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241
GATE Electrical 2021 | Question: 51
A $\text{100 Hz}$ square wave, switching between $\text{0 V}$ and $\text{5 V}$, is applied to a $\text{CR}$ high-pass filter circuit as shown. The output voltage waveform across the resistor is $\text{6.2 V}$ peak-to-peak. If the resistance $R$ is $\text{820 $\Omega$}$, then the value $C$ is ______________$\mu F$. (Round off to $2$ decimal places.)
A $\text{100 Hz}$ square wave, switching between $\text{0 V}$ and $\text{5 V}$, is applied to a $\text{CR}$ high-pass filter circuit as shown. The output voltage waveform...
Arjun
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Arjun
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Feb 19, 2021
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GATE Electrical 2021 | Question: 52
A $\text{CMOS}$ Schmitt-trigger inverter has a low output level of $\text{0 V}$ and a high output level of $\text{5 V}$. It has input thresholds of $\text{1.6 V}$ and $\text{2.4 V}$. The input capacitance and output resistance of the Schmitt-trigger are negligible. The frequency of the oscillator shown is ____________$\text{Hz}$.(Round off to $2$ decimal places.)
A $\text{CMOS}$ Schmitt-trigger inverter has a low output level of $\text{0 V}$ and a high output level of $\text{5 V}$. It has input thresholds of $\text{1.6 V}$ and $\t...
Arjun
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Arjun
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Feb 19, 2021
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GATE Electrical 2021 | Question: 53
Consider the boost converter shown. Switch $Q$ is operating at $\text{25 kHz}$ with a duty cycle of $0.6$. Assume the diode and switch to be ideal. Under steady-state condition, the average resistance $R_{\text{in}}$ as seen by the source is __________ $\Omega$. (Round off to $2$ decimal places).
Consider the boost converter shown. Switch $Q$ is operating at $\text{25 kHz}$ with a duty cycle of $0.6$. Assume the diode and switch to be ideal. Under steady-state con...
Arjun
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Feb 19, 2021
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244
GATE Electrical 2021 | Question: 54
Consider the buck-boost converter shown. Switch $Q$ is operating at $\text{25 kHz}$ and $0.75$ duty-cycle. Assume diode and switch to be ideal. Under steady-state condition, the average current flowing through the indicator is ____________$A$.
Consider the buck-boost converter shown. Switch $Q$ is operating at $\text{25 kHz}$ and $0.75$ duty-cycle. Assume diode and switch to be ideal. Under steady-state conditi...
Arjun
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Arjun
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GATE Electrical 2021 | Question: 55
A single-phase full-bridge inverter fed by a $\text{325 V DC}$ produces a symmetric quasi-square waveform across '$ab$' as shown. To achieve a modulation index of $0.8$, the angle $\theta$ expressed in degrees should be _______________. ( ... is defined as the ratio of the peak of the fundamental component of $V_{ab}$ to the applied $\text{DC}$ value.)
A single-phase full-bridge inverter fed by a $\text{325 V DC}$ produces a symmetric quasi-square waveform across '$ab$' as shown. To achieve a modulation index of $0.8$, ...
Arjun
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Arjun
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246
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?$\text{d}$...
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Calculus
gate2020-ee
calculus
polynomials
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247
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?...
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Calculus
gate2020-ee
calculus
definite-integral
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248
GATE Electrical 2020 | Question: 3
Which of the following statements is true about the two sided Laplace transform? It exists for every signal that may or may not have a Fourier transform. It has no poles for any bounded signal that is non-zero only inside a finite time ... a signal can be expressed as a weighted sum of shifted one sided exponentials, then its Laplace Transform will have no poles.
Which of the following statements is true about the two sided Laplace transform?It exists for every signal that may or may not have a Fourier transform.It has no poles fo...
