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281

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 ________.

makhdoom ghaya

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makhdoom ghaya asked Jan 29, 2017

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282

GATE Electrical 2019 | GA Question: 1
I am not sure if the bus that has been booked will be able to ______ all the students. sit deteriorate fill accommodate

I am not sure if the bus that has been booked will be able to ______ all the students.sitdeterioratefillaccommodate

Arjun

15.9k points

Arjun asked Feb 12, 2019

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283

GATE Electrical 2024 | Question: 49
Consider the stable closed-loop system shown in the figure. The magnitude and phase values of the frequency response of $\text{G(s)}$ are given in the table. The value of the gain $K_{I}(>0)$ for a $50^{\circ}$ phase margin is __________ (rounded off to $2$ ... -80 \\ \hline 2.0 & -18 & -130 \\ \hline 10.0 & -40 & -200 \\ \hline \end{array}

Consider the stable closed-loop system shown in the figure. The magnitude and phase values of the frequency response of $\text{G(s)}$ are given in the table. The value of...

Arjun

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Arjun asked Feb 16

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284

GATE Electrical 2015 Set 1 | Question: 53
The transfer function of a second order real system with a perfectly flat magnitude response of unity has a pole at $(2 − j3)$. List all the poles and zeroes. Poles at $(2 \pm j3)$, no zeroes. Poles at $(\pm 2 − j3)$, one zero at origin. Poles at $(2 − j3)$, $(−2 + j3)$, zeroes at $(−2 − j3)$, $(2 + j3)$. Poles at $(2 \pm j3)$, zeroes at $(−2 \pm j3)$.

The transfer function of a second order real system with a perfectly flat magnitude response of unity has a pole at $(2 − j3)$. List all the poles and zeroes.Poles at $...

makhdoom ghaya

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makhdoom ghaya asked Feb 11, 2017

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285

GATE Electrical 2014 Set 2 | Question: 27
Let $X$ be a random variable with probability density function $f(x)=\begin{cases} 0.2,& \text{for } \mid x \mid \leq 1\\ 0.1,& \text{for }1< \mid x \mid \leq 4\\ 0 & \text{otherwise } \end{cases} \\$ The probability $P(0.5 < X < 5)$ is ______.

Let $X$ be a random variable with probability density function$f(x)=\begin{cases} 0.2,& \text{for } \mid x \mid \leq 1\\ 0.1,& \text{for }1< \mid x \mid \leq 4\\ 0 & \tex...

makhdoom ghaya

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makhdoom ghaya asked Feb 11, 2017

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286

GATE Electrical 2023 | Question: 8
The Fourier transform $X(\omega)$ of the signal $x(t)$ is given by $\begin{aligned} X(\omega) & =1, \text { for }|\omega|<W_o \\ & =0, \text { for }|\omega|>W_0 \end{aligned}$ Which one of the following statements is true? $x(t)$ tends to be an impulse as ... At $t=\frac{\pi}{2 W_0}, x(t)=-\frac{1}{\pi}$ At $t=\frac{\pi}{2 W_0}, x(t)=\frac{1}{\pi}$

The Fourier transform $X(\omega)$ of the signal $x(t)$ is given by$$\begin{aligned}X(\omega) & =1, \text { for }|\omega|<W_o \\& =0, \text { for }|\omega|>W_0\end{aligned...

admin

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admin asked May 20, 2023

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287

GATE Electrical 2021 | Question: 3
Let $f\left ( x \right )$ be a real-valued function such that ${f}'\left ( x_{0} \right )=0$ for some $x _{0} \in\left ( 0,1 \right ),$ and ${f}''\left ( x \right )> 0$ for all $x \in \left ( 0,1 \right )$. ... has no local minimum in $(0,1)$ one local maximum in $(0,1)$ exactly one local minimum in $(0,1)$ two distinct local minima in $(0,1)$

Let $f\left ( x \right )$ be a real-valued function such that ${f}'\left ( x_{0} \right )=0$ for some $x _{0} \in\left ( 0,1 \right ),$ and ${f}''\left ( x \right ) 0$ fo...

