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201
GATE Electrical 2021 | Question: 28
Let $\left ( -1 -j \right ), \left ( 3 -j \right ), \left ( 3 + j \right )$ and $\left ( -1+ j \right )$ be the vertices of a rectangle $C$ in the complex plane. Assuming that $C$ is traversed in counter-clockwise direction, the value of the contour integral $\oint _{C}\dfrac{dz}{z^{2}\left ( z-4 \right )}$ is $j\pi /2$ $0$ $-j\pi /8$ $j\pi /16$
Let $\left ( -1 -j \right ), \left ( 3 -j \right ), \left ( 3 + j \right )$ and $\left ( -1+ j \right )$ be the vertices of a rectangle $C$ in the complex plane. Assuming...
Arjun
15.9k
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Arjun
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Feb 19, 2021
Calculus
gateee-2021
calculus
contour-plots
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202
GATE Electrical 2021 | Question: 29
In the circuit, switch '$S$' is in the closed position for a very long time. If the switch is opened at time $t = 0$, then in $i_{L} (t)$ amperes, for $t\geq0$ is $8e^{-10t}$ $10$ $8+2e^{-10t}$ $10\left ( 1-e^{-2t} \right )$
In the circuit, switch '$S$' is in the closed position for a very long time. If the switch is opened at time $t = 0$, then in $i_{L} (t)$ amperes, for $t\geq0$ is$8e^{-10...
Arjun
15.9k
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Arjun
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Feb 19, 2021
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203
GATE Electrical 2021 | Question: 30
The input impedance, $Z_{in}\left ( s \right )$ for the network shown is $\frac{23s^{2}+46s+20}{4s+5}$ $6s+4$ $7s+4$ $\frac{25s^{2}+46s+20}{4s+5}$
The input impedance, $Z_{in}\left ( s \right )$ for the network shown is$\frac{23s^{2}+46s+20}{4s+5}$$6s+4$$7s+4$$\frac{25s^{2}+46s+20}{4s+5}$
Arjun
15.9k
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Arjun
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Feb 19, 2021
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GATE Electrical 2021 | Question: 31
The casual signal with $z$-transformer $Z^{2}\left ( Z-a \right )^{-2}$ is ($u[n]$ is the unit step signal) $a^{2n}u\left [ n \right ]$ $\left ( n+1 \right )a^{n}u\left [ n \right ]$ $n^{-1}a^{n}u\left [ n \right ]$ $n^{2}a^{n}u\left [ n \right ]$
The casual signal with $z$-transformer $Z^{2}\left ( Z-a \right )^{-2}$ is ($u[n]$ is the unit step signal)$a^{2n}u\left [ n \right ]$$\left ( n+1 \right )a^{n}u\left [ n...
Arjun
15.9k
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Arjun
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Feb 19, 2021
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205
GATE Electrical 2021 | Question: 32
Let $f(t)$ be an even function, i.e. $f(-t)=f(t)$ for all $t$. Let the Fourier transform of $f(t)$ be defined as $F\left ( \omega \right )=\int\limits_{-\infty }^{\infty }\:f\left ( t \right )e^{-j\omega t}dt$ ... $f\left ( 0 \right )< 1$ $f\left ( 0 \right )> 1$ $f\left ( 0 \right )= 1$ $f\left ( 0 \right )= 0$
Let $f(t)$ be an even function, i.e. $f(-t)=f(t)$ for all $t$. Let the Fourier transform of $f(t)$ be defined as $F\left ( \omega \right )=\int\limits_{-\infty }^{\infty ...
Arjun
15.9k
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Arjun
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Transform Theory
gateee-2021
transform-theory
fourier-transform
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206
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
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207
GATE Electrical 2021 | Question: 34
In the figure shown, self-impedances of the two transmission lines are $1.5j\:p.u$ each, and $Z_{m}=0.5j \:p.u$ is the mutual impedance. Bus voltages shown in the figure are in $p.u$. Given that $\delta>0$, the maximum steady-state real power that can be transferred ... $2\left | E \right |\left | V \right |$ $\frac{3\left | E \right |\left | V \right |}{2}$
In the figure shown, self-impedances of the two transmission lines are $1.5j\:p.u$ each, and $Z_{m}=0.5j \:p.u$ is the mutual impedance. Bus voltages shown in the figure ...
Arjun
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208
GATE Electrical 2021 | Question: 35
A $3$-Bus network is shown. Consider generators as ideal voltage sources. If rows $1,\:2$ and $3$ of the $Y_{Bus}$ matrix correspond to Bus $1,\:2$ and $3$, respectively, then $Y_{Bus}$ ...