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GATE Electrical 2020 | Question: 4
Consider a signal $x\left [ n \right ]=\left ( \dfrac{1}{2} \right )^{n}1\left [ n \right ],$ where $1\left [ n \right ]=0$ if $n< 0$, and $1\left [ n \right ]= 1$ if $n \geq 0.$ The z-transform of $x\left [ n-k \right ],\:k> 0$ is ... of convergence being $\mid z \mid< 2$ $\mid z \mid> 2$ $\mid z \mid < \dfrac{1}{2}$ $\mid z \mid > \dfrac{1}{2}$
Consider a signal $x\left [ n \right ]=\left ( \dfrac{1}{2} \right )^{n}1\left [ n \right ],$ where $1\left [ n \right ]=0$ if $n< 0$, and $1\left [ n \right ]= 1$ if $n ...
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GATE Electrical 2020 | Question: 5
The value of the following complex integral, with $\text{C}$ representing the unit circle centered at origin in the counterclockwise sense, is: $\int _{C}\frac{z^{2}+1}{z^{2}-2z}\:dz$ $8\pi i$ $-8\pi i$ $-\pi i$ $\pi i$
The value of the following complex integral, with $\text{C}$ representing the unit circle centered at origin in the counterclockwise sense, is:$$\int _{C}\frac{z^{2}+1}{z...
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1.9k
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Feb 28, 2020
Complex Variables
gate2020-ee
complex-variables
cauchys-integral-theorem
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251
GATE Electrical 2020 | Question: 6
$x_{R}$ and $x_{A}$ are, respectively, the rms and average values of $x\left ( t \right )=x\left ( t-T \right ),$ and similarly, $y_{R}$ and $y_{A}$ are, respectively, the rms and average values of $y\left ( t \right )=kx\left ( t \right ).\:k,T$ are independent of ... $y_{A}\neq kx_{A} ;\:y_{R}= kx_{R}$ $y_{A}\neq kx_{A} ;\:y_{R}\neq kx_{R}$
$x_{R}$ and $x_{A}$ are, respectively, the rms and average values of $x\left ( t \right )=x\left ( t-T \right ),$ and similarly, $y_{R}$ and $y_{A}$ are, respectively, th...
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252
GATE Electrical 2020 | Question: 7
A three-phase cylindrical rotor synchronous generator has a synchronous reactance $X_{s}$ and a negligible armature resistance. The magnitude of per phase terminal voltage is $V_{A}$ and the magnitude of per phase induced emf is $E_{A}$. Considering the following two statements, ... is true and $Q$ is false $P$ is false and $Q$ is false $P$ is true and $Q$ is true
A three-phase cylindrical rotor synchronous generator has a synchronous reactance $X_{s}$ and a negligible armature resistance. The magnitude of per phase terminal voltag...
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253
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...
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GATE Electrical 2020 | Question: 9
Out of the following options, the most relevant information needed to specify the real power $\text{(P)}$ at the $\text{PV}$ buses in a load flow analysis is solution of economic load dispatch rated power output of the generator rated voltage of the generator base power of the generator
Out of the following options, the most relevant information needed to specify the real power $\text{(P)}$ at the $\text{PV}$ buses in a load flow analysis issolution of e...
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GATE Electrical 2020 | Question: 10
Consider a linear time-invariant system whose input $\text{r(t)}$ and output $\text{y(t)}$ are related by the following differential equation: $\frac{d^{2}y\left ( t \right )}{dt^{2}}+4y\left ( t \right )=6r\left ( t \right )$ The poles of this system are at $+2j,-2j$ $+2,-2$ $+4,-4$ $+4j,-4j$
Consider a linear time-invariant system whose input $\text{r(t)}$ and output $\text{y(t)}$ are related by the following differential equation:$$\frac{d^{2}y\left ( t \rig...
