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81
GATE Electrical 2023 | Question: 27
Consider the $\mathrm{OP} \mathrm{AMP} $ based circuit shown in the figure. Ignore the conduction drops of diodes $\text{D}_{1}$ and $\text{D}_{2}$. All the components are ideal and the breakdown voltage of the Zener is $5 \mathrm{~V}.$ Which of the ... minimum values of the output voltage $\text{V}_{O} $ are $+5 \mathrm{~V}$ and $-10 \mathrm{~V}$, respectively.
Consider the $\mathrm{OP} \mathrm{AMP} $ based circuit shown in the figure. Ignore the conduction drops of diodes $\text{D}_{1}$ and $\text{D}_{2}$. All the components a...
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82
GATE Electrical 2023 | Question: 38
A three phase $415 \mathrm{~V}, 50 \mathrm{~Hz}, \text { 6-pole, } 960 \text { RPM, 4 HP}$ squirrel cage induction motor drives a constant torque load at rated speed operating from rated supply and delivering rated output. If the ... in $\text { RPM}$ (neglecting the stator leakage impedance and rotational losses) is ________ (Round off to the nearest integer).
A three phase $415 \mathrm{~V}, 50 \mathrm{~Hz}, \text { 6-pole, } 960 \text { RPM, 4 HP}$ squirrel cage induction motor drives a constant torque load at rated speed oper...
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83
GATE Electrical 2023 | Question: 3
In the Nyquist plot of the open-loop transfer function $G(s)H(s) = \frac{3s+5}{s-1}$ corresponding to the feedback loop shown in the figure, the infinite semi-circular arc of the Nyquist contour in s-plane is mapped into a point at $G(s)H(s) = \infty$ $G(s)H(s) = 0$ $G(s)H(s) = 3$ $G(s)H(s) = -5$
In the Nyquist plot of the open-loop transfer function$$G(s)H(s) = \frac{3s+5}{s-1}$$corresponding to the feedback loop shown in the figure, the infinite semi-circular ar...
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84
GATE Electrical 2023 | Question: 12
The four stator conductors $\left(\mathrm{A}, \mathrm{A}^{\prime}, \mathrm{B}\right.$ and $\left.\mathrm{B}^{\prime}\right)$ of a rotating machine are carrying $\mathrm{DC}$ currents of the same value, the directions of which are shown in the figure (i). The rotor coils ... with $E_{a-a^{\prime}}$ leading $E_{b-b^{\prime}}$ $E_{a-a^{\prime}}=E_{b-b^{\prime}}=0$
The four stator conductors $\left(\mathrm{A}, \mathrm{A}^{\prime}, \mathrm{B}\right.$ and $\left.\mathrm{B}^{\prime}\right)$ of a rotating machine are carrying $\mathrm{D...
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85
GATE Electrical 2023 | Question: 8
The Fourier transform $X(\omega)$ of the signal $x(t)$ is given by $\begin{aligned} X(\omega) & =1, \text { for }|\omega|<W_o \\ & =0, \text { for }|\omega|>W_0 \end{aligned}$ Which one of the following statements is true? $x(t)$ tends to be an impulse as ... At $t=\frac{\pi}{2 W_0}, x(t)=-\frac{1}{\pi}$ At $t=\frac{\pi}{2 W_0}, x(t)=\frac{1}{\pi}$
The Fourier transform $X(\omega)$ of the signal $x(t)$ is given by$$\begin{aligned}X(\omega) & =1, \text { for }|\omega|<W_o \\& =0, \text { for }|\omega|>W_0\end{aligned...
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86
GATE Electrical 2023 | Question: 23
A $50 \mathrm{~Hz}, 275 ~\mathrm{kV}$ line of length $400 \mathrm{~km}$ has the following parameters: Resistance, $R=0.035 ~\Omega / \mathrm{km} ;$ Inductance, $L=1 ~\mathrm{mH} / \mathrm{km} ;$ ... $2$ decimal places).
