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124
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.
​​​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 syste...
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126
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)$$...
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128
GATE Electrical 2024 | Question: 31
For the three-bus lossless power network shown in the figure, the voltage magnitudes at all the buses are equal to $1$ ... of the following options is correct? $\gamma=m \beta$ $\beta=m \gamma$ $\alpha=m \gamma$ $\alpha=m \beta$
​​​​For the three-bus lossless power network shown in the figure, the voltage magnitudes at all the buses are equal to $1$ per unit (pu), and the differences of t...
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132
GATE Electrical 2024 | Question: 35
Which of the following differential equations is/are nonlinear? $t x(t)+\frac{d x(t)}{d t}=t^{2} e^{t}, \quad x(0)=0$ $\frac{1}{2} e^{t}+x(t) \frac{d x(t)}{d t}=0, \quad x(0)=0$ $x(t) \cos t-\frac{d x(t)}{d t} \sin t=1, \quad x(0)=0$ $x(t)+e^{\left(\frac{d x(t)}{d t}\right)}=1, \quad x(0)=0$
Which of the following differential equations is/are nonlinear?$t x(t)+\frac{d x(t)}{d t}=t^{2} e^{t}, \quad x(0)=0$$\frac{1}{2} e^{t}+x(t) \frac{d x(t)}{d t}=0, \quad x(...
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133
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 $V_{\beta}$ ... $\left[\begin{array}{cc}-1 & 1 \\ 1 & 1\end{array}\right]$
​​​​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 $V_{\beta}$ as $\left[\begi...
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135
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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140
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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147
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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148
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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156
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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157
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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