A $3$-Bus network is shown. Consider generators as ideal voltage sources. If rows $1,\:2$ and $3$ of the $Y_{Bus}$ matrix correspond to Bus $1,\:2$ and $3$, respectively,...
Arjun
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209
GATE Electrical 2021 | Question: 36
Suppose $I_{A},\:I_{B}$ and $I_{C}$ are a set of unbalanced current phasors in a three-phase system. The phase-$B$ zero-sequence current $I_{B0}=0.1\angle 0^{\circ}$ $p.u$. If phase-$A$ current $I_{A}=1.1\angle 0^{\circ}$ $p.u$ and phase-$C$ ... $1.1\angle -120^{\circ}+0.1\angle 0^{\circ}$ $1\angle -120^{\circ}+0.1\angle 0^{\circ}$
Suppose $I_{A},\:I_{B}$ and $I_{C}$ are a set of unbalanced current phasors in a three-phase system. The phase-$B$ zero-sequence current $I_{B0}=0.1\angle 0^{\circ}$ $p.u...
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15.9k
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210
GATE Electrical 2021 | Question: 37
A counter is constructed with three $D$ flip-flops. The input-output pairs are named $(D_{0},\:Q_{0})$, $(D_{1},\:Q_{1})$ and $(D_{2},\:Q_{2})$, where the subscript $0$ denotes the least significant bit. The output sequence is desired to be the Gray- ... $\overline{Q_{2}}Q_{0}+Q_{1}\overline{Q_{0}}$ $Q_{2}Q_{1}+\overline{Q_{2}}\:\overline{Q_{1}}$
A counter is constructed with three $D$ flip-flops. The input-output pairs are named $(D_{0},\:Q_{0})$, $(D_{1},\:Q_{1})$ and $(D_{2},\:Q_{2})$, wher...
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Analog and Digital Electronics
gateee-2021
analog-and-digital-electronics
sequential-circuit
flip-flops
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211
GATE Electrical 2021 | Question: 39
A three-phase balanced voltage is applied to the load shown. The phase sequence is $\text{RYB}$. The ratio $\frac{\left | I_{B} \right |}{|I_{R}|}$ is ____________.
A three-phase balanced voltage is applied to the load shown. The phase sequence is $\text{RYB}$. The ratio $\frac{\left | I_{B} \right |}{|I_{R}|}$ is ____________.
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Arjun
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numerical-answers
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212
GATE Electrical 2021 | Question: 40
In the given circuit, for maximum power to be delivered to $R_{L}$, its value should be ______________ $\Omega$. (Round off to $2$ decimal places.)
In the given circuit, for maximum power to be delivered to $R_{L}$, its value should be ______________ $\Omega$.(Round off to $2$ decimal places.)
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213
GATE Electrical 2021 | Question: 41
One coulomb of point charge moving with a uniform velocity $10\:\hat{X}$ $\text{m/s}$ enters the region $x\geq 0$ having a magnetic flux density $\overrightarrow{B}=\left ( 10y\:\hat{X} + 10x\:\hat{Y}+10\:\hat{Z}\right )T$. The magnitude of force on the ... ($\hat{X}$, $\hat{Y}$, and $\hat{Z}$ are unit vectors along $x$-axis, $y$-axis and $z$-axis, respectively.)
One coulomb of point charge moving with a uniform velocity $10\:\hat{X}$ $\text{m/s}$ enters the region $x\geq 0$ having a magnetic flux density $\overrightarrow{B}=\left...
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numerical-answers
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214
GATE Electrical 2021 | Question: 42
Consider a large parallel plate capacitor. The gap $d$ between the two plates is filled entirely with a dielectric slab of relative permittivity $5$. The plates are initially charged to a potential difference of $V$ volts and then disconnected from the source ... of the new electric field $E_{2}$ in the gap to the original electric field $E_{1}$ is ________.
Consider a large parallel plate capacitor. The gap $d$ between the two plates is filled entirely with a dielectric slab of relative permittivity $5$. The plates are initi...
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Arjun
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Feb 19, 2021
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GATE Electrical 2021 | Question: 43
Consider a continuous-time signal $x(t)$ defined by $x(t)=0$ for $\left | t \right |> 1$, and $x\left ( t \right )=1-\left | t \right |$ for $\left | t \right |\leq 1$. Let the Fourier transform of $x(t)$ ... $X\left ( \omega \right )$ is ___________.