A $50 \mathrm{~Hz}, 275 ~\mathrm{kV}$ line of length $400 \mathrm{~km}$ has the following parameters: Resistance, $R=0.035 ~\Omega / \mathrm{km} ;$ Inductance, $L=1 ~\mat...
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87
GATE Electrical 2023 | Question: 20
A separately excited $\text{DC}$ motor rated $400 \mathrm{~V}, 15 \mathrm{~A}, 1500\mathrm{~ RPM}$ drives a constant torqueload at rated speed operating from $400 \mathrm{~V}$ $\text{DC}$ supply drawing rated current. The armature ... field current unaltered then the resultant speed of the motor in $\mathrm{~ RPM}$ is_________ (Round off to the nearest integer).
A separately excited $\text{DC}$ motor rated $400 \mathrm{~V}, 15 \mathrm{~A}, 1500\mathrm{~ RPM}$ drives a constant torqueload at rated speed operating from $400 \mathrm...
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88
GATE Electrical 2023 | Question: 7
A continuous-time system that is initially at rest is described by $ \frac{d y(t)}{d t}+3 y(t)=2 x(t),$ where$x(t)$ is the input voltage and $y(t)$ is the output voltage. The impulse response of the system is $3 e^{-2 t}$ $\frac{1}{3} e^{-2 t} u(t)$ $2 e^{-3 t} u(t)$ $2 e^{-3 t}$
A continuous-time system that is initially at rest is described by $$ \frac{d y(t)}{d t}+3 y(t)=2 x(t),$$ where$x(t)$ is the input voltage and $y(t)$ is the output voltag...
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GATE Electrical 2023 | Question: 46
Neglecting the delays due to the logic gates in the circuit shown in figure, the decimal equivalent of the binary sequence $\text{[ABCD]}$ of initial logic states, which will not change with clock, is_______.
Neglecting the delays due to the logic gates in the circuit shown in figure, the decimal equivalent of the binary sequence $\text{[ABCD]}$ of initial logic states, which ...
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GATE Electrical 2023 | Question: 4
Consider a unity-gain negative feedback system consisting of the plant $G(s)$ (given below) and a proportional-integral controller. Let the proportional gain and integral gain be $3$ and $1,$ respectively. For a unit step reference input, the final values of the controller output and ... respectively, are $G(s)=\frac{1}{s-1}$ $\infty, \infty$ $1,0$ $1,-1$ $-1,1$
Consider a unity-gain negative feedback system consisting of the plant $G(s)$ (given below) and a proportional-integral controller. Let the proportional gain and integral...
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91
GATE Electrical 2023 | Question: 17
Which of the following statement(s) is/are true? If an $\text{LTI}$ system is causal, it is stable A discrete time $\text{LTI}$ system is causal if and only if its response to a step input $u[n]$ is $0$ for $n<0$ ... the system is stable If the impulse response $0<|h[n]|<1$ for all $n$, then the $\text{LTI}$ system is stable.
Which of the following statement(s) is/are true? If an $\text{LTI}$ system is causal, it is stableA discrete time $\text{LTI}$ system is causal if and only if its respons...
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GATE Electrical 2023 | Question: 11
The expressions of fuel cost of two thermal generating units as a function of the respective power generation $P_{G 1}$ and $P_{G 2}$ ... Both $P_{G 1}$ and $F$ will increase $P_{G 1}$ will increase and $F$ will decrease Both $P_{G 1}$ and $F$ will decrease
The expressions of fuel cost of two thermal generating units as a function of the respective power generation $P_{G 1}$ and $P_{G 2}$ are given as $F_{1}\left(P_{G 1}\rig...
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93
GATE Electrical 2023 | Question: 50
The two-bus power system shown in figure (i) has one alternator supplying a synchronous motor load through a $Y- \Delta$ transformer. The positive, negative and zero-sequence diagrams of the system are shown in figures (ii), (iii) and (iv), respectively. All ... phase ' $b$ ' to ' $c$ ') in p.u. is__________ (Round off to $2$ decimal places).
