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362
GATE Electrical 2018 | Question: 22
A $1000 \times 1000$ bus admittance matrix for an electric power system has $8000$ non-zero elements. The minimum number of branches (transmission lines and transformers) in this system are _________ (up to $2$ decimal places).
A $1000 \times 1000$ bus admittance matrix for an electric power system has $8000$ non-zero elements. The minimum number of branches (transmission lines and transformers)...
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363
GATE Electrical 2015 Set 2 | Question: 47
A three-winding transformer is connected to an $AC$ voltage source as shown in the figure. The number of turns are as follows: $N_{1} = 100, N_{2} = 50, N_{3} = 50$ ... in Ampere? $1\angle 90^{\circ}$ $1\angle 270^{\circ}$ $4\angle 90^{\circ}$ $4\angle 270^{\circ}$
A three-winding transformer is connected to an $AC$ voltage source as shown in the figure. The number of turns are as follows: $N_{1} = 100, N_{2} = 50, N_{3} = 50$. If t...
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366
GATE Electrical 2012 | Question: 6
A system with transfer function $G(s) =\frac{(s^2+9)(s+2)}{(s+1)(s+3)(s+4)}$ is excited by $\sin (\omega t)$. The steady-state output of the system is zero at $\omega = 1 \text{ rad/s}$ $\omega = 2\text{ rad/s}$ $\omega = 3 \text{ rad/s}$ $\omega = 4 \text{ rad/s}$
A system with transfer function $$G(s) =\frac{(s^2+9)(s+2)}{(s+1)(s+3)(s+4)}$$ is excited by $\sin (\omega t)$. The steady-state output of the system is zero at$\omega = ...
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369
GATE Electrical 2015 Set 2 | Question: 55
For the system governed by the set of equations: $dx_{1}/dt=2x_{1}+x_{2}+u$ $dx_{2}/dt=-2x_{1}+u$ $y=3 x_{1}$ the transfer function $Y(s)/U(s)$ is given by $3(s+1)/(s^{2}-2s+2)$ $3(2s+1)/(s^{2}-2s+1)$ $(s+1)/(s^{2}-2s+1)$ $3(2s+1)/(s^{2}-2s+2)$
For the system governed by the set of equations:$dx_{1}/dt=2x_{1}+x_{2}+u$$dx_{2}/dt=-2x_{1}+u$$y=3 x_{1}$the transfer function $Y(s)/U(s)$ is given by$3(s+1)/(s^{2}-2s+2...
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370
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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373
GATE Electrical 2019 | Question: 34
In the circuit below, the operational amplifier is ideal. If $V_1=10$ mV and $V_2=50$ mV, he output voltage $(V_{\text{out}})$ is $100$ mV $400$ mV $500$ mV $600$ mV
In the circuit below, the operational amplifier is ideal. If $V_1=10$ mV and $V_2=50$ mV, he output voltage $(V_{\text{out}})$ is$100$ mV$400$ mV$500$ mV$600$ mV
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374
GATE Electrical 2019 | Question: 46
A $220$ V DC shunt motor takes $3$ A at no-load. It draws $25$ A when running at full-load at $1500$ rpm. The armature and shunt resistance are $0.5 \: \Omega$ and $220 \: \Omega$, respectively. The no-load speed in rpm (round off to two decimal places) is _____.
A $220$ V DC shunt motor takes $3$ A at no-load. It draws $25$ A when running at full-load at $1500$ rpm. The armature and shunt resistance are $0.5 \: \Omega$ and $220 \...
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375
GATE Electrical 2012 | Question: 10
The slip of an induction motor normally does not depend on rotor speed synchronous speed shaft torque core-loss component
The slip of an induction motor normally does not depend onrotor speedsynchronous speedshaft torquecore-loss component
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378
GATE Electrical 2017 Set 1 | Question: 22
Consider the unity feedback control system shown. The value of $K$ that results in a phase margin of the system to be $30^{\circ}$ is _________. (Give the answer up to two decimal places.)
