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101
GATE Electrical 2023 | Question: 24
In the following differential equation, the numerically obtained value of $y(t),$ at $t=1,$ is ___________ (Round off to $2$ decimal places). $\frac{d y}{d t}=\frac{e^{-\alpha t}}{2+\alpha t}, \quad \alpha=0.01$ and $y(0)=0$
In the following differential equation, the numerically obtained value of $y(t),$ at $t=1,$ is ___________ (Round off to $2$ decimal places). $\frac{d y}{d t}=\frac{e^{-...
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102
GATE Electrical 2023 | Question: 36
Consider the state-space description of an $\text{LTI}$ ... for which the steady-state output of the system will be zero, is ________(Round off to the nearest integer).
Consider the state-space description of an $\text{LTI}$ system with matrices$\qquad A=\left[\begin{array}{cc}0 & 1 \\-1 & -2\end{array}\right], B=\left[\begin{array}{l}0 ...
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105
GATE Electrical 2023 | Question: 42
The admittance parameters of the passive resistive two-port network shown in the figure are $y_{11}=5 S, y_{22}=1 S, y_{12}=y_{21}=-2.5 S$ The power delivered to the load resistor $ R_{L}$ in Watt is _______(Round off to $2$ decimal places).
The admittance parameters of the passive resistive two-port network shown in the figure are$$y_{11}=5 S, y_{22}=1 S, y_{12}=y_{21}=-2.5 S$$The power delivered to the load...
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106
GATE Electrical 2023 | Question: 37
A three-phase synchronous motor with synchronous impedance of $0.1+\mathrm{j} 0.3 \text { per unit } $ per phase has a static stability limit of $2.5 \text { per unit.}$ The corresponding excitation voltage in per unit is _________ (Round off to $2$ decimal places).
A three-phase synchronous motor with synchronous impedance of $0.1+\mathrm{j} 0.3 \text { per unit } $ per phase has a static stability limit of $2.5 \text { per unit.}$ ...
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109
GATE Electrical 2023 | Question: 55
A quadratic function of two variables is given as $ f\left(x_{1}, x_{2}\right)=x_{1}^{2}+2 x_{2}^{2}+3 x_{1}+3 x_{2}+x_{1} x_{2}+1$ The magnitude of the maximum rate of change of the function at the point $(1,1)$ is__________(Round off to the nearest integer). }
A quadratic function of two variables is given as $$ f\left(x_{1}, x_{2}\right)=x_{1}^{2}+2 x_{2}^{2}+3 x_{1}+3 x_{2}+x_{1} x_{2}+1$$The magnitude of the maximum rate of...
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111
GATE Electrical 2023 | Question: 40
The discrete-time Fourier transform of a signal $ x[n]$ is $X (\Omega)=(1+\cos \Omega) e^{-j \Omega}$ Consider that $ x_{p}[n]$ is a periodic signal of period $ \mathrm{N}=5$ ... $a_{3}$ is_____________ (Round off to $3$ decimal places).
The discrete-time Fourier transform of a signal $ x[n]$ is $X (\Omega)=(1+\cos \Omega) e^{-j \Omega}$ Consider that $ x_{p}[n]$ is a periodic signal of period $ \mathrm{N...
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113
GATE Electrical 2023 | Question: 41
For the circuit shown, if $ i=\sin 1000 t,$ the instantaneous value of the Thevenin's equivalent voltage (in Volts) across the terminals $a-b$ at time $t=5 \mathrm{~ms}$ is__________(Round off to $2$ decimal places).
For the circuit shown, if $ i=\sin 1000 t,$ the instantaneous value of the Thevenin's equivalent voltage (in Volts) across the terminals $a-b$ at time $t=5 \mathrm{~ms}$...
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116
GATE Electrical 2023 | Question: 39
The period of the discrete-time signal $ x[n]$ described by the equation below is $N=$________ (Round off to the nearest integer). $x[n]=1+3 \sin \left(\frac{15 \pi}{8} n+\frac{3 \pi}{4}\right)-5 \sin \left(\frac{\pi}{3} n-\frac{\pi}{4}\right)$
The period of the discrete-time signal $ x[n]$ described by the equation below is $N=$________ (Round off to the nearest integer).$$x[n]=1+3 \sin \left(\frac{15 \pi}{8} n...
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117
GATE Electrical 2023 | Question: 47
In a given $8$-bit general purpose micro-controller there are following flags. $\text{C-Carry, A-Auxiliary Carry, O-Overflow flag, P-Parity}$ ($0$ for even, $1$ for odd) $\text{R0}$ and $\text{R1}$ are the two general purpose registers of the micro-controller. After execution ...
In a given $8$-bit general purpose micro-controller there are following flags. $\text{C-Carry, A-Auxiliary Carry, O-Overflow flag, P-Parity}$ ($0$ for even, $1$ for odd) ...
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119
GATE Electrical 2023 | Question: 52
The closed curve shown in the figure is described by $r=1+\cos \theta,$ where $r=\sqrt{x^{2}+y^{2}} ; x=r \cos \theta, y=r \sin \theta$ The magnitude of the line integral of the vector field $ F=-y \hat{\imath}+x \hat{\jmath}$ around the closed curve is __________(Round off to $2$ decimal places).
The closed curve shown in the figure is described by $r=1+\cos \theta,$ where $r=\sqrt{x^{2}+y^{2}} ; x=r \cos \theta, y=r \sin \theta$ The magnitude of the line integra...
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