The two-bus power system shown in figure (i) has one alternator supplying a synchronous motor load through a $Y- \Delta$ transformer. The positive, negative and zero-sequ...
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94
GATE Electrical 2023 | Question: 15
One million random numbers are generated from a statistically stationary process with a Gaussian distribution with mean zero and standard deviation $\sigma_o$. The $\sigma_o$ is estimated by randomly drawing out $10,000$ numbers of samples $\left(x_n\right)$. The ... $E\left(\hat{\sigma}_1\right)=E\left(\hat{\sigma}_2\right)$
One million random numbers are generated from a statistically stationary process with a Gaussian distribution with mean zero and standard deviation $\sigma_o$.The $\sigma...
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GATE Electrical 2023 | Question: 18
The bus admittance $\left(Y_{\text {bus }}\right)$ matrix of a $3$-bus power system is given below. Considering that there is no shunt inductor connected to any of the buses, which of the following can $\text{NOT}$ be true? Line charging ... capacitor of finite value is present in line$ 2-3$ only and shunt capacitor of finite value is present in bus $3$ only
The bus admittance $\left(Y_{\text {bus }}\right)$ matrix of a $3$-bus power system is given below.Considering that there is no shunt inductor connected to any of the bus...
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96
GATE Electrical 2023 | Question: 25
Three points in the $x-y$ plane are $(-1,0.8),(0,2.2)$ and $(1,2.8).$ The value of the slope of the best fit straight line in the least square sense is___________(Round off to $2$ decimal places)
Three points in the $x-y$ plane are $(-1,0.8),(0,2.2)$ and $(1,2.8).$ The value of the slope of the best fit straight line in the least square sense is___________(Round o...
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97
GATE Electrical 2023 | Question: 31
The three-bus power system shown in the figure has one alternator connected to bus $2$ which supplies $200 \mathrm{MW}$ and $40 \text{MVAr}$ power. Bus $3$ is infinite bus having a voltage of magnitude $\left|V_3\right|=1.0$ p.u. and angle of $-15^{\circ}$. A ... $3 \quad$ Slack bus Bus $1 \quad P-|V|$ bus Bus $2 \quad P-Q$ bus Bus $3 \quad$ Slack bus
The three-bus power system shown in the figure has one alternator connected to bus $2$ which supplies $200 \mathrm{MW}$ and $40 \text{MVAr}$ power. Bus $3$ is infinite bu...
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GATE Electrical 2023 | Question: 16
A semiconductor switch needs to block voltage $\text{V}$ of only one polarity $\text{(V>0)}$ during OFF state as shown in figure (i) and carry current in both directions during $\text{ON}$ state as shown in figure (ii). Which of the following switch combination(s) will realize the same?
A semiconductor switch needs to block voltage $\text{V}$ of only one polarity $\text{(V>0)}$ duringOFF state as shown in figure (i) and carry current in both directions d...
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GATE Electrical 2023 | Question: 29
A $3$-phase, star-connected, balanced load is supplied from a $3$-phase, $400 \mathrm{~V (rms),}$ balanced voltage source with phase sequence $\text{R-Y-B},$ as shown in the figure. If the wattmeter reading is $-400 \mathrm{~W}$ and the line ... $0.5$ leading $0.866$ leading $0.707$ lagging
A $3$-phase, star-connected, balanced load is supplied from a $3$-phase, $400 \mathrm{~V (rms),}$ balanced voltage source with phase sequence $\text{R-Y-B},$ as shown in ...
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GATE Electrical 2023 | Question: 44
The circuit shown in the figure is initially in the steady state with the switch $K$ in open condition and $\bar{K}$ in closed condition. The switch $ K$ is closed and $\bar{K}$ is opened simultaneously at the instant $t=t_{1},$ where ... there is no transient in the voltage across the $ 100 \mu \mathrm{F}$ capacitor, is_________(Round off to $2$ decimal places).
The circuit shown in the figure is initially in the steady state with the switch $K$ in open condition and $\bar{K}$ in closed condition. The switch $ K$ is closed and $...
