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241
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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Complex Variables
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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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Calculus
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maxima-minima
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GATE Electrical 2021 | Question: 4
For the network shown, the equivalent Thevenin voltage and Thevenin impedance as seen across terminals ‘$\text{ab}$’ is $\text{10 V}$ in series with $12\:\Omega$ $\text{65 V}$ in series with $15\:\Omega$ $\text{50 V}$ in series with $2\:\Omega$ $\text{35 V}$ in series with $2\:\Omega$
For the network shown, the equivalent Thevenin voltage and Thevenin impedance as seen across terminals ‘$\text{ab}$’ is$\text{10 V}$ in series with $12\:\Omega$$\text...
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GATE Electrical 2021 | Question: 5
Which one of the following vector functions represents a magnetic field $\overrightarrow{B}$? $\text{($\hat{X}, \hat{Y}$ and $\hat{Z}$ are unit vectors along x-axis, y-axis, and z-axis, respectively)}$ $10x\hat{X}+20y\hat{Y}-30z\hat{Z}$ $10y\hat{X}+20x\hat{Y}-10z\hat{Z}$ $10z\hat{X}+20y\hat{Y}-30x\hat{Z}$ $10x\hat{X}-30z\hat{Y}+20y\hat{Z}$
Which one of the following vector functions represents a magnetic field $\overrightarrow{B}$?$\text{($\hat{X}, \hat{Y}$ and $\hat{Z}$ are unit vectors along x-axis, y-axi...
Arjun
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Calculus
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GATE Electrical 2021 | Question: 6
If the input $x(t)$ and output $y(t)$ of a system are related as $y\left ( t \right )=\text{max}\left ( 0,x\left ( t \right ) \right ),$ then the system is linear and time-variant linear and time-invariant non-linear and time-variant non-linear and time-invariant
If the input $x(t)$ and output $y(t)$ of a system are related as $y\left ( t \right )=\text{max}\left ( 0,x\left ( t \right ) \right ),$ then the system islinear and time...
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GATE Electrical 2021 | Question: 7
Two discrete-time linear time-invariant systems with impulse responses $h_{1}\left [ n \right ]=\delta \left [ n-1 \right ]+\delta \left [ n+1 \right ]$ and $h_{2}\left [ n \right ]=\delta \left [ n\right ]+\delta \left [ n-1 \right ]$ are connected in ... $\delta \left [ n\right ]\delta \left [ n-1\right ]+\delta \left [ n-2\right ]\delta \left [ n+1 \right ]$
Two discrete-time linear time-invariant systems with impulse responses $h_{1}\left [ n \right ]=\delta \left [ n-1 \right ]+\delta \left [ n+1 \right ]$ and $h_{2}\left [...
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GATE Electrical 2021 | Question: 8
Consider the table given: ... $\text{P-T-Y, Q-V-Z, R-S-X}$ $\text{P-U-X, Q-V-Y, R-T-Z}$
Consider the table given:$\begin{array}{|cl|cI|cI|}\hline&\textbf{Constructional feature} & \textbf{Machine type} & \textbf{Mitigation} \\ \hline &\text{P. Damper bars} ...
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GATE Electrical 2021 | Question: 9
Consider a power system consisting of $N$ number of buses. Buses in this power system are categorized into slack bus, $PV$ buses and $PQ$ buses for load flow study. The number of $PQ$ buses is $N_{L}$. The balanced Newton-Raphson method is used to carry out load flow study ... $\left ( N-1 \right )\times \left ( N-1+N_{L} \right )$
Consider a power system consisting of $N$ number of buses. Buses in this power system are categorized into slack bus, $PV$ buses and $PQ$ buses for load flow study. The n...
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Arjun
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GATE Electrical 2021 | Question: 10
Two generators have cost functions $F_{1}$ and $F_{2}$ . Their incremental-cost characteristics are $\dfrac{dF_{1}}{dP_{1}}=40+0.2P_{1}$ $\dfrac{dF_{2}}{dP_{2}}=32+0.4P_{2}$ They need to deliver a combined load of $260$ $\text{MW}$. Ignoring the network losses, for ... $P_{1}=P_{2}=130$ $P_{1}=160, P_{2}=100$ $P_{1}=140, P_{2}=120$ $P_{1}=120, P_{2}=140$
Two generators have cost functions $F_{1}$ and $F_{2}$ . Their incremental-cost characteristics are$\dfrac{dF_{1}}{dP_{1}}=40+0.2P_{1}$$\dfrac{dF_{2}}{dP_{2}}=32+0.4P_{2}...
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GATE Electrical 2021 | Question: 11
For the closed-loop system shown, the transfer function $\dfrac{E\left ( s \right )}{R\left ( s \right )}$ is $\frac{G}{1+GH}$ $\frac{GH}{1+GH}$ $\frac{1}{1+GH}$ $\frac{1}{1+G}$
For the closed-loop system shown, the transfer function $\dfrac{E\left ( s \right )}{R\left ( s \right )}$ is$\frac{G}{1+GH}$$\frac{GH}{1+GH}$$\frac{1}{1+GH}$$\frac{1}{1+...