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Feb 28, 2020
Signals and Systems
gate2020-ee
signals-and-systems
linear-time-invariant-system
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GATE Electrical 2020 | Question: 11
A single-phase, full-bridge diode rectifier fed from a $230$ $\text{V}$, $50$ $\text{Hz}$ sinusoidal source supplies a series combination of finite resistance, $\text{R}$, and a very large inductance, $\text{L}$. The two most dominant frequency components in the source current are: $50\:Hz,\:0\:Hz$ $50\:Hz,\:100\:Hz$ $50\:Hz,\:150\:Hz$ $150\:Hz,\:250\:Hz$
A single-phase, full-bridge diode rectifier fed from a $230$ $\text{V}$, $50$ $\text{Hz}$ sinusoidal source supplies a series combination of finite resistance, $\text{R}$...
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GATE Electrical 2020 | Question: 12
Thyristor $T_{1}$ is triggered at an angle $\alpha$ (in degree), and $T_{2}$ at angle $180^{\circ}+\alpha$, in each cycle of the sinusoidal input voltage. Assume both thyristors to be ideal. To control the load power over the range $0$ to $\text{2 k W}$, the minimum ... $0^{\circ}$ to $120^{\circ}$ $60^{\circ}$ to $120^{\circ}$ $60^{\circ}$ to $180^{\circ}$
Thyristor $T_{1}$ is triggered at an angle $\alpha$ (in degree), and $T_{2}$ at angle $180^{\circ}+\alpha$, in each cycle of the sinusoidal input voltage. Assume both thy...
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thyristor
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GATE Electrical 2020 | Question: 13
Which of the options is an equivalent representation of the signal flow graph shown here?
Which of the options is an equivalent representation of the signal flow graph shown here?
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GATE Electrical 2020 | Question: 14
A common-source amplifier with a drain resistance, $R_{D}=4.7\:k\Omega$, is powered using a $10\:V$ power supply. Assuming that the transconductance, $g_{m}$, is $520\:\mu A/V$, the voltage gain of the amplifier is closest to: $-2.44$ $-1.22$ $1.22$ $2.44$
A common-source amplifier with a drain resistance, $R_{D}=4.7\:k\Omega$, is powered using a $10\:V$ power supply. Assuming that the transconductance, $g_{m}$, is $520\:\m...
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GATE Electrical 2020 | Question: 15
A sequence detector is designed to detect precisely $3$ digital inputs, with overlapping sequences detectable. For the sequence $\text{(1,0,1)}$ and input data $(1,1,0,1,0,0,1,1,0,1,0,1,1,0)$, what is the output of this detector? $1,1,0,0,0,0,1,1,0,1,0,0$ $0,1,0,0,0,0,0,1,0,1,0,0$ $0,1,0,0,0,0,0,1,0,1,1,0$ $0,1,0,0,0,0,0,0,1,0,0,0$
A sequence detector is designed to detect precisely $3$ digital inputs, with overlapping sequences detectable. For the sequence $\text{(1,0,1)}$ and input data $(1,1,0,1,...
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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,\:\...
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1.9k
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Feb 28, 2020
Differential Equations
gate2020-ee
numerical-answers
differential-equations
initial-and-boundary-value-problems
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262
GATE Electrical 2020 | Question: 17
A three-phase, $\text{50 Hz}$, $4$-pole induction motor runs at no-load with a slip of $1\%$. With full load, the slip increases to $5 \%$. The $\%$ speed regulation of the motor (rounded off to $2$ decimal places) is _____________________.
A three-phase, $\text{50 Hz}$, $4$-pole induction motor runs at no-load with a slip of $1\%$. With full load, the slip increases to $5 \%$. The $\%$ speed regulation of t...
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GATE Electrical 2020 | Question: 18
Currents through ammeters $\text{A2}$ and $\text{A3}$ in the figure are $1\angle 10^{\circ}\:and\:1\angle 70^{\circ}$, respectively. The reading of the ammeter $\text{A1}$ (rounded off to $3$ decimal places) is_______$\text{A}$.
Currents through ammeters $\text{A2}$ and $\text{A3}$ in the figure are $1\angle 10^{\circ}\:and\:1\angle 70^{\circ}$, respectively. The reading of the ammeter $\text{A1}...