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GATE Electrical 2023 | Question: 24
In the following differential equation, the numerically obtained value of $y(t),$ at $t=1,$ is ___________ (Round off to $2$ decimal places). $\frac{d y}{d t}=\frac{e^{-\alpha t}}{2+\alpha t}, \quad \alpha=0.01$ and $y(0)=0$
In the following differential equation, the numerically obtained value of $y(t),$ at $t=1,$ is ___________ (Round off to $2$ decimal places). $\frac{d y}{d t}=\frac{e^{-...
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GATE Electrical 2023 | Question: 36
Consider the state-space description of an $\text{LTI}$ ... for which the steady-state output of the system will be zero, is ________(Round off to the nearest integer).
Consider the state-space description of an $\text{LTI}$ system with matrices$\qquad A=\left[\begin{array}{cc}0 & 1 \\-1 & -2\end{array}\right], B=\left[\begin{array}{l}0 ...
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GATE Electrical 2023 | Question: 30
An $8$-bit $\text{ADC}$ converts analog voltage in the range of $0$ to $+5 \mathrm{~V}$ to the corresponding digital code as per the conversion characteristics shown in figure. For $V_{\text {in }}=1.9922 \mathrm{~V}$, which of the following digital output, given in hex, is true? $64 \mathrm{H}$ $65 \mathrm{H}$ $66 \mathrm{H}$ $67 \mathrm{H}$
An $8$-bit $\text{ADC}$ converts analog voltage in the range of $0$ to $+5 \mathrm{~V}$ to the corresponding digital code as per the conversion characteristics shown in f...
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GATE Electrical 2023 | Question: 51
An infinite surface of linear current density $\mathbf{K}=5 \hat{\mathbf{a}}_{\mathbf{x}} \mathbf{A} / \mathbf{m}$ exists on the $\text{x-y}$ plane, as shown in the figure. The magnitude of the magnetic field intensity $(\mathbf{H})$ at a point $(1,1,1)$ due to the surface current in Ampere/meter is _________ (Round off to $2$ decimal places).
An infinite surface of linear current density $\mathbf{K}=5 \hat{\mathbf{a}}_{\mathbf{x}} \mathbf{A} / \mathbf{m}$ exists on the $\text{x-y}$ plane, as shown in the fig...
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GATE Electrical 2023 | Question: 42
The admittance parameters of the passive resistive two-port network shown in the figure are $y_{11}=5 S, y_{22}=1 S, y_{12}=y_{21}=-2.5 S$ The power delivered to the load resistor $ R_{L}$ in Watt is _______(Round off to $2$ decimal places).
The admittance parameters of the passive resistive two-port network shown in the figure are$$y_{11}=5 S, y_{22}=1 S, y_{12}=y_{21}=-2.5 S$$The power delivered to the load...
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GATE Electrical 2023 | Question: 37
A three-phase synchronous motor with synchronous impedance of $0.1+\mathrm{j} 0.3 \text { per unit } $ per phase has a static stability limit of $2.5 \text { per unit.}$ The corresponding excitation voltage in per unit is _________ (Round off to $2$ decimal places).
A three-phase synchronous motor with synchronous impedance of $0.1+\mathrm{j} 0.3 \text { per unit } $ per phase has a static stability limit of $2.5 \text { per unit.}$ ...
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GATE Electrical 2023 | Question: 45
The circuit shown in the figure has reached steady state with thyristor ' $\text{T}$ ' in $\mathrm{OFF}$ condition. Assume that the latching and holding currents of the thyristor are zero. The thyristor is turned $\mathrm{ON}$ ... in microseconds for which the thyristor would conduct, before it turns off, is ________(Round off to $2$ decimal places).
The circuit shown in the figure has reached steady state with thyristor ' $\text{T}$ ' in $\mathrm{OFF}$ condition. Assume that the latching and holding currents of the t...