Arjun

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Arjun asked Feb 19, 2021

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288

GATE Electrical 2014 Set 1 | Question: 20
In an oscilloscope screen, linear sweep is applied at the vertical axis horizontal axis origin both horizontal and vertical axis

In an oscilloscope screen, linear sweep is applied at thevertical axishorizontal axisoriginboth horizontal and vertical axis

makhdoom ghaya

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makhdoom ghaya asked Feb 11, 2017

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289

GATE Electrical 2015 Set 1 | Question: 50
A $200/400$ V, $50$ Hz, two-winding transformer is rated at $20$ kVA. Its windings are connected as an auto-transformer of rating $200/600$ V. A resistive load of $12 \Omega$ is connected to the high voltage ($600$ V) side of the auto-transformer. The value of equivalent load resistance (in Ohm) as seen from low voltage side is _________.

A $200/400$ V, $50$ Hz, two-winding transformer is rated at $20$ kVA. Its windings are connected as an auto-transformer of rating $200/600$ V. A resistive load of $12 \Om...

makhdoom ghaya

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makhdoom ghaya asked Feb 11, 2017

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290

GATE Electrical 2023 | Question: 12
The four stator conductors $\left(\mathrm{A}, \mathrm{A}^{\prime}, \mathrm{B}\right.$ and $\left.\mathrm{B}^{\prime}\right)$ of a rotating machine are carrying $\mathrm{DC}$ currents of the same value, the directions of which are shown in the figure (i). The rotor coils ... with $E_{a-a^{\prime}}$ leading $E_{b-b^{\prime}}$ $E_{a-a^{\prime}}=E_{b-b^{\prime}}=0$

The four stator conductors $\left(\mathrm{A}, \mathrm{A}^{\prime}, \mathrm{B}\right.$ and $\left.\mathrm{B}^{\prime}\right)$ of a rotating machine are carrying $\mathrm{D...

admin

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admin asked May 20, 2023

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291

GATE Electrical 2015 Set 1 | Question: 9
A moving average function is given by $y(t) = \dfrac{1}{T} \displaystyle \int_{t-T}^{t} u(\tau ) d \tau$. If the input $u$ is a sinusoidal signal of frequency $\dfrac{1}{2T}Hz$ then in steady state, the output $y$ will lag $u$ (in degree) by __________ .

A moving average function is given by $y(t) = \dfrac{1}{T} \displaystyle \int_{t-T}^{t} u(\tau ) d \tau$. If the input $u$ is a sinusoidal signal of frequency $\dfrac{1}{...

makhdoom ghaya

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makhdoom ghaya asked Feb 11, 2017

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292

GATE Electrical 2021 | Question: 2
Let $p\left ( z\right )=z^{3}+\left ( 1+j \right )z^{2}+\left ( 2+j \right )z+3$, where $z$ ... $p\left ( z \right )=0$ come in conjugate pairs All the roots cannot be real

Let $p\left ( z\right )=z^{3}+\left ( 1+j \right )z^{2}+\left ( 2+j \right )z+3$, where $z$ is a complex number.Which one of the following is true?$\text{conjugate}\:\lef...

Arjun

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Arjun asked Feb 19, 2021

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293

GATE Electrical 2016 Set 2 | Question: 3
The following figure shows the connection of an ideal transformer with primary to secondary turns ratio of $1:100$. The applied primary voltage is $100 V$ (rms), $50 Hz, AC$. The rms value of the current $I$, in ampere, is _________.