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GATE Electrical 2020 | Question: 19
The Thevenin equivalent voltage, $V_{TH}$, in $\text{V}$ (rounded off to $2$ decimal places) of the network shown below, is _______
The Thevenin equivalent voltage, $V_{TH}$, in $\text{V}$ (rounded off to $2$ decimal places) of the network shown below, is _______
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GATE Electrical 2020 | Question: 20
A double pulse measurement for an inductively loaded circuit controlled by the $\text{IGBT}$ switch is carried out to evaluate the reverse recovery characteristics of the diode, $\text{D}$, represented approximately as a piecewise linear plot of current vs time ... $4$) at which the $\text{IGBT}$ experiences the highest current stress is _________.
A double pulse measurement for an inductively loaded circuit controlled by the $\text{IGBT}$ switch is carried out to evaluate the reverse recovery characteristics of the...
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GATE Electrical 2020 | Question: 21
A single-phase, $\text{4 kVA}$, $200\: V/100 \: V$, $50 \: Hz$ transformer with laminated $\text{CRGO}$ steel core has rated no-load loss of $450 \: W$. When the high-voltage winding is excited with $160 \: V$, $40 \: Hz$ ... $\text{25 Hz}$ sinusoidal ac source, the no-load losses will be _____________________$\text{W}$ (rounded off to $2$ decimal places).
A single-phase, $\text{4 kVA}$, $200\: V/100 \: V$, $50 \: Hz$ transformer with laminated $\text{CRGO}$ steel core has rated no-load loss of $450 \: W$. When the high-vo...
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GATE Electrical 2020 | Question: 22
A single-phase inverter is fed from a $100 \: V$ dc source and is controlled using a quasi-square wave modulation scheme to produce an output waveform, $\nu\left ( t \right )$, as shown. The angle $\sigma$ is adjusted to ... $2$ decimal places).
A single-phase inverter is fed from a $100 \: V$ dc source and is controlled using a quasi-square wave modulation scheme to produce an output waveform, $\nu\left ( t \rig...
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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 $...
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GATE Electrical 2020 | Question: 24
Consider a negative unity feedback system with forward path transfer function $G\left ( s \right )=\dfrac{K}{\left ( s+a \right )\left ( s-b \right )\left ( s+c \right )}$, where $\text{K, a, b, c}$ are positive real numbers. For a Nyquist path ... $\text{s}$-plane is__________.
Consider a negative unity feedback system with forward path transfer function $G\left ( s \right )=\dfrac{K}{\left ( s+a \right )\left ( s-b \right )\left ( s+c \right )}...
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GATE Electrical 2020 | Question: 25
The cross-section of a metal-oxide-semiconductor structure is shown schematically. Starting from an uncharged condition, a bias of $\text{+3 V}$ is applied to the gate contact with respect to the body contact. The charge inside the silicon ... , expressed as a multiple of $\text{Q}$ (absolute value in Coulombs, rounded off to the nearest integer) is___________
The cross-section of a metal-oxide-semiconductor structure is shown schematically. Starting from an uncharged condition, a bias of $\text{+3 V}$ is applied to the gate co...
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GATE Electrical 2020 | Question: 26
For real numbers, $\text{x}$ and $\text{y}$, with $y=3x^{2}+3x+1$, the maximum and minimum value of $\text{y}$ for $\text{x}$ $\in \left [ -2,0 \right ]$ are respectively, ______. $7$ and $1/4$ $7$ and $1$ $-2$ and $-1/2$ $1$ and $1/4$
For real numbers, $\text{x}$ and $\text{y}$, with $y=3x^{2}+3x+1$, the maximum and minimum value of $\text{y}$ for $\text{x}$ $\in \left [ -2,0 \right ]$ are respectively...
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Feb 28, 2020
Calculus
gate2020-ee
calculus
maxima-minima
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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...