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GATE Electrical 2021 | Question: 12
Inductance is measured by Schering bridge Maxwell bridge Kelvin bridge Wien bridge
Inductance is measured bySchering bridgeMaxwell bridgeKelvin bridgeWien bridge
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GATE Electrical 2021 | Question: 13
Suppose the circles $x^{2}+y^{2}=1$ and $\left ( x-1\right )^{2}+\left ( y-1 \right )^{2}=r^{2}$ intersect each other orthogonally at the point $\left ( u,v \right )$. Then $u+v=$ _______________.
Suppose the circles $x^{2}+y^{2}=1$ and $\left ( x-1\right )^{2}+\left ( y-1 \right )^{2}=r^{2}$ intersect each other orthogonally at the point $\left ( u,v \right )$. Th...
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Calculus
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GATE Electrical 2021 | Question: 14
In the given circuit, the value of capacitor $C$ that makes current $I=0$ is ________________ $\mu F$.
In the given circuit, the value of capacitor $C$ that makes current $I=0$ is ________________ $\mu F$.
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GATE Electrical 2021 | Question: 15
Two single-core power cables have total conductor resistances of $0.7\;\Omega$ and $0.5\;\Omega$, respectively, and their insulation resistances (between core and sheath) are $600\;M\Omega$ and $900\;M\Omega$, respectively. When the two cables are joined in series, the ratio of insulation resistance to conductor resistance is ___________$\times 10^{6}$.
Two single-core power cables have total conductor resistances of $0.7\;\Omega$ and $0.5\;\Omega$, respectively, and their insulation resistances (between core and sheath)...
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GATE Electrical 2021 | Question: 16
In the given circuit, for voltage $V_y$ to be zero, the value of $\beta$ should be _________. (Round off to $2$ decimal places).
In the given circuit, for voltage $V_y$ to be zero, the value of $\beta$ should be _________. (Round off to $2$ decimal places).
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GATE Electrical 2021 | Question: 17
A $1\;\mu C$ point charge is held at the origin of a cartesian coordinate system. If a second point charge of $10\;\mu C$ is moved from $\left ( 0,10,0 \right )$ to $\left ( 5,5,5\right )$ and subsequently to $\left ( 5,0,0\right )$, ... decimal places). Take $\dfrac{1}{4\pi \varepsilon _{0}}=9\times 10^{9}$ in $\text{SI}$ units. All coordinates are in meters.
A $1\;\mu C$ point charge is held at the origin of a cartesian coordinate system. If a second point charge of $10\;\mu C$ is moved from $\left ( 0,10,0 \right )$ to $\lef...
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GATE Electrical 2021 | Question: 18
The power input to a $\text{500 V, 50 Hz, 6-pole, 3-phase}$ induction motor running at $975 \text{RPM}$ is $40 \text{ kW}$ . The total stator losses are $1 \text{ kW}$. If the total friction and windage losses are $2.025\text{ kW}$, then the efficiency is _____________$\%$.
The power input to a $\text{500 V, 50 Hz, 6-pole, 3-phase}$ induction motor running at $975 \text{RPM}$ is $40 \text{ kW}$ . The total stator losses are $1 \text{ kW}$. I...
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GATE Electrical 2021 | Question: 19
An alternator with internal voltage of $1\angle \delta _{1}\text{p.u}$ and synchronous reactance of $\text{0.4 p.u}$ is connected by a transmission line of reactance $\text{0.1 p.u}$ ... $2$ decimal places.) (Machines are of non-salient type. Neglect resistances.)
An alternator with internal voltage of $1\angle \delta _{1}\text{p.u}$ and synchronous reactance of $\text{0.4 p.u}$ is connected by a transmission line of reactance $\te...
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GATE Electrical 2021 | Question: 20
The Bode magnitude plot for the transfer function $\frac{V_{o}\left ( s \right )}{V_{i}\left ( s \right )}$ of the circuit is as shown. The value of $R$ is _____________$\Omega$. (Round off to $2$ decimal places.)
The Bode magnitude plot for the transfer function $\frac{V_{o}\left ( s \right )}{V_{i}\left ( s \right )}$ of the circuit is as shown. The value of $R$ is _____________$...
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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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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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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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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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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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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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Calculus
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calculus
polynomials
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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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probability-and-statistics
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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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Calculus
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calculus
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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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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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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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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
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Transform Theory
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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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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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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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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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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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Linear Algebra
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linear-algebra
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determinant
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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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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.)
Arjun
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Arjun
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279
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...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2021
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gateee-2021
numerical-answers
+
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0
votes
0
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280
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...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2021
new
gateee-2021
numerical-answers
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