The following figure shows the connection of an ideal transformer with primary to secondary turns ratio of $1:100$. The applied primary voltage is $100 V$ (rms), $50 Hz, ...

makhdoom ghaya

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makhdoom ghaya asked Jan 29, 2017

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294

GATE Electrical 2021 | Question: 33
In a single-phase transformer, the total iron loss is $2500\:W$ at nominal voltage of $440\:V$ and frequency $50\:Hz$. The total iron loss is $850\:W$ at $220\:V$ and $25\:Hz$. Then, at nominal voltage and frequency, the hysteresis loss and eddy current loss ... $1600\:W$ and $900\:W$ $900\:W$ and $1600\:W$ $250\:W$ and $600\:W$ $600\:W$ and $250\:W$

In a single-phase transformer, the total iron loss is $2500\:W$ at nominal voltage of $440\:V$ and frequency $50\:Hz$. The total iron loss is $850\:W...

Arjun

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Arjun asked Feb 19, 2021

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295

GATE Electrical 2019 | Question: 14
The open loop transfer function of a unity feedback system is given by $G(s)=\frac{\pi e^{-0.25s}}{s}$ In $G(s)$ plane, the Nyquist plot of $G(s)$ passes through the negative real axis at the point $(-0.5,j0)$ $(-0.75,j0)$ $(-1.25,j0)$ $(-1.5,j0)$

The open loop transfer function of a unity feedback system is given by$$G(s)=\frac{\pi e^{-0.25s}}{s}$$In $G(s)$ plane, the Nyquist plot of $G(s)$ passes through the nega...

Arjun

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Arjun asked Feb 12, 2019

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296

GATE Electrical 2019 | Question: 23
The total impedance of the secondary winding, leads, and burden of a $5$ A CT is $0.01 \: \Omega$. If the fault current is $20$ times the rated primary current of the CT, the VA output of the CT is_________

The total impedance of the secondary winding, leads, and burden of a $5$ A CT is $0.01 \: \Omega$. If the fault current is $20$ times the rated primary current of the CT,...

Arjun

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Arjun asked Feb 12, 2019

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297

GATE Electrical 2019 | Question: 25
The output voltage of a single-phase full-bridge voltage source inverter is controlled by unipolar PWM with one pulse per half cycle. For the fundamental rms Component of the output voltage to be $75 \%$ of DC voltage, the required pulse width in degrees (round off up to one decimal place) is ___________.

The output voltage of a single-phase full-bridge voltage source inverter is controlled by unipolar PWM with one pulse per half cycle. For the fundamental rms Component of...

Arjun

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Arjun asked Feb 12, 2019

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298

GATE Electrical 2024 | Question: 46
The single line diagram of a lossless system is shown in the figure. The system is operating in steady-state at a stable equilibrium point with the power output of the generator being $P_{\max } \sin \delta$, where $\delta$ is the load angle ... , the accelerating area on the power angle curve is __________ times $P_{\max }$ (rounded off to $2$ decimal places).

The single line diagram of a lossless system is shown in the figure. The system is operating in steady-state at a stable equilibrium point with the power output of the ge...

Arjun

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Arjun asked Feb 16

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299

GATE Electrical 2023 | Question: 23
A $50 \mathrm{~Hz}, 275 ~\mathrm{kV}$ line of length $400 \mathrm{~km}$ has the following parameters: Resistance, $R=0.035 ~\Omega / \mathrm{km} ;$ Inductance, $L=1 ~\mathrm{mH} / \mathrm{km} ;$ ... $2$ decimal places).

A $50 \mathrm{~Hz}, 275 ~\mathrm{kV}$ line of length $400 \mathrm{~km}$ has the following parameters: Resistance, $R=0.035 ~\Omega / \mathrm{km} ;$ Inductance, $L=1 ~\mat...

admin

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admin asked May 20, 2023

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300

GATE Electrical 2017 Set 2 | Question: 23
The mean square value of the given periodic waveform $f(t)$ is __________.

The mean square value of the given periodic waveform $f(t)$ is __________.

Arjun

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Arjun asked Feb 26, 2017

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301

GATE Electrical 2015 Set 2 | Question: 45
A symmetrical square wave of $50\%$ duty cycle has amplitude of $\pm15$ V and time period of $0.4\pi$ ms. This square wave is applied across a series $RLC$ circuit with $R = 5 \Omega$, $L = 10$ mH, and $C = 4 \mu F$. The amplitude of the $5000$ rad/s component of the capacitor voltage (in Volt) is ______.

