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41
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 $1010$ $1110$ $0110$ $0001$
​​​​​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$$...
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46
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).
Two passive two-port networks $\mathbf{P}$ and $\mathbf{Q}$ are connected as shown in the figure. The impedance matrix of network $\mathbf{P}$ is $Z_{\mathbf{P}}=\left[\b...
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47
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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48
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).
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 (r...
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49
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).
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 ...
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58
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? $\gamma=m \beta$ $\beta=m \gamma$ $\alpha=m \gamma$ $\alpha=m \beta$
​​​​For the three-bus lossless power network shown in the figure, the voltage magnitudes at all the buses are equal to $1$ per unit (pu), and the differences of t...
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63
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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66
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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67
GATE Electrical 2023 | Question: 35
The expected number of trials for first occurrence of a "head" in a biased coin is known to be $4.$ The probability of first occurrence of a "head" in the second trial is ____________(Round off to $3$ decimal places).
The expected number of trials for first occurrence of a "head" in a biased coin is known to be $4.$ The probability of first occurrence of a "head" in the second trial is...
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68
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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69
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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71
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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73
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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74
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$$\begin{array}{ll} \qquad \qquad\textbf{A} & \qquad \textbf{B} \\ \quad...
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76
GATE Electrical 2023 | Question: 21
For the signals $x(t)$ and $y(t)$ shown in the figure, $z(t)=x(t) * y(t)$ is maximum at $t=T_1$. Then $T_1$ in seconds is_________ (Round off to the nearest integer).
For the signals $x(t)$ and $y(t)$ shown in the figure, $z(t)=x(t) * y(t)$ is maximum at $t=T_1$. Then $T_1$ in seconds is_________ (Round off to the nearest integer).
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77
GATE Electrical 2023 | Question: 26
The magnitude and phase plots of an $\text{LTI}$ system are shown in the figure. The transfer function of the system is $2.51 e^{-0.032 s}$ $\frac{e^{-2.514 s}}{s+1}$ $1.04 e^{-2.514 s}$ $2.51 e^{-1.047 s}$
The magnitude and phase plots of an $\text{LTI}$ system are shown in the figure. The transfer function of the system is $2.51 e^{-0.032 s}$$\frac{e^{-2.514 s}}{s+1}$$1.04...
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78
GATE Electrical 2023 | Question: 22
For the circuit shown in the figure, $V_{1}=8 \mathrm{~V}, \mathrm{DC}$ and $I_{1}=8 \mathrm{~A}, \mathrm{DC}$. The voltage $V_{a b}$ in Volts is____________(Round off to $1$ decimal place).
For the circuit shown in the figure, $V_{1}=8 \mathrm{~V}, \mathrm{DC}$ and $I_{1}=8 \mathrm{~A}, \mathrm{DC}$. The voltage $V_{a b}$ in Volts is____________(Round off to...
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