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161
GATE Electrical 2021 | Question: 21
A signal generator having a source resistance of $50\:\Omega$ is set to generate a $\text{1 kHz}$ sinewave. Open circuit terminal voltage is $\text{10 V}$ peak-to-peak. Connecting a capacitor across the terminals reduces the voltage to $\text{8 V}$ peak-to-peak. The value of this capacitor is _____________$\mu F$. (Round off to $2$ decimal places.)
A signal generator having a source resistance of $50\:\Omega$ is set to generate a $\text{1 kHz}$ sinewave. Open circuit terminal voltage is $\text{10 V}$ peak-to-peak. C...
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Feb 19, 2021
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162
GATE Electrical 2021 | Question: 22
A $16$-bit synchronous binary up-counter is clocked with a frequency $f_{\text{CLK}}$.The two most significant bits are $\text{OR-ed}$ together to form an output $Y$. Measurements show that $Y$ is periodic, and the duration for which $Y$ remains high ... $f_{\text{CLK}}$ is ____________$\text{MHz}.$ (Round off to $2$ decimal places.)
A $16$-bit synchronous binary up-counter is clocked with a frequency $f_{\text{CLK}}$.The two most significant bits are $\text{OR-ed}$ together to form an output $Y$. Mea...
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Feb 19, 2021
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163
GATE Electrical 2021 | Question: 23
In the $\text{BJT}$ circuit shown, beta of the $\text{PNP}$ transistor is $100$. Assume $V_{\text{BE}}=-0.7\;V$. The voltage across $R_{c}$ will be $\text{5 V}$ when $R_{2}$ is __________ $k \Omega$. (Round off to $2$ decimal places.)
In the $\text{BJT}$ circuit shown, beta of the $\text{PNP}$ transistor is $100$. Assume $V_{\text{BE}}=-0.7\;V$. The voltage across $R_{c}$ will be $\text{5 V}$ when $R_{...
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Feb 19, 2021
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164
GATE Electrical 2021 | Question: 24
In the circuit shown, the input $V_{i}$ is a sinusoidal $\text{AC}$ voltage having an $\text{RMS}$ value of $230\;V\pm 20\%$. The worst-case peak-inverse voltage seen across any diode is ____________$V$. (Round off to $2$ decimal places.)
In the circuit shown, the input $V_{i}$ is a sinusoidal $\text{AC}$ voltage having an $\text{RMS}$ value of $230\;V\pm 20\%$. The worst-case peak-inverse voltage seen ac...
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Feb 19, 2021
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GATE Electrical 2021 | Question: 25
In the circuit shown, a $\text{5 V}$ Zener diode is used to regulate the voltage across load $R_{0}$. The input is an unregulated $DC$ voltage with a minimum value of $\text{6 V}$ and a maximum value of $\text{8 V}$ ... dissipation of $\text{2.5 W}$. Assuming the Zener diode to be ideal, the minimum value of $R_{0}$ is _________________ $\Omega$.
In the circuit shown, a $\text{5 V}$ Zener diode is used to regulate the voltage across load $R_{0}$. The input is an unregulated $DC$ voltage with a minimum value of $\t...
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Feb 19, 2021
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166
GATE Electrical 2021 | Question: 26
In the open interval $\left ( 0,1 \right )$, the polynomial $p\left ( x \right) =x^{4}-4x^{3}+2$ has two real roots one real root three real roots no real roots
In the open interval $\left ( 0,1 \right )$, the polynomial $p\left ( x \right) =x^{4}-4x^{3}+2$ hastwo real rootsone real rootthree real rootsno real roots
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Feb 19, 2021
Calculus
gateee-2021
calculus
polynomials
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167
GATE Electrical 2021 | Question: 27
Suppose the probability that a coin toss shows "head" is $p$, where $0<p<1$. The coin is tossed repeatedly until the first "head" appears. The expected number of tosses required is $p/\left ( 1-p \right )$ $\left ( 1-p \right )/p$ $1/p$ $1/p^{2}$
Suppose the probability that a coin toss shows "head" is $p$, where $0<p<1$. The coin is tossed repeatedly until the first "head" appears. The expected number of tosses r...
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Feb 19, 2021
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probability-and-statistics
probability
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168
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...
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Feb 19, 2021
Calculus
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calculus
contour-plots
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169
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...
