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162
GATE Electrical 2022 | Question: 32
Consider a matrix $A = \begin{bmatrix} 1 & 0 & 0\\ 0 & 4 & -2\\ 0 & 1 & 1 \end{bmatrix}$. The matrix $A$ satisfies the equation $6A^{-1} = A^{2} + cA + dl$, where $c$ and $d$ are scalars and $I$ is the identity matrix. Then $\left ( c + d \right )$ is equal to $5$ $17$ $-6$ $11$
Consider a matrix $A = \begin{bmatrix} 1 & 0 & 0\\ 0 & 4 & -2\\ 0 & 1 & 1 \end{bmatrix}$.The matrix $A$ satisfies the equation $6A^{-1} = A^{2} + cA + dl$, where $c$ and ...
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163
GATE Electrical 2022 | Question: 44
Let the probability density function of a random variable $x$ be given as $f\left ( x \right ) = ae^{-2\left | x \right |}$ The value of $’a’$ is _________________.
Let the probability density function of a random variable $x$ be given as $$f\left ( x \right ) = ae^{-2\left | x \right |}$$ The value of $’a’$ is _________________....
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165
GATE Electrical 2022 | Question: 34
The current gain $( I_{\text{out}}/I_{\text{in}})$ in the circuit with an ideal current amplifier given below is $\dfrac{C_{f}}{C_{c}}$ $\dfrac{-C_{f}}{C_{c}}$ $\dfrac{C_{c}}{C_{f}}$ $\dfrac{-C_{c}}{C_{f}}$
The current gain $( I_{\text{out}}/I_{\text{in}})$ in the circuit with an ideal current amplifier given below is$\dfrac{C_{f}}{C_{c}}$$\dfrac{-C_{f}}{C_{c}}$$\dfrac{C_{c}...
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166
GATE Electrical 2022 | Question: 36
Let a casual $\text{LTI}$ system be governed by the following differential equation $y\left ( t \right ) + \dfrac{1}{4}\dfrac{dy}{dt} = 2x\left ( t \right )$, where $x(t)$ and $y(t)$ ... $8e^{-\frac{1}{4}t}u\left ( t \right )$ $8e^{-4t}u\left ( t \right )$
Let a casual $\text{LTI}$ system be governed by the following differential equation $y\left ( t \right ) + \dfrac{1}{4}\dfrac{dy}{dt} = 2x\left ( t \right )$, where $x(t)...
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167
GATE Electrical 2022 | Question: 35
If the magnetic field intensity $(H)$ in a conducting region is given by the expression. $H = x^{2} \hat{i} + x^{2}y^{2}\hat{j} + x^{2}y^{2}z^{2}k$ $\text{A/m}$. The magnitude of the current density, in $A/m^{2}$, at $x = 1\;m, y = 2\; m$ and $z = 1\; m$, is $8$ $12$ $16$ $20$
If the magnetic field intensity $(H)$ in a conducting region is given by the expression. $H = x^{2} \hat{i} + x^{2}y^{2}\hat{j} + x^{2}y^{2}z^{2}k$ $\text{A/m}$. The magn...
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171
GATE Electrical 2022 | Question: 40
Let, $f\left ( x,y, z \right ) = 4x^{2} + 7xy + 3xz^{2}$. The direction in which the function $\text{f(x, y, z)}$ increases most rapidly at point $P = (1,0,2)$ is $20\hat{i} + 7\hat{j}$ $20\hat{i} + 7\hat{j} + 12\hat{k}$ $20\hat{i} + 12\hat{k}$ $20\hat{i}$
Let, $f\left ( x,y, z \right ) = 4x^{2} + 7xy + 3xz^{2}$. The direction in which the function $\text{f(x, y, z)}$ increases most rapidly at point $P = (1,0,2)$ is$20\hat{...
