2024 | Question: 16
To obtain the Boolean function $\text{F(X, Y)}=\text{X} \bar{\text{Y}}+\bar{\text{X}}$, the inputs $\text{PQRS}$ in the figure should be $1010$ $1110$ $0110$ $0001$

To obtain the Boolean function $\text{F(X, Y)}=\text{X} \bar{\text{Y}}+\bar{\text{X}}$, the inputs $\text{PQRS}$ in the figure should be$1010$$1110$$0110$$...

Arjun

15.9k points

Arjun asked Feb 16

1 votes

1 answer

110

GATE Electrical 2023 | GA Question: 6
Students of all the departments of a college who have successfully completed the registration process are eligible to vote in the upcoming college elections. However, by the time the due date for registration was over, it was found that suprisingly none of the students ... from the Department of Human Sciences. (i) and (ii) (i) and (iii) only (i) only (iii)

Students of all the departments of a college who have successfully completed the registration process are eligible to vote in the upcoming college elections. However, by ...

admin

1.7k points

admin asked May 20, 2023

1 votes

0 answers

111

GATE Electrical 2022 | Question: 4
The geometric mean radius of a conductor, having four equal strands with each strand of radius $’r’$, as shown in the figure below, is $4\:r$ $1.414\:r$ $2\:r$ $1.723\:r$

The geometric mean radius of a conductor, having four equal strands with each strand of radius $’r’$, as shown in the figure below, is $4\:r$$1.414\:r$$2\:r$$1.723\:r...

Arjun

15.9k points

Arjun asked Feb 15, 2022

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0 answers

112

GATE Electrical 2017 Set 2 | Question: 25
In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is $100 \times 100$. If there are $20$PV buses in addition to $PQ$ buses and a slack bus, the total number of buses in the system is ______.

In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is $100 \times 100$. If there are $20$PV buses in addition to $PQ$...

Arjun

15.9k points

Arjun asked Feb 26, 2017

1 votes

1 answer

113

GATE Electrical 2021 | GA Question: 5
$\textit{Oasis}$ is to $\textit{sand}$ as $\textit{island}$ is to _____________ Which one of the following options maintains a similar logical relation in the above sentence? Stone Land Water Mountain

$\textit{Oasis}$ is to $\textit{sand}$ as $\textit{island}$ is to _____________Which one of the following options maintains a similar logical relation in the above senten...

Arjun

15.9k points

Arjun asked Feb 19, 2021

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0 answers

114

GATE Electrical 2014 Set 1 | Question: 10
For a periodic square wave, which one of the following statements is TRUE? The Fourier series coefficients do not exist. The Fourier series coefficients exist but the reconstruction converges at no point. The Fourier series ... the reconstruction converges at most points. The Fourier series coefficients exist and the reconstruction converges at every point.

For a periodic square wave, which one of the following statements is TRUE?The Fourier series coefficients do not exist.The Fourier series coefficients exist but the recon...

makhdoom ghaya

9.4k points

makhdoom ghaya asked Feb 11, 2017

0 votes

0 answers

115

GATE Electrical 2024 | Question: 12
Consider the cascaded system as shown in the figure. Neglecting the faster component of the transient response, which one of the following options is a firstorder pole-only approximation such that the steady-state values of the unit step responses of the original and the approximated systems ... $\frac{2}{s+1}$ $\frac{1}{s+20}$ $\frac{2}{s+20}$

Consider the cascaded system as shown in the figure. Neglecting the faster component of the transient response, which one of the following options is a firsto...

Arjun

15.9k points

Arjun asked Feb 16

2 votes

1 answer

116

GATE Electrical 2020 | GA Question: 4
Stock markets _______ at the news of the coup. poised plunged plugged probed

Stock markets _______ at the news of the coup.poisedplungedpluggedprobed

go_editor

1.9k points

go_editor asked Feb 28, 2020

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117

GATE Electrical 2020 | Question: 33
The static electric field inside a dielectric medium with relative permittivity, $\varepsilon _{r}=2.25$, expressed in cylindrical coordinate system is given by the following expression $E=a_{r}2r+a_{\varphi }\left ( \frac{3}{r} \right )+a_{z}6$ ... $3\varepsilon _{0}$ $4\varepsilon _{0}$ $5\varepsilon _{0}$ $9\varepsilon _{0}$

The static electric field inside a dielectric medium with relative permittivity, $\varepsilon _{r}=2.25$, expressed in cylindrical coordinate system is given by the follo...

go_editor

1.9k points

go_editor asked Feb 28, 2020

0 votes

1 answer

118

GATE Electrical 2019 | GA Question: 3
The missing number in the given sequence $343,1331,$_____$,4913$ is $3375$ $2744$ $2197$ $4096$

The missing number in the given sequence $343,1331,$_____$,4913$ is$3375$$2744$$2197$$4096$

Arjun

15.9k points

Arjun asked Feb 12, 2019

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0 answers

119

GATE Electrical 2019 | Question: 26
Consider a $2\times 2$ matrix $M=\begin{bmatrix} v_1 & v_2 \end{bmatrix}$, where $v_1$ and $v_2$ are the column vectors. Suppose $M^{-1}=\begin{bmatrix} u_1^T \\ u_2^T \end{bmatrix}$, where $u_1^T$ and $u_2^T$ are ... True and Statement $2$ is false Statement $2$ is true and Statement $1$ is false Both the Statements are true Both the statements are false

Consider a $2\times 2$ matrix $M=\begin{bmatrix} v_1 & v_2 \end{bmatrix}$, where $v_1$ and $v_2$ are the column vectors. Suppose $M^{-1}=\begin{bmatrix} u_1^T \\ u_2^T \e...

Arjun

15.9k points

Arjun asked Feb 12, 2019

1 votes

1 answer

120

GATE Electrical 2023 | GA Question: 4
A recent survey shows that $65 \%$ of tobacco users were advised to stop consuming tobacco. The survey also shows that $3$ out of $10$ tobacco users attempted to stop using tobacco. Based only on the information in the ... $65 \%$ of tobacco users successfully stopped consuming tobacco.

A recent survey shows that $65 \%$ of tobacco users were advised to stop consuming tobacco. The survey also shows that $3$ out of $10$ tobacco users attempted to stop us...

admin

1.7k points

admin asked May 20, 2023