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101
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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102
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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103
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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104
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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105
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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106
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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107
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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108
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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109
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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110
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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111
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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112
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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113
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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114
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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115
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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116
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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117
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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118
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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119
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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120
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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