A symmetrical square wave of $50\%$ duty cycle has amplitude of $\pm15$ V and time period of $0.4\pi$ ms. This square wave is applied across a series $RLC$ circuit with $...

makhdoom ghaya

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makhdoom ghaya asked Feb 11, 2017

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302

GATE Electrical 2018 | Question: 50
The figure shows two buck converters connected in parallel. The common input dc voltage for the converters has a value of $100 \: V$. The converters have inductors of identical value. The load resistance is $1 \: \Omega$. The capacitor voltage has negligible ... of $i_{s1}$, the current of switch $S1$ (in Ampere), is ____________ (up to $2$ decimal places).

The figure shows two buck converters connected in parallel. The common input dc voltage for the converters has a value of $100 \: V$. The converters have inductors of ide...

Arjun

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Arjun asked Feb 19, 2018

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303

GATE Electrical 2014 Set 2 | Question: 4
All the values of the multi-valued complex function $1^i$,where $i=\sqrt{-1}$ are purely imaginary. real and non-negative on the unit circle. equal in real and imaginary parts.

All the values of the multi-valued complex function $1^i$,where $i=\sqrt{-1}$ arepurely imaginary.real and non-negativeon the unit circle.equal in real and imaginary part...

makhdoom ghaya

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makhdoom ghaya asked Feb 11, 2017

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304

GATE Electrical 2015 Set 1 | Question: 49
A DC motor has the following specifications: $10$ hp, $37.5$ A, $230$ V; flux/pole $= 0.01$ Wb, number of poles $= 4$, number of conductors $= 666$, number of parallel paths $= 2$. Armature resistance$ = 0.267 \Omega$. The ... The motor operates from a $230$ V DC supply. If the motor runs at $1000$ rpm, the output torque produced (in Nm) is ________.

A DC motor has the following specifications: $10$ hp, $37.5$ A, $230$ V; flux/pole $= 0.01$ Wb, number of poles $= 4$, number of conductors $= 666$, number of parallel pa...

makhdoom ghaya

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makhdoom ghaya asked Feb 11, 2017

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305

GATE Electrical 2020 | Question: 2
Which of the following is true for all possible non-zero choices of integers $m,n;m\neq n,$ or all possible non-zero choices of real numbers $p,q;p\neq q,$ ...

Which of the following is true for all possible non-zero choices of integers $m,n;m\neq n,$ or all possible non-zero choices of real numbers $p,q;p\neq q,$ as applicable?...

go_editor

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go_editor asked Feb 28, 2020

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306

GATE Electrical 2020 | Question: 27
The vector function expressed by $F=a_{x}\left ( 5y-k_{1} z\right )+a_{y}\left ( 3z+k_{2}x \right )+a_{z}\left ( k_{3} y-4x\right )$ represents a conservative field, where $a_{x}, a_{y},a_{z}$ are unit vectors along $x, y$ and $z$ directions, respectively. The values of constants ... $k_{1}=3, k_{2}=8,k_{3}=5$ $k_{1}=4, k_{2}=5,k_{3}=3$ $k_{1}=0, k_{2}=0,k_{3}=0$

The vector function expressed by$$F=a_{x}\left ( 5y-k_{1} z\right )+a_{y}\left ( 3z+k_{2}x \right )+a_{z}\left ( k_{3} y-4x\right )$$represents a conservative field, wher...

go_editor

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go_editor asked Feb 28, 2020

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1 answer

307

GATE Electrical 2014 Set 3 | GA Question: 3
Choose the word that is opposite in meaning to the word “coherent”. sticky well-connected rambling friendly

Choose the word that is opposite in meaning to the word “coherent”.stickywell-connectedrambling friendly

makhdoom ghaya

9.4k points

makhdoom ghaya asked Feb 11, 2017

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308

GATE Electrical 2015 Set 1 | Question: 36
A parallel plate capacitor is partially filled with glass of dielectric constant $4.0$ as shown below. The dielectric strengths of air and glass are $30$ kV/cm and $300$ kV/cm, respectively. The maximum voltage (in kilovolts), which can be applied across the capacitor without any breakdown, is ______.