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173
GATE Electrical 2022 | Question: 37
Let an input $x\left ( t \right ) = 2 \sin \left ( 10 \pi t \right ) + 5 \cos \left ( 15 \pi t \right ) + 7 \sin \left ( 42 \pi t \right ) + 4 \cos \left ( 45 \pi t \right )$ is passed through an $\text{LTI}$ ... $2 \sin \left ( 10 \pi t \right ) + 4 \cos \left ( 45 \pi t \right )$
Let an input $x\left ( t \right ) = 2 \sin \left ( 10 \pi t \right ) + 5 \cos \left ( 15 \pi t \right ) + 7 \sin \left ( 42 \pi t \right ) + 4 \cos \left ( 45 \pi t \righ...
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174
GATE Electrical 2022 | Question: 45
In the circuit shown below, the magnitude of the voltage $V_{1}$ in volts, across the $8\:k\Omega$ resistor is ______. (round off to nearest integer)
In the circuit shown below, the magnitude of the voltage $V_{1}$ in volts, across the $8\:k\Omega$ resistor is ______. (round off to nearest integer)
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175
GATE Electrical 2022 | Question: 43
As shown in the figure below, two concentric conducting spherical shells, centered at $r = 0$ and having radii $r = c$ and $r = d$ are maintained at potentials such that the potential $\text{V(r)}$ at $r = c$ is $V_{1}$ and $\text{V(r)}$ at $r = d$ is $V_{2}$. Assume ...
As shown in the figure below, two concentric conducting spherical shells, centered at $r = 0$ and having radii $r = c$ and $r = d$ are maintained at potentials such that ...
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177
GATE Electrical 2019 | Question: 19
The current $I$ is flowing in the circuit shown below in amperes (round off to one decimal place) is _________
The current $I$ is flowing in the circuit shown below in amperes (round off to one decimal place) is _________
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179
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180
GATE Electrical 2021 | Question: 48
The waveform shown in solid line is obtained by clipping a full-wave rectified sinusoid (shown dashed). The ratio of the $\text{RMS}$ value of the full-wave rectified waveform to the $\text{RMS}$ value of the clipped waveform is _______________. (Round off to $2$ decimal places.)
The waveform shown in solid line is obtained by clipping a full-wave rectified sinusoid (shown dashed). The ratio of the $\text{RMS}$ value of the full-wave rectified wav...
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181
GATE Electrical 2021 | Question: 4
For the network shown, the equivalent Thevenin voltage and Thevenin impedance as seen across terminals ‘$\text{ab}$’ is $\text{10 V}$ in series with $12\:\Omega$ $\text{65 V}$ in series with $15\:\Omega$ $\text{50 V}$ in series with $2\:\Omega$ $\text{35 V}$ in series with $2\:\Omega$
For the network shown, the equivalent Thevenin voltage and Thevenin impedance as seen across terminals ‘$\text{ab}$’ is$\text{10 V}$ in series with $12\:\Omega$$\text...
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182
GATE Electrical 2021 | Question: 39
A three-phase balanced voltage is applied to the load shown. The phase sequence is $\text{RYB}$. The ratio $\frac{\left | I_{B} \right |}{|I_{R}|}$ is ____________.
A three-phase balanced voltage is applied to the load shown. The phase sequence is $\text{RYB}$. The ratio $\frac{\left | I_{B} \right |}{|I_{R}|}$ is ____________.
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186
GATE Electrical 2021 | Question: 8
Consider the table given: ... $\text{P-T-Y, Q-V-Z, R-S-X}$ $\text{P-U-X, Q-V-Y, R-T-Z}$
Consider the table given:$\begin{array}{|cl|cI|cI|}\hline&\textbf{Constructional feature} & \textbf{Machine type} & \textbf{Mitigation} \\ \hline &\text{P. Damper bars} ...
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187
GATE Electrical 2021 | Question: 35
A $3$-Bus network is shown. Consider generators as ideal voltage sources. If rows $1,\:2$ and $3$ of the $Y_{Bus}$ matrix correspond to Bus $1,\:2$ and $3$, respectively, then $Y_{Bus}$ ...
A $3$-Bus network is shown. Consider generators as ideal voltage sources. If rows $1,\:2$ and $3$ of the $Y_{Bus}$ matrix correspond to Bus $1,\:2$ and $3$, respectively,...
