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1
GATE Electrical 2024 | Question: 1
Which one of the following matrices has an inverse? $\left[\begin{array}{ccc}1 & 4 & 8 \\ 0 & 4 & 2 \\ 0.5 & 2 & 4\end{array}\right]$ ... $\left[\begin{array}{ccc}1 & 4 & 8 \\ 0 & 4 & 2 \\ 3 & 12 & 24\end{array}\right]$
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GATE Electrical 2024 | Question: 2
The number of junctions in the circuit is $6$ $7$ $8$ $9$
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GATE Electrical 2024 | Question: 3
All the elements in the circuit are ideal. The power delivered by the $10 \mathrm{~V}$ source in watts is $0$ $50$ $100$ dependent on the value of $\alpha$
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GATE Electrical 2024 | Question: 4
The circuit shown in the figure with the switch $\text{S}$ open, is in steady state. After the switch $\text{S}$ is closed, the time constant of the circuit in seconds is $1.25$ $0$ $1$ $1.5$
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GATE Electrical 2024 | Question: 5
Suppose signal $y(t)$ is obtained by the time-reversal of signal $x(t)$, i.e., $y(t)=x(-t),-\infty<t<\infty$. Which one of the following options is always true for the convolution of $x(t)$ and $y(t)$? It is an even signal. It is an odd signal. It is a causal signal. It is an anti-causal signal.
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GATE Electrical 2024 | Question: 6
If $u(t)$ is the unit step function, then the region of convergence $\text{(ROC)}$ of the Laplace transform of the signal \[ x(t)=e^{t^{2}}[u(t-1)-u(t-10)] \] is $-\infty<\operatorname{Re}(s)<\infty$ $\operatorname{Re}(s) \geq 10$ $\operatorname{Re}(s) \leq 1$ $1 \leq \operatorname{Re}(s) \leq 10$
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GATE Electrical 2024 | Question: 7
A three phase, $50 \mathrm{~Hz}, 6$ pole induction motor runs at $960 \mathrm{rpm}$. The stator copper loss, core loss, and the rotational loss of the motor can be neglected. The percentage efficiency of the motor is $92$ $94$ $96$ $98$
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GATE Electrical 2024 | Question: 8
Which one of the following options represents possible voltage polarities in a single phase two winding transformer? Here, $V_{p}$ is the applied primary voltage, $E_{p}$ is the induced primary voltage, $V_{s}$ is the open circuit secondary voltage, and $E_{s}$ is the induced secondary voltage.
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GATE Electrical 2024 | Question: 9
The figure shows the single line diagram of a 4-bus power network. Branches $b_{1}$, $b_{2}, b_{3}$, and $b_{4}$ have impedances $4 z, z, 2 z$, and $4 z$ per-unit (pu), respectively, where $z=r+j x$, with $r>0$ and $x>0$. The ... $b_{1}$ $b_{2}$ $b_{3}$ $b_{4}$
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GATE Electrical 2024 | Question: 10
For the block-diagram shown in the figure, the transfer function $\frac{C(s)}{R(s)}$ is $\frac{G(s)}{1+2 G(s)}$ $-\frac{G(s)}{1+2 G(s)}$ $\frac{G(s)}{1-2 G(s)}$ $-\frac{G(s)}{1-2 G(s)}$
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GATE Electrical 2024 | Question: 11
Consider the standard second-order system of the form $\frac{\omega_{n}^{2}}{s^{2}+2 \zeta \omega_{n} s+\omega_{n}^{2}}$ with the poles $p$ and $p^{*}$ having negative real parts. The pole locations are also shown ... is more than that of System $1$. Settling times of both the systems are the same. Settling time cannot be computed from the given information.
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12
GATE Electrical 2024 | Question: 12
Consider the cascaded system as shown in the figure. Neglecting the faster component of the transient response, which one of the following options is a firstorder pole-only approximation such that the steady-state values of the unit step responses of the original and the approximated systems ... $\frac{2}{s+1}$ $\frac{1}{s+20}$ $\frac{2}{s+20}$
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GATE Electrical 2024 | Question: 13
The table lists two instrument transformers and their features: \begin{array}{|l|l|} \hline \text{ Instrument Transformers } &\text{ Features } \\ \hline & \text{P}) \text{Primary is connected in parallel to the grid} \\ \hline \text{X}) \text{ ... $\mathrm{Q}$ and $\mathrm{S}$; $\mathrm{Y}$ matches with $\mathrm{P}$ and $\mathrm{R}$.
