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GATE 2024 Electrical | GA Question: 8
The chart below shows the data of the number of cars bought by Millennials and Gen $\text{X}$ people in a country from the year $2010$ to $2020$ as well as the yearly fuel consumption of the country (in Million liters). Considering the data ... buyers from $2015$ to $2020$ is more than the increase in the number of Millennial car buyers from $2010$ to $2015$.
The chart below shows the data of the number of cars bought by Millennials and Gen $\text{X}$ people in a country from the year $2010$ to $2020$ as well as the yearly ...
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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.
Which of the following options is/are correct for the Automatic Generation Control (AGC) and Automatic Voltage Regulator (AVR) installed with synchronous gene...
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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 $1.25$ $0$ $1$ $1.5$
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...
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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 $\frac{G(s)}{1+2 G(s)}$ $-\frac{G(s)}{1+2 G(s)}$ $\frac{G(s)}{1-2 G(s)}$ $-\frac{G(s)}{1-2 G(s)}$
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)}$$...
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GATE Electrical 2024 | Question: 55
A single-phase full-controlled thyristor converter bridge is used for regenerative braking of a separately excited $\text{DC}$ motor with the following specifications: Rated armature voltage $210 \mathrm{~V}$ ... the triggering angle of the converter bridge in degrees should be ____________ (rounded off to $2$ decimal places).
A single-phase full-controlled thyristor converter bridge is used for regenerative braking of a separately excited $\text{DC}$ motor with the following specifications:Rat...
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GATE 2024 Electrical | GA Question: 5
If, for non-zero real variables $x, y$, and real parameter $a>1$, \[ x: y=(a+1):(a-1) \text {, } \] then, the ratio $\left(x^{2}-y^{2}\right):\left(x^{2}+y^{2}\right)$ is $2 a:\left(a^{2}+1\right)$ $a:\left(a^{2}+1\right)$ $2 a:\left(a^{2}-1\right)$ $a:\left(a^{2}-1\right)$
If, for non-zero real variables $x, y$, and real parameter $a>1$,\[x: y=(a+1):(a-1) \text {, }\]then, the ratio $\left(x^{2}-y^{2}\right):\left(x^{2}+y^{2}\right)$ ...
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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 $0$ $\frac{7}{5 \sqrt{2}}$ $7$ $21$
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 $x, y, z$ respecti...
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GATE Electrical 2024 | Question: 35
Which of the following differential equations is/are nonlinear? $t x(t)+\frac{d x(t)}{d t}=t^{2} e^{t}, \quad x(0)=0$ $\frac{1}{2} e^{t}+x(t) \frac{d x(t)}{d t}=0, \quad x(0)=0$ $x(t) \cos t-\frac{d x(t)}{d t} \sin t=1, \quad x(0)=0$ $x(t)+e^{\left(\frac{d x(t)}{d t}\right)}=1, \quad x(0)=0$
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$$\frac{1}{2} e^{t}+x(t) \frac{d x(t)}{d t}=0, \quad x(...
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GATE Electrical 2024 | Question: 17
If the following switching devices have similar power ratings, which one of them is the fastest? $\text{SCR}$ $\text{GTO}$ $\text{IGBT}$ $\text{Power MOSFET}$
If the following switching devices have similar power ratings, which one of them is the fastest?$\text{SCR}$$\text{GTO}$$\text{IGBT}$$\text{Power MOSFET}$
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GATE Electrical 2024 | Question: 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 ... $b_{1}$ $b_{2}$ $b_{3}$ $b_{4}$
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 $4 z$ p...
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31
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.
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 +\cdots+x[n] \\\left\{T_{2} x\right\...
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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 $Y(z)=X\left(z^{2}\right)$ ... $Y(z)=\frac{1}{2}\left[X\left(z^{2}\right)+X\left(-z^{2}\right)\right]$
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)$$...
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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.
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 stateme...
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34
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 $\mathrm{R}$.
The table lists two instrument transformers and their features:\begin{array}{|l|l|}\hline \text{ Instrument Transformers } &\text{ Features } \\\hline & \text{P}) ...
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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 $\bar{P} S+\bar{Q} \bar{S}$ $\bar{P} \bar{Q}+\bar{Q} \bar{S}$ $\bar{P} Q+R \bar{S}$ $P \bar{S}+Q \bar{R}$
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}...
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36
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 $3.13 \mathrm{~mA}$
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_{...
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37
GATE Electrical 2024 | Question: 43
If the energy of a continuous-time signal $x(t)$ is $\text{E}$ and the energy of the signal $2 x(2 t-1)$ is $c E$, then $c$ is ___________ (rounded off to $1$ decimal place).
If the energy of a continuous-time signal $x(t)$ is $\text{E}$ and the energy of the signal $2 x(2 t-1)$ is $c E$, then $c$ is ___________ (rounded off to $1$ decimal pla...
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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 $92$ $94$ $96$ $98$
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 moto...
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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).
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: 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 ... $\frac{2}{s+1}$ $\frac{1}{s+20}$ $\frac{2}{s+20}$
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 firsto...
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