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108
GATE Electrical 2023 | Question: 53
A signal $ x(t)=2 \cos (180 \pi t) \cos (60 \pi t)$ is sampled at $ 200 \mathrm{~Hz} $ and then passed through an ideal low pass filter having cut-off frequency of $100 \mathrm{~Hz}.$ The maximum frequency present in the filtered signal in $ \mathrm{Hz}$ is ________ (Round off to the nearest integer).
A signal $ x(t)=2 \cos (180 \pi t) \cos (60 \pi t)$ is sampled at $ 200 \mathrm{~Hz} $ and then passed through an ideal low pass filter having cut-off frequency of $100 \...
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GATE Electrical 2023 | Question: 55
A quadratic function of two variables is given as $ f\left(x_{1}, x_{2}\right)=x_{1}^{2}+2 x_{2}^{2}+3 x_{1}+3 x_{2}+x_{1} x_{2}+1$ The magnitude of the maximum rate of change of the function at the point $(1,1)$ is__________(Round off to the nearest integer). }
A quadratic function of two variables is given as $$ f\left(x_{1}, x_{2}\right)=x_{1}^{2}+2 x_{2}^{2}+3 x_{1}+3 x_{2}+x_{1} x_{2}+1$$The magnitude of the maximum rate of...
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GATE Electrical 2023 | Question: 34
All the elements in the circuit shown in the following figure are ideal. Which of the following statements is/are true? When switch $\text{S}$ is $\mathrm{ON}$, both $D_{1}$ and $D_{2}$ conducts and $D_{3}$ is reverse biased When switch $\text{S}$ ... conduct When switch $\text{S}$ is $\mathrm{OFF}, D_{1}$ conducts, $D_{2}$ is reverse biased and $D_{3}$ conducts
All the elements in the circuit shown in the following figure are ideal. Which of the following statements is/are true? When switch $\text{S}$ is $\mathrm{ON}$, both $D_{...
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GATE Electrical 2023 | Question: 40
The discrete-time Fourier transform of a signal $ x[n]$ is $X (\Omega)=(1+\cos \Omega) e^{-j \Omega}$ Consider that $ x_{p}[n]$ is a periodic signal of period $ \mathrm{N}=5$ ... $a_{3}$ is_____________ (Round off to $3$ decimal places).
The discrete-time Fourier transform of a signal $ x[n]$ is $X (\Omega)=(1+\cos \Omega) e^{-j \Omega}$ Consider that $ x_{p}[n]$ is a periodic signal of period $ \mathrm{N...
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112
GATE Electrical 2023 | Question: 54
A balanced delta connected load consisting of the series connection of one resistor $(R=15 \; \Omega)$ and a capacitor $(C=212.21 \; \mu \mathrm{F})$ in each phase is connected to threephase, $50 \mathrm{~Hz}, 415 \mathrm{~V}$ supply ... to be negligible, the magnitude of the voltage across the terminals $V_{A B}$ in Volts is (Round off to the nearest integer).
A balanced delta connected load consisting of the series connection of one resistor $(R=15 \; \Omega)$ and a capacitor $(C=212.21 \; \mu \mathrm{F})$ in each phase is con...
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113
GATE Electrical 2023 | Question: 41
For the circuit shown, if $ i=\sin 1000 t,$ the instantaneous value of the Thevenin's equivalent voltage (in Volts) across the terminals $a-b$ at time $t=5 \mathrm{~ms}$ is__________(Round off to $2$ decimal places).
For the circuit shown, if $ i=\sin 1000 t,$ the instantaneous value of the Thevenin's equivalent voltage (in Volts) across the terminals $a-b$ at time $t=5 \mathrm{~ms}$...
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GATE Electrical 2023 | Question: 48
The single phase rectifier consisting of three thyristors $T_{1}, T_{2}, T_{3}$ and a diode $D_{1}$ feed power to a $10 \mathrm{~A}$ constant current load. $ T_{1}$ and $ T_{3} $ are fired at $ \alpha=60^{\circ} $ and $ T_{2}$ is ... zero crossing of $ V_{i n} .$ The average voltage $V_{O} $ across the load in volts is _________(Round off to $2$ decimal places).