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Feb 19, 2021
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170
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$$\frac{25s^{2}+46s+20}{4s+5}$
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Feb 19, 2021
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GATE Electrical 2021 | Question: 31
The casual signal with $z$-transformer $Z^{2}\left ( Z-a \right )^{-2}$ is ($u[n]$ is the unit step signal) $a^{2n}u\left [ n \right ]$ $\left ( n+1 \right )a^{n}u\left [ n \right ]$ $n^{-1}a^{n}u\left [ n \right ]$ $n^{2}a^{n}u\left [ n \right ]$
The casual signal with $z$-transformer $Z^{2}\left ( Z-a \right )^{-2}$ is ($u[n]$ is the unit step signal)$a^{2n}u\left [ n \right ]$$\left ( n+1 \right )a^{n}u\left [ n...
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Feb 19, 2021
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172
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 ...
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Feb 19, 2021
Transform Theory
gateee-2021
transform-theory
fourier-transform
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173
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...
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Feb 19, 2021
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174
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 ...
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Feb 19, 2021
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175
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,...
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Feb 19, 2021
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176
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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Feb 19, 2021
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177
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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Feb 19, 2021
Analog and Digital Electronics
gateee-2021
analog-and-digital-electronics
sequential-circuit
flip-flops
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178
GATE Electrical 2021 | Question: 38
Let $A$ be a $10\times10$ matrix such that $A^{5}$ is a null matrix, and let $I$ be the $10\times10$ identity matrix. The determinant of $\text{A+I}$ is ___________________.
Let $A$ be a $10\times10$ matrix such that $A^{5}$ is a null matrix, and let $I$ be the $10\times10$ identity matrix. The determinant of $\text{A+I}$ is _________________...
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Feb 19, 2021
Linear Algebra
gateee-2021
numerical-answers
linear-algebra
matrices
determinant
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179
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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Feb 19, 2021
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180
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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Feb 19, 2021
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181
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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Feb 19, 2021
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182
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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Feb 19, 2021
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numerical-answers
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183
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...
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Feb 19, 2021
Transform Theory
gateee-2021
numerical-answers
transform-theory
fourier-transform
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184
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...
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Feb 19, 2021
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185
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...
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Feb 19, 2021
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186
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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Feb 19, 2021
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numerical-answers
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187
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...
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Feb 19, 2021
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numerical-answers
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188
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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Feb 19, 2021
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numerical-answers
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189
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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Feb 19, 2021
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190
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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Feb 19, 2021
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191
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...
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Feb 19, 2021
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numerical-answers
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192
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...
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Feb 19, 2021
new
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numerical-answers
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193
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...
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Feb 19, 2021
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numerical-answers
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194
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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Feb 19, 2021
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numerical-answers
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195
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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Feb 19, 2021
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196
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
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Feb 12, 2019
Verbal Aptitude
gate2019-ee
verbal-ability
most-appropriate-word
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votes
1
answer
197
GATE Electrical 2019 | GA Question: 2
The passengers were angry ______ the airline staff about the delay. on about with towards
The passengers were angry ______ the airline staff about the delay.onaboutwithtowards
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Feb 12, 2019
Verbal Aptitude
gate2019-ee
verbal-ability
prepositions
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1
answer
198
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$
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Feb 12, 2019
Analytical Aptitude
gate2019-ee
analytical-aptitude
logical-reasoning
sequence-series
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199
GATE Electrical 2019 | GA Question: 4
It takes two hours for a person $X$ to mow the lawn. $Y$ can mow the same lawn in four hours. How long (in minutes) will it take $X$ and $Y,$ if they work together to mow the lawn$?$ $60$ $80$ $90$ $120$
It takes two hours for a person $X$ to mow the lawn. $Y$ can mow the same lawn in four hours. How long (in minutes) will it take $X$ and $Y,$ if they work together to mow...
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Feb 12, 2019
Quantitative Aptitude
gate2019-ee
numerical-ability
work-time
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votes
1
answer
200
GATE Electrical 2019 | GA Question: 5
Newspapers are a constant source of delight and recreation for me. The ________ trouble is that I read _______ many of them. even, quite even, too only, quite only, too
Newspapers are a constant source of delight and recreation for me. The ________ trouble is that I read _______ many of them.even, quiteeven, tooonly, quiteonly, too
asked
Feb 12, 2019
Verbal Aptitude
gate2019-ee
verbal-ability
most-appropriate-word
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