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GATE Electrical 2024 | Question: 14
Simplified form of the Boolean function \[ F(P, Q, R, S)=\bar{P} \bar{Q}+\bar{P} Q S+P \bar{Q} \bar{R} \bar{S}+P \bar{Q} R \bar{S} \] is $\bar{P} S+\bar{Q} \bar{S}$ $\bar{P} \bar{Q}+\bar{Q} \bar{S}$ $\bar{P} Q+R \bar{S}$ $P \bar{S}+Q \bar{R}$
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GATE Electrical 2024 | Question: 15
In the circuit, the present value of $Z$ is $1$. Neglecting the delay in the combinatorial circuit, the values of $S$ and $Z$, respectively, after the application of the clock will be $S=0, Z=0$ $S=0, Z=1$ $S=1, Z=0$ $S=1, Z=1$
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16
GATE Electrical 2024 | Question: 16
To obtain the Boolean function $\text{F(X, Y)}=\text{X} \bar{\text{Y}}+\bar{\text{X}}$, the inputs $\text{PQRS}$ in the figure should be $1010$ $1110$ $0110$ $0001$
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17
GATE Electrical 2024 | Question: 17
If the following switching devices have similar power ratings, which one of them is the fastest? $\text{SCR}$ $\text{GTO}$ $\text{IGBT}$ $\text{Power MOSFET}$
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GATE Electrical 2024 | Question: 18
A single-phase triac based $\text{AC}$ voltage controller feeds a series $\text{RL}$ load. The input $\text{AC}$ supply is $230 \mathrm{~V}, 50 \mathrm{~Hz}$. The values of $\mathrm{R}$ and $\mathrm{L}$ are $10 \Omega$ ... minimum triggering angle of the triac to obtain controllable output voltage is $15^{\circ}$ $30^{\circ}$ $45^{\circ}$ $60^{\circ}$
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19
GATE Electrical 2024 | Question: 19
Let $\text{X}$ be a discrete random variable that is uniformly distributed over the set $\{-10,-9, \cdots, 0, \cdots, 9,10\}$. Which of the following random variables is/are uniformly distributed? $X^{2}$ $X^{3}$ $(X-5)^{2}$ $(X+10)^{2}$
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GATE Electrical 2024 | Question: 20
Which of the following complex functions is/are analytic on the complex plane? $f(z)=j \operatorname{Re}(z)$ $f(z)=\operatorname{Im}(z)$ $f(z)=e^{|z|}$ $f(z)=z^{2}-z$
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21
GATE Electrical 2024 | Question: 21
Consider the complex function $f(z)=\cos z+e^{z^{2}}$. The coefficient of $z^{5}$ in the Taylor series expansion of $f(z)$ about the origin is __________ (rounded off to $1$ decimal place).
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GATE Electrical 2024 | Question: 22
The sum of the eigenvalues of the matrix $A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]^{2}$ is ____________(rounded off to the nearest integer).
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GATE Electrical 2024 | Question: 23
Let $X(\omega)$ be the Fourier transform of the signal \[ x(t)=e^{-t^{4}} \cos t, \quad-\infty < t < \infty.\] The value of the derivative of $X(\omega)$ at $\omega=0$ is (rounded off to 1 decimal place).
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24
GATE Electrical 2024 | Question: 24
The incremental cost curves of two generators (Gen $\text{A}$ and Gen $\text{B}$) in a plant supplying a common load are shown in the figure. If the incremental cost of supplying the common load is Rs.$7400$ per MWh, then the common load in $\text{MW$ is _____________ (rounded off to the nearest integer).
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25
GATE Electrical 2024 | Question: 25
A forced commutated thyristorized step-down chopper is shown in the figure. Neglect the $\text{ON}$-state drop across the power devices. Assume that the capacitor is initially charged to $50 \mathrm{~V}$ with the polarity shown in the figure. ... in microseconds, when $\mathrm{Th}_{\mathrm{A}}$ is triggered, is _____________ (rounded off to the nearest integer).
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26
GATE Electrical 2024 | Question: 26
Consider a vector $\bar{u}=2 \hat{x}+\hat{y}+2 \hat{z}$, where $\hat{x}, \hat{y}, \hat{z}$ represent unit vectors along the coordinate axes $x, y, z$ respectively. The directional derivative of the function $f(x, y, z)=2 \ln (x y)+\ln (y z)+3 \ln (x z)$ at the point $(x, y, z)=(1,1,1)$ in the direction of $\bar{u}$ is $0$ $\frac{7}{5 \sqrt{2}}$ $7$ $21$
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27
GATE Electrical 2024 | Question: 27
The input $x(t)$ and the output $y(t)$ of a system are related as \[ y(t)=e^{-t} \int_{-\infty}^{t} e^{\tau} x(\tau) d \tau, \quad-\infty < t < \infty. \] The system is nonlinear. linear and time-invariant. linear but not time-invariant. noncausal.
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28
GATE Electrical 2024 | Question: 28
Consider the discrete-time systems $T_{1}$ and $T_{2}$ defined as follows: \[ \begin{array}{c} \left\{T_{1} x\right\}[n]=x[0]+x[1]+\cdots+x[n] \\ \left\{T_{2} x\right\}[n]=x[0]+\frac{1}{2} x[1]+\cdots+\frac{1}{2^{n}} x[n] \ ... $T_{1}$ is BIBO stable but $T_{2}$ is not BIBO stable. $T_{1}$ is not BIBO stable but $T_{2}$ is BIBO stable.