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190
GATE Electrical 2021 | Question: 50
An air-core radio-frequency transformer as shown has a primary winding and a secondary winding. The mutual inductance $M$ between the windings of the transformer is ____________ $\mu H$.(Round off to $2$ decimal places.)
An air-core radio-frequency transformer as shown has a primary winding and a secondary winding. The mutual inductance $M$ between the windings of the transformer is _____...
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191
GATE Electrical 2021 | Question: 6
If the input $x(t)$ and output $y(t)$ of a system are related as $y\left ( t \right )=\text{max}\left ( 0,x\left ( t \right ) \right ),$ then the system is linear and time-variant linear and time-invariant non-linear and time-variant non-linear and time-invariant
If the input $x(t)$ and output $y(t)$ of a system are related as $y\left ( t \right )=\text{max}\left ( 0,x\left ( t \right ) \right ),$ then the system islinear and time...
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192
GATE Electrical 2021 | Question: 30
The input impedance, $Z_{in}\left ( s \right )$ for the network shown is $\frac{23s^{2}+46s+20}{4s+5}$ $6s+4$ $7s+4$ $\frac{25s^{2}+46s+20}{4s+5}$
The input impedance, $Z_{in}\left ( s \right )$ for the network shown is$\frac{23s^{2}+46s+20}{4s+5}$$6s+4$$7s+4$$\frac{25s^{2}+46s+20}{4s+5}$
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193
GATE Electrical 2021 | Question: 20
The Bode magnitude plot for the transfer function $\frac{V_{o}\left ( s \right )}{V_{i}\left ( s \right )}$ of the circuit is as shown. The value of $R$ is _____________$\Omega$. (Round off to $2$ decimal places.)
The Bode magnitude plot for the transfer function $\frac{V_{o}\left ( s \right )}{V_{i}\left ( s \right )}$ of the circuit is as shown. The value of $R$ is _____________$...
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195
GATE Electrical 2021 | Question: 14
In the given circuit, the value of capacitor $C$ that makes current $I=0$ is ________________ $\mu F$.
In the given circuit, the value of capacitor $C$ that makes current $I=0$ is ________________ $\mu F$.
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197
GATE Electrical 2021 | Question: 24
In the circuit shown, the input $V_{i}$ is a sinusoidal $\text{AC}$ voltage having an $\text{RMS}$ value of $230\;V\pm 20\%$. The worst-case peak-inverse voltage seen across any diode is ____________$V$. (Round off to $2$ decimal places.)
In the circuit shown, the input $V_{i}$ is a sinusoidal $\text{AC}$ voltage having an $\text{RMS}$ value of $230\;V\pm 20\%$. The worst-case peak-inverse voltage seen ac...
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198
GATE Electrical 2021 | Question: 11
For the closed-loop system shown, the transfer function $\dfrac{E\left ( s \right )}{R\left ( s \right )}$ is $\frac{G}{1+GH}$ $\frac{GH}{1+GH}$ $\frac{1}{1+GH}$ $\frac{1}{1+G}$
For the closed-loop system shown, the transfer function $\dfrac{E\left ( s \right )}{R\left ( s \right )}$ is$\frac{G}{1+GH}$$\frac{GH}{1+GH}$$\frac{1}{1+GH}$$\frac{1}{1+...
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199
GATE Electrical 2021 | Question: 16
In the given circuit, for voltage $V_y$ to be zero, the value of $\beta$ should be _________. (Round off to $2$ decimal places).
In the given circuit, for voltage $V_y$ to be zero, the value of $\beta$ should be _________. (Round off to $2$ decimal places).
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200
GATE Electrical 2021 | Question: 23
In the $\text{BJT}$ circuit shown, beta of the $\text{PNP}$ transistor is $100$. Assume $V_{\text{BE}}=-0.7\;V$. The voltage across $R_{c}$ will be $\text{5 V}$ when $R_{2}$ is __________ $k \Omega$. (Round off to $2$ decimal places.)
In the $\text{BJT}$ circuit shown, beta of the $\text{PNP}$ transistor is $100$. Assume $V_{\text{BE}}=-0.7\;V$. The voltage across $R_{c}$ will be $\text{5 V}$ when $R_{...
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