Consider a continuous-time signal $x(t)$ defined by $x(t)=0$ for $\left | t \right | 1$, and $x\left ( t \right )=1-\left | t \right |$ for $\left | t \right |\leq 1$. Le...
Arjun
15.9k
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Arjun
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Feb 19, 2021
Transform Theory
gateee-2021
numerical-answers
transform-theory
fourier-transform
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216
GATE Electrical 2021 | Question: 44
A belt-driven $\text{DC}$ shunt generator running at $300\: \text{RPM}$ delivers $100 \:\text{kW}$ to a $200 \:V\: \text{DC}$ grid. It continues to run as a motor when the belt breaks, taking $10 \:\text{kW}$ from the $\text{DC}$ grid ... drop is $2 \:V$. Ignoring armature reaction, the speed of the motor is _____ $\text{RPM}$. (Round off to $2$ decimal places.)
A belt-driven $\text{DC}$ shunt generator running at $300\: \text{RPM}$ delivers $100 \:\text{kW}$ to a $200 \:V\: \text{DC}$ grid. It continues to run as a motor when th...
Arjun
15.9k
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Arjun
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Feb 19, 2021
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numerical-answers
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217
GATE Electrical 2021 | Question: 45
An $8$-pole, $50 \:Hz$, three-phase, slip-ring induction motor has an effective rotor resistance of $0.08\:\Omega$ per phase. Its speed at maximum torque is $650 \text{ RPM}$. The additional resistance per ... Round off to $2$ decimal places.) Neglect magnetizing current and stator leakage impedance. Consider equivalent circuit parameters referred to stator.
An $8$-pole, $50 \:Hz$, three-phase, slip-ring induction motor has an effective rotor resistance of $0.08\:\Omega$ per phase. Its speed at maximum torque is $650 \text{ R...
Arjun
15.9k
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Arjun
asked
Feb 19, 2021
new
gateee-2021
numerical-answers
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218
GATE Electrical 2021 | Question: 46
Consider a closed-loop system as shown. $G_{P}\left ( s \right )=\dfrac{14.4}{s\left ( 1+0.1s \right )}$ is the plant transfer function and $G_{c}(S)=1$ is the compensator. For a unit-step input, the output response has damped oscillations. The damped natural frequency is ___________________ $\text{rad/s}$. (Round off to $2$ decimal places.)
Consider a closed-loop system as shown. $G_{P}\left ( s \right )=\dfrac{14.4}{s\left ( 1+0.1s \right )}$ is the plant transfer function and $G_{c}(S)=1$ is the compensato...
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Arjun
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numerical-answers
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219
GATE Electrical 2021 | Question: 47
In the given figure, plant $G_{P}\left ( s \right )=\dfrac{2.2}{\left ( 1+0.1s \right )\left ( 1+0.4s \right )\left ( 1+1.2s \right )}$ ... is a unit step, the steady-state error should not exceed $0.1$ unit. The minimum value of $K$ is _____________. (Round off to $2$ decimal places.)
In the given figure, plant $G_{P}\left ( s \right )=\dfrac{2.2}{\left ( 1+0.1s \right )\left ( 1+0.4s \right )\left ( 1+1.2s \right )}$ and compensator $G_{C}\left ( s \r...
Arjun
15.9k
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Arjun
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Feb 19, 2021
new
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numerical-answers
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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...
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Arjun
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GATE Electrical 2021 | Question: 49
The state space representation of a first-order system is given as $\overset{\bullet }{x}=-x+u$ $y=x$ where,$x$ is the state variable, $u$ is the control input and $y$ is the controlled output. Let $u=-Kx$ be the control law, where $K$ is the controller gain. To place a closed-loop pole at $-2$, the value of $K$ is ___________________.
The state space representation of a first-order system is given as $\overset{\bullet }{x}=-x+u$$y=x$where,$x$ is the state variable, $u$ is the control input and $y$ is t...
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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 _____...
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Arjun
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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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new
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numerical-answers
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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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numerical-answers
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225
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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Arjun
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Feb 19, 2021
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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...
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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$, ...
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Arjun
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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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Feb 28, 2020
Calculus
gate2020-ee
calculus
definite-integral
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229
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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Feb 28, 2020
Complex Variables
gate2020-ee
complex-variables
cauchys-integral-theorem
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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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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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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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1.9k
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Feb 28, 2020
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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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1.9k
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Feb 28, 2020
Signals and Systems
gate2020-ee
signals-and-systems
linear-time-invariant-system
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237
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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238
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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239
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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