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43
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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50
GATE Electrical 2024 | Question: 50
In the given circuit, the diodes are ideal. The current $\text{I}$ through the diode $\text{D} 1$ in milliamperes is __________(rounded off to two decimal places).
In the given circuit, the diodes are ideal. The current $\text{I}$ through the diode $\text{D} 1$ in milliamperes is __________(rounded off to two decimal places).
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51
GATE Electrical 2024 | Question: 51
A difference amplifier is shown in the figure. Assume the op-amp to be ideal. The $\text{CMRR}$ (in $\mathrm{dB}$ ) of the difference amplifier is ___________ (rounded off to $2$ decimal places).
A difference amplifier is shown in the figure. Assume the op-amp to be ideal. The $\text{CMRR}$ (in $\mathrm{dB}$ ) of the difference amplifier is ___________ (rounded of...
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59
GATE 2024 Electrical | Question: 4
​​​​A shopkeeper buys shirts from a producer and sells them at $20 \%$ profit. A customer has to pay ₹ $3,186.00$ including $18 \%$ taxes, per shirt. At what price did the shopkeeper buy each shirt from the producer? ₹ $2,500.00$ ₹ $1,975.40$ ₹ $2,250.00$ ₹ $2,548.80$
​​​​A shopkeeper buys shirts from a producer and sells them at $20 \%$ profit. A customer has to pay ₹ $3,186.00$ including $18 \%$ taxes, per shirt. At what pr...
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60
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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66
GATE Electrical 2023 | Question: 1
For a given vector $\mathbf{w}=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]^{\mathrm{T}}$, the vector normal to the plane defined by $\mathbf{w}^{\mathrm{T}} \mathbf{x}=1$ ... $\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]^T$
For a given vector $\mathbf{w}=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]^{\mathrm{T}}$, the vector normal to the plane defined by $\mathbf{w}^{\mathrm{T}} \math...
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67
GATE Electrical 2023 | Question: 2
For the block diagram shown in the figure, the transfer function $\frac{\text{Y(s)}}{\text{R(s)}}$ is $\frac{2s+3}{s+1}$ $\frac{3s+2}{s-1}$ $\frac{s+1}{3s+2}$ $\frac{3s+2}{s+1}$
For the block diagram shown in the figure, the transfer function $\frac{\text{Y(s)}}{\text{R(s)}}$ is$\frac{2s+3}{s+1}$ $\frac{3s+2}{s-1}$ $\frac{s+1}{3s+2}$ $\frac{3s+2}...
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68
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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70
GATE Electrical 2023 | Question: 5
The following columns present various modes of induction machine operation and the ranges of slip ... $a-r, b-q$, and $c-p$ $a-p, b-r$, and $c-q$ $a-q, b-p$, and $c-r$
The following columns present various modes of induction machine operation and the ranges of slip$$\begin{array}{ll} \qquad \qquad\textbf{A} & \qquad \textbf{B} \\ \quad...
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71
GATE Electrical 2023 | Question: 6
A $10-\text { pole, } 50 \mathrm{~Hz}, 240 \mathrm{~V},$ single phase induction motor runs at $540 ~\mathrm{RPM}$ while driving rated load. The frequency of induced rotor currents due to backward field is $100 \mathrm{~Hz}$ $95 \mathrm{~Hz}$ $10 \mathrm{~Hz}$ $5 \mathrm{~Hz}$
A $10-\text { pole, } 50 \mathrm{~Hz}, 240 \mathrm{~V},$ single phase induction motor runs at $540 ~\mathrm{RPM}$ while driving rated load. The frequency of induced rotor...
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72
GATE Electrical 2023 | Question: 7
A continuous-time system that is initially at rest is described by $ \frac{d y(t)}{d t}+3 y(t)=2 x(t),$ where$x(t)$ is the input voltage and $y(t)$ is the output voltage. The impulse response of the system is $3 e^{-2 t}$ $\frac{1}{3} e^{-2 t} u(t)$ $2 e^{-3 t} u(t)$ $2 e^{-3 t}$
A continuous-time system that is initially at rest is described by $$ \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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76
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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78
GATE Electrical 2023 | Question: 13
The chopper circuit shown in figure (i) feeds power to a $5 \text { A DC}$ constant current source. The switching frequency of the chopper is $100 ~\mathrm{kHz}.$ ... $10 \mathrm{~V}$ $6 \mathrm{~V}$ $12 \mathrm{~V}$ $20 \mathrm{~V}$
The chopper circuit shown in figure (i) feeds power to a $5 \text { A DC}$ constant current source. The switching frequency of the chopper is $100 ~\mathrm{kHz}.$ All the...
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79
GATE Electrical 2023 | Question: 14
In the figure, the vectors $\mathbf{u}$ and $\mathbf{v}$ are related as: $\mathbf{A u}=\mathbf{v}$ by a transformation matrix A. The correct choice of $\mathbf{A}$ ... $\left[\begin{array}{ll}\frac{4}{5} & -\frac{3}{5} \\ \frac{3}{5} & -\frac{4}{5}\end{array}\right]$
In the figure, the vectors $\mathbf{u}$ and $\mathbf{v}$ are related as: $\mathbf{A u}=\mathbf{v}$ by a transformation matrix A. The correct choice of $\mathbf{A}$ is$\le...
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