The single phase rectifier consisting of three thyristors $T_{1}, T_{2}, T_{3}$ and a diode $D_{1}$ feed power to a $10 \mathrm{~A}$ constant current load. $ T_{1}$ and ...
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115
GATE Electrical 2023 | Question: 43
When the winding $\text{c-d}$ of the single-phase, $50 \mathrm{~Hz},$ two winding transformer is supplied from an $\mathrm{AC}$ current source of frequency $50 \mathrm{~Hz},$ ... linear and neglecting core loss, the self-inductance of the winding $a-b$ in millihenry is __________(Round off to $1$ decimal place).
When the winding $\text{c-d}$ of the single-phase, $50 \mathrm{~Hz},$ two winding transformer is supplied from an $\mathrm{AC}$ current source of frequency $50 \mathrm{~H...
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GATE Electrical 2023 | Question: 39
The period of the discrete-time signal $ x[n]$ described by the equation below is $N=$________ (Round off to the nearest integer). $x[n]=1+3 \sin \left(\frac{15 \pi}{8} n+\frac{3 \pi}{4}\right)-5 \sin \left(\frac{\pi}{3} n-\frac{\pi}{4}\right)$
The period of the discrete-time signal $ x[n]$ described by the equation below is $N=$________ (Round off to the nearest integer).$$x[n]=1+3 \sin \left(\frac{15 \pi}{8} n...
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GATE Electrical 2023 | Question: 47
In a given $8$-bit general purpose micro-controller there are following flags. $\text{C-Carry, A-Auxiliary Carry, O-Overflow flag, P-Parity}$ ($0$ for even, $1$ for odd) $\text{R0}$ and $\text{R1}$ are the two general purpose registers of the micro-controller. After execution ...
In a given $8$-bit general purpose micro-controller there are following flags. $\text{C-Carry, A-Auxiliary Carry, O-Overflow flag, P-Parity}$ ($0$ for even, $1$ for odd) ...
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GATE Electrical 2023 | Question: 33
In the figure, the electric field $\boldsymbol{E}$ and the magnetic field $\boldsymbol{B}$ point to $\mathrm{x}$ and $\mathrm{z}$ directions, respectively, and have constant magnitudes. A positive charge q' is released from rest at the origin ... plane only. The trajectory of the charge will be a circle. The charge will progress in the direction of $\mathbf{y}$.
In the figure, the electric field $\boldsymbol{E}$ and the magnetic field $\boldsymbol{B}$ point to $\mathrm{x}$ and $\mathrm{z}$ directions, respectively, and have cons...
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GATE Electrical 2023 | Question: 52
The closed curve shown in the figure is described by $r=1+\cos \theta,$ where $r=\sqrt{x^{2}+y^{2}} ; x=r \cos \theta, y=r \sin \theta$ The magnitude of the line integral of the vector field $ F=-y \hat{\imath}+x \hat{\jmath}$ around the closed curve is __________(Round off to $2$ decimal places).
The closed curve shown in the figure is described by $r=1+\cos \theta,$ where $r=\sqrt{x^{2}+y^{2}} ; x=r \cos \theta, y=r \sin \theta$ The magnitude of the line integra...
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120
GATE Electrical 2023 | Question: 32
Consider the following equation in a $2-\text{D}$ real-space. $\left|x_{1}\right|^{p}+\left|x_{2}\right|^{p}=1 \text { for } p>0$ Which of the following statement(s) is/are true? When $p=2$, the area enclosed by the curve is $\pi$. When $p$ ... $p$ tends to $0,$ the area enclosed by the curve is $1.$ When $p=1$, the area enclosed by the curve is $2.$
Consider the following equation in a $2-\text{D}$ real-space. $\left|x_{1}\right|^{p}+\left|x_{2}\right|^{p}=1 \text { for } p>0$ Which of the following statement(s) is/a...
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