A parallel plate capacitor is partially filled with glass of dielectric constant $4.0$ as shown below. The dielectric strengths of air and glass are $30$ kV/cm and $300$ ...

makhdoom ghaya

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makhdoom ghaya asked Feb 11, 2017

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309

GATE Electrical 2020 | Question: 23
A single $50 \: Hz$ synchronous generator on droop control was delivering $100 \: MW$ power to a system. Due to increase in load, generator power had to be increased by $10 \: MW$ ... At this condition, the power in $\text{MW}$ supplied by the generator is _________________ (rounded off to $2$ decimal places).

A single $50 \: Hz$ synchronous generator on droop control was delivering $100 \: MW$ power to a system. Due to increase in load, generator power had to be increased by $...

go_editor

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go_editor asked Feb 28, 2020

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310

GATE Electrical 2015 Set 1 | Question: 4
Consider a function $\overrightarrow{f}=\dfrac{1}{r^{2}} \hat{r}$ where $r$ is the distance from the origin and $\hat{r}$ is the unit vector in the radial direction. The divergence of this function over a sphere of radius $R$, which includes the origin, is $0$ $2 \pi$ $4 \pi$ $R \pi$

Consider a function $\overrightarrow{f}=\dfrac{1}{r^{2}} \hat{r}$ where $r$ is the distance from the origin and $\hat{r}$ is the unit vector in the radial direction. The ...

makhdoom ghaya

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makhdoom ghaya asked Feb 11, 2017

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311

GATE Electrical 2016 Set 2 | Question: 32
Let $P=\begin{bmatrix} 3&1 \\ 1 & 3 \end{bmatrix}$ Consider the set $S$ of all vectors $\begin{pmatrix} x\\ y \end{pmatrix}$ such that $a^{2}+b^{2}=1$ ... with major axis along $\begin{pmatrix} 1\\ 1 \end{pmatrix}$ An ellipse with minor axis along $\begin{pmatrix} 1\\ 1 \end{pmatrix}$

Let $P=\begin{bmatrix} 3&1 \\ 1 & 3\end{bmatrix}$ Consider the set $S$ of all vectors $\begin{pmatrix}x\\ y\end{pmatrix}$ such that $a^{2}+b^{2}=1$ where $\begin{pmatrix}...

makhdoom ghaya

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makhdoom ghaya asked Jan 29, 2017

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312

GATE Electrical 2021 | Question: 50
An air-core radio-frequency transformer as shown has a primary winding and a secondary winding. The mutual inductance $M$ between the windings of the transformer is ____________ $\mu H$.(Round off to $2$ decimal places.)

An air-core radio-frequency transformer as shown has a primary winding and a secondary winding. The mutual inductance $M$ between the windings of the transformer is _____...

Arjun

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Arjun asked Feb 19, 2021

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1 answer

313

GATE Electrical 2015 Set 2 | Question: 38
A Boolean function $f(A, B, C, D) = \prod (1,5,12,15)$ is to be implemented using an $8 \times 1$ multiplexer ($A$ is $MSB$). The inputs $ABC$ are connected to the select inputs $S_{2} S_{1} S_{0}$ of the multiplexer respectively. Which one of the following ... $D, 1, D, 1, 1, 1, \overline{D}, D$ $\overline{D}, 0, \overline{D}, 0, 0, 0,D, \overline{D}$

A Boolean function $f(A, B, C, D) = \prod (1,5,12,15)$ is to be implemented using an $8 \times 1$ multiplexer ($A$ is $MSB$). The inputs $ABC$ are connected to the selec...

makhdoom ghaya

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makhdoom ghaya asked Feb 11, 2017

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314

GATE Electrical 2022 | Question: 12
A charger supplies $100\:W$ at $20\:V$ for charging the battery of a laptop. The power devices, used in the converter inside the charger, operate at a switching frequency of $200$ $\text{kHz}$. Which power device is best suited for this purpose? $\text{IGBT}$ Thyristor $\text{MOSFET}$ $\text{BJT}$

A charger supplies $100\:W$ at $20\:V$ for charging the battery of a laptop. The power devices, used in the converter inside the charger, operate at a switching frequency...