Consider the unity feedback control system shown. The value of $K$ that results in a phase margin of the system to be $30^{\circ}$ is _________. (Give the answer up to tw...
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379
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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381
GATE Electrical 2019 | Question: 41
A $0.1 \mu F$ capacitor charged to $100$ V is discharged through a $1 \: k \Omega$ resistor. The time in ms (round off to two decimal places) required for the voltage across the capacitor to drop to $1$ V is _________
A $0.1 \mu F$ capacitor charged to $100$ V is discharged through a $1 \: k \Omega$ resistor. The time in ms (round off to two decimal places) required for the voltage acr...
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385
GATE Electrical 2020 | Question: 40
Let $a_{r},\:a_{\phi }$ and $a_{z}$ be unit vectors along $r,\:\phi$ and $z$ ... $z$-axis with its base at the origin is: $54\:\pi$ $90\:\pi$ $108\:\pi$ $180\:\pi$
Let $a_{r},\:a_{\phi }$ and $a_{z}$ be unit vectors along $r,\:\phi$ and $z$ directions, respectively in the cylindrical coordinate system. For the electric flux density ...
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392
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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393
GATE Electrical 2012 | Question: 40
Assuming both the voltages sources are in phase, the value of R for which maximum power is transferred from circuit A to circuit B is $0.8 \: \Omega$ $1.4 \: \Omega$ $2 \: \Omega$ $2.8 \: \Omega$
Assuming both the voltages sources are in phase, the value of R for which maximum power is transferred from circuit A to circuit B is$0.8 \: \Omega$$1.4 \: \Omega$$2 \: \...
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394
GATE Electrical 2012 | Question: 22
The sequence components of the fault current are as follows: $I_{\text{positive}} = j1.5$ pu, $I_{\text{negative}} =- j0.5$ pu, $I_{\text{zero}} = – j1$ pu. The type of fault in the system is LG LL LLG LLLG
The sequence components of the fault current are as follows: $I_{\text{positive}} = j1.5$ pu, $I_{\text{negative}} =- j0.5$ pu, $I_{\text{zero}} = – j1$ pu. The type of...
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395
GATE Electrical 2017 Set 2 | Question: 21
For the given $2$-port network, the value of transfer impedance $z_{21}$ in ohms is _________.
For the given $2$-port network, the value of transfer impedance $z_{21}$ in ohms is _________.
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396
GATE Electrical 2017 Set 2 | Question: 30
In the circuit shown below, the value of capacitor $C$ required for maximum power to be transferred to the load is $1$ nF $1 \mu F$ $1$ mF $10$ mF
In the circuit shown below, the value of capacitor $C$ required for maximum power to be transferred to the load is $1$ nF$1 \mu F$$1$ mF$10$ mF
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399
GATE Electrical 2022 | Question: 36
Let a casual $\text{LTI}$ system be governed by the following differential equation $y\left ( t \right ) + \dfrac{1}{4}\dfrac{dy}{dt} = 2x\left ( t \right )$, where $x(t)$ and $y(t)$ ... $8e^{-\frac{1}{4}t}u\left ( t \right )$ $8e^{-4t}u\left ( t \right )$
Let a casual $\text{LTI}$ system be governed by the following differential equation $y\left ( t \right ) + \dfrac{1}{4}\dfrac{dy}{dt} = 2x\left ( t \right )$, where $x(t)...
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400
GATE Electrical 2021 | Question: 31
The casual signal with $z$-transformer $Z^{2}\left ( Z-a \right )^{-2}$ is ($u[n]$ is the unit step signal) $a^{2n}u\left [ n \right ]$ $\left ( n+1 \right )a^{n}u\left [ n \right ]$ $n^{-1}a^{n}u\left [ n \right ]$ $n^{2}a^{n}u\left [ n \right ]$
The casual signal with $z$-transformer $Z^{2}\left ( Z-a \right )^{-2}$ is ($u[n]$ is the unit step signal)$a^{2n}u\left [ n \right ]$$\left ( n+1 \right )a^{n}u\left [ n...
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