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Calculus
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calculus
field-vectors
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273
GATE Electrical 2020 | Question: 28
A $250 V$ dc shunt motor has an armature resistance of $0.2\:\Omega$ and a field resistance of $100\:\Omega$. When the motor is operated on no-load at rated voltage, it draws an armature current of $5 \: A$ and runs at $1200 \: rpm$. ... conditions. The speed of the motor, in $\text{rpm}$ under this loaded condition, is closest to: $1200$ $1000$ $1220$ $900$
A $250 V$ dc shunt motor has an armature resistance of $0.2\:\Omega$ and a field resistance of $100\:\Omega$. When the motor is operated on no-load at rated voltage, it d...
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GATE Electrical 2020 | Question: 29
Two buses, $\text{i and j}$, are connected with a transmission line admittance $y.$ ...
Two buses, $\text{i and j}$, are connected with a transmission line admittance $y.$, at the two ends of which there are ideal transformers with turns ratios as shown. Bus...
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GATE Electrical 2020 | Question: 30
Consider the diode circuit shown below. The diode, D, obeys the current-voltage characteristic $I_{D}=I_{S}\left ( exp\left ( \dfrac{V_{D}}{nV_{T}} \right )-1 \right )$, where $n> 1, V_{T}> 0, V_{D}$ is the voltage across the diode and $I_{D}$ is the ... $R_{1}$ and small $R_{2}$. Large $R_{1}$ and small $R_{2}$. Small $R_{1}$ and large $R_{2}$.
Consider the diode circuit shown below. The diode, D, obeys the current-voltage characteristic $I_{D}=I_{S}\left ( exp\left ( \dfrac{V_{D}}{nV_{T}} \right )-1 \right )$, ...
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GATE Electrical 2020 | Question: 31
A non-ideal diode is biased with a voltage of $-0.03 \: V$, and a diode current of $I_{1}$ is measured. The thermal voltage is $26 \: mV$ and the ideality factor for the diode is $15/13$. The voltage, in $V$, at which the measured current increases to $1.5 \: I_{1}$ is closest to: $-0.02$ $-0.09$ $-1.50$ $-4.50$
A non-ideal diode is biased with a voltage of $-0.03 \: V$, and a diode current of $I_{1}$ is measured. The thermal voltage is $26 \: mV$ and the ideality factor for the ...
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GATE Electrical 2020 | Question: 32
A benchtop dc power supply acts as an ideal $4 \: A$ current source as long as its terminal voltage is below $10 \: V$. Beyond this point, it begins to behave as an ideal $10 \: V$ voltage source for all load currents going down to $0 \: A$. When connected to an ideal rheostat, find ... $2.5 \Omega, 4 \: A, 10 \: V$ $2.5 \Omega, 4 \: A , 5 \: V$
A benchtop dc power supply acts as an ideal $4 \: A$ current source as long as its terminal voltage is below $10 \: V$. Beyond this point, it begins to behave as an ideal...
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278
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...
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279
GATE Electrical 2020 | Question: 34
Consider a permanent magnet dc $\text{(PMDC)}$ motor which is initially at rest. At $t=0$, a dc voltage of $5 V$ is applied to the motor. Its speed monotonically increase from $0 \text{ rad/s}$ to $6.32 \text{ rad/s}$ in $0.5 \: s$ ... $\dfrac{10}{0.5s+1} \\$ $\dfrac{2}{0.5s+1} \\$ $\dfrac{2}{s+0.5} \\$ $\dfrac{10}{s+0.5}$
Consider a permanent magnet dc $\text{(PMDC)}$ motor which is initially at rest. At $t=0$, a dc voltage of $5 V$ is applied to the motor. Its speed monotonically increase...
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280
GATE Electrical 2020 | Question: 35
Which of the following options is correct for the system shown below? $4^{th}$ order and stable $3^{rd}$ order and stable $4^{th}$ order and unstable $3^{rd}$ order and unstable
Which of the following options is correct for the system shown below?$4^{th}$ order and stable$3^{rd}$ order and stable$4^{th}$ order and unstable$3^{rd}$ order and unsta...
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