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29
GATE Electrical 2024 | Question: 29
If the $Z$-transform of a finite-duration discrete-time signal $x[n]$ is $X(z)$, then the $Z$ transform of the signal $y[n]=x[2 n]$ is $Y(z)=X\left(z^{2}\right)$ ... $Y(z)=\frac{1}{2}\left[X\left(z^{2}\right)+X\left(-z^{2}\right)\right]$
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30
GATE Electrical 2024 | Question: 30
A $3$-phase, $11 \mathrm{kV}, 10 \mathrm{MVA}$ synchronous generator is connected to an inductive load of power factor $(\sqrt{3} / 2)$ via a lossless line with a per-phase inductive reactance of $5 \Omega$. The per-phase synchronous reactance ... power factor at the terminal of the generator is $0.63$ lagging. $0.87$ lagging. $0.63$ leading. $0.87$ leading.
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31
GATE Electrical 2024 | Question: 31
For the three-bus lossless power network shown in the figure, the voltage magnitudes at all the buses are equal to $1$ ... of the following options is correct? $\gamma=m \beta$ $\beta=m \gamma$ $\alpha=m \gamma$ $\alpha=m \beta$
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32
GATE Electrical 2024 | Question: 32
A $\text{BJT}$ biasing circuit is shown in the figure, where $V_{B E}=0.7 \mathrm{~V}$ and $\beta=100$. The Quiescent Point values of $V_{C E}$ and $I_{C}$ are respectively $4.6 \mathrm{~V}$ and $2.46 \mathrm{~mA}$ $3.5 \mathrm{~V}$ and $2.46 \mathrm{~mA}$ $2.61 \mathrm{~V}$ and $3.13 \mathrm{~mA}$ $4.6 \mathrm{~V}$ and $3.13 \mathrm{~mA}$
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33
GATE Electrical 2024 | Question: 33
Let $f(t)$ be a real-valued function whose second derivative is positive for $-\infty < t < \infty.$ Which of the following statements is/are always true? $f(t)$ has at least one local minimum. $f(t)$ cannot have two distinct local minima. $f(t)$ has at least one local maximum. The minimum value of $f(t)$ cannot be negative.
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34
GATE Electrical 2024 | Question: 34
Consider the function $f(t)=(\max (0, t))^2$ for $-\infty<t<\infty$, where $\max (a, b)$ denotes the maximum of $a$ and $b$. Which of the following statements is/are true? $f(t)$ is not ... differentiable and its derivative is continuous. $f(t)$ is differentiable but its derivative is not continuous. $f(t)$ and its derivative are differentiable.
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35
GATE Electrical 2024 | Question: 35
Which of the following differential equations is/are nonlinear? $t x(t)+\frac{d x(t)}{d t}=t^{2} e^{t}, \quad x(0)=0$ $\frac{1}{2} e^{t}+x(t) \frac{d x(t)}{d t}=0, \quad x(0)=0$ $x(t) \cos t-\frac{d x(t)}{d t} \sin t=1, \quad x(0)=0$ $x(t)+e^{\left(\frac{d x(t)}{d t}\right)}=1, \quad x(0)=0$
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36
GATE Electrical 2024 | Question: 36
For a two-phase network, the phase voltages $V_{p}$ and $V_{q}$ are to be expressed in terms of sequence voltages $V_{\alpha}$ and $V_{\beta}$ ... $\left[\begin{array}{cc}-1 & 1 \\ 1 & 1\end{array}\right]$
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37
GATE Electrical 2024 | Question: 37
Which of the following options is/are correct for the Automatic Generation Control (AGC) and Automatic Voltage Regulator (AVR) installed with synchronous generators? AGC response has a local effect on frequency while AVR response ... . AGC regulates the generator's mechanical power input while AVR regulates the field current of the synchronous generator.
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38
GATE Electrical 2024 | Question: 38
Two passive two-port networks $\mathbf{P}$ and $\mathbf{Q}$ are connected as shown in the figure. The impedance matrix of network $\mathbf{P}$ ... $\beta$ in $\Omega$ is ____________(rounded off to $2$ decimal places).
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39
GATE Electrical 2024 | Question: 39
For the circuit shown in the figure, the source frequency is $5000 \mathrm{rad} / \mathrm{sec}$. The mutual inductance between the magnetically coupled inductors is $5 \mathrm{mH}$ with their self inductances being $125 \mathrm{mH}$ and $1 \mathrm{mH}$ ... the terminals $\text{P}$ and $\text{Q}$ in $\Omega$ is ____________ (rounded off to $2$ decimal places).
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40
GATE Electrical 2024 | Question: 40
In the circuit shown, $Z_{1}=50 \angle-90^{\circ} \Omega$ and $Z_{2}=200 \angle-30^{\circ} \Omega$. It is supplied by a three phase $400 \mathrm{~V}$ source with the phase sequence being R-Y-B. Assume the watt meters $W_{1}$ ... The magnitude of the difference between the readings of $W_{1}$ and $W_{2}$ in watts is __________ (rounded off to $2$ decimal places).
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