Arjun

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Arjun asked Feb 15, 2022

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315

GATE Electrical 2020 | Question: 16
Consider the initial value problem below. The value of y at $x=\ln{2}$, (rounded off to $3$ decimal places) is ______________. $\frac{\mathrm{d} y}{\mathrm{d} x}=2x-y,\:\:y\left ( 0 \right )=1$

Consider the initial value problem below. The value of y at $x=\ln{2}$, (rounded off to $3$ decimal places) is ______________.$$\frac{\mathrm{d} y}{\mathrm{d} x}=2x-y,\:\...

go_editor

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go_editor asked Feb 28, 2020

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316

GATE Electrical 2018 | Question: 54
The equivalent circuit of a single phase induction motor is shown in the figure, where the parameters are $R_1 =R_2=X_{l1}=X_{l2} = 12 \Omega$, $X_M=240 \: \Omega$ and $S$ is the slip. At no-load, the motor speed can be approximated to the synchronous speed. The no-load lagging power factor of the motor is __________ (up to $3$ decimal places).

The equivalent circuit of a single phase induction motor is shown in the figure, where the parameters are $R_1 =R_2=X_{l1}=X_{l2} = 12 \Omega$, $X_M=240 \: \Omega$ and $S...

Arjun

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Arjun asked Feb 19, 2018

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317

GATE Electrical 2014 Set 3 | Question: 29
The Norton’s equivalent source in amperes as seen into the terminals $X$ and $Y$ is _______.

The Norton’s equivalent source in amperes as seen into the terminals $X$ and $Y$ is _______.

makhdoom ghaya

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makhdoom ghaya asked Feb 11, 2017

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318

GATE Electrical 2020 | Question: 8
A lossless transmission line with $0.2$ $\text{pu}$ reactance per phase uniformly distributed along the length of the line, connecting a generator bus to a load bus, is protected up to $80 \%$ of its length by a distance relay placed at the generator bus. ... a solid three phase-to-ground fault on the transmission line is closest to: $1.00$ $3.61$ $5.00$ $6.25$

A lossless transmission line with $0.2$ $\text{pu}$ reactance per phase uniformly distributed along the length of the line, connecting a generator bus to a load bus, is p...

go_editor

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go_editor asked Feb 28, 2020

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319

GATE Electrical 2018 | Question: 17
Consider a non-singular $2 \times 2$ square matrix $\textbf{A}$. If $\text{trace}(\textbf{A})=4$ and $\text{trace}(\textbf{A}^2)=5$, the determinant of the matrix $\textbf{A}$ is _________ (up to $1$ decimal place).

Consider a non-singular $2 \times 2$ square matrix $\textbf{A}$. If $\text{trace}(\textbf{A})=4$ and $\text{trace}(\textbf{A}^2)=5$, the determinant of the matrix $\textb...

Arjun

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Arjun asked Feb 19, 2018

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320

GATE Electrical 2022 | Question: 29
The damping ratio and undamped natural frequency of a closed loop system as shown in the figure, are denoted as $\zeta$ and $\omega_{n}$, respectively. The values of $\zeta$ and $\omega_{n}$ are $\zeta = 0.5$ and $\omega _{n} =10$ rad/s $\zeta = 0.1$ ... $\zeta = 0.707$ and $\omega _{n} =10$ rad/s $\zeta = 0.707$ and $\omega _{n} =100$ rad/s

The damping ratio and undamped natural frequency of a closed loop system as shown in the figure, are denoted as $\zeta$ and $\omega_{n}$, respectively. The values of $\ze...

Arjun

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Arjun asked Feb 15, 2022