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441

GATE Electrical 2017 Set 2 | Question: 8
Two resistors with nominal resistance values $R_{1}$ and $R_{2}$ have additive uncertainties $\bigtriangleup R_{1}$ and $\bigtriangleup R_{2}$, respectively. When these resistances are connected in parallel, the standard deviation of the error in the equivalent ...

Two resistors with nominal resistance values $R_{1}$ and $R_{2}$ have additive uncertainties $\bigtriangleup R_{1}$ and $\bigtriangleup R_{2}$, respectively. When these r...

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442

GATE Electrical 2017 Set 2 | Question: 9
A stationary closed Lissajous pattern on an oscilloscope has $3$ horizontal tangencies and $2$ vertical tangencies for a horizontal input with frequency $3$kHz. The frequency of the vertical input is $1.5$kHz $2$kHz $3$kHz $4.5$kHz

A stationary closed Lissajous pattern on an oscilloscope has $3$ horizontal tangencies and $2$ vertical tangencies for a horizontal input with frequency $3$kHz. The frequ...

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443

GATE Electrical 2017 Set 1 | Question: 19
The equivalent resistance between the terminals $A$ and $B$ is __________ $\Omega$.

The equivalent resistance between the terminals $A$ and $B$ is __________ $\Omega$.

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444

GATE Electrical 2017 Set 2 | Question: 34
The root locus of the feedback control system having the characteristic equation $s^{2}+6Ks+2s+5=0$ where $K>0$, enters into the real axis at. $s=-1$ $s=-\sqrt{5}$ $s=-5$ $s=\sqrt{5}$

The root locus of the feedback control system having the characteristic equation $s^{2}+6Ks+2s+5=0$ where $K>0$, enters into the real axis at.$s=-1$$s=-\sqrt{5}$$s=-5$$s=...

Arjun

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445

GATE Electrical 2017 Set 2 | Question: 29
For the balanced $Y-Y$ connected $3$-phase circuit shown in the figure below, the line-line voltage is $208$ V rms and the total power absorbed by the load is $432$ W at a power factor of $0.6$ leading. The approximate value of the impedance $Z$ ... $60 \angle 53.1^{\circ}\Omega $ $60 \angle -53.1^{\circ}\Omega $ $180 \angle -53.1^{\circ}\Omega $

For the balanced $Y-Y$ connected $3$-phase circuit shown in the figure below, the line-line voltage is $208$ V rms and the total power absorbed by the load is $432$ W at ...

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446

GATE Electrical 2017 Set 1 | Question: 35
The approximate transfer characteristic for the circuit shown below with an ideal operational amplifier and diode will be

The approximate transfer characteristic for the circuit shown below with an ideal operational amplifier and diode will be

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447

GATE Electrical 2017 Set 1 | Question: 54
The positive, negative, and zero sequence reactances of a wye-connected synchronous generator are $0.2$pu, $0.2$pu, and $0.1$pu, respectively. The generator is an open circuit with a terminal voltage of $1$pu. The minimum value of ... fault occurs at the terminals is ___________ (assume fault impedance to be zero). (Give the answer up to one decimal place.)

The positive, negative, and zero sequence reactances of a wye-connected synchronous generator are $0.2$pu, $0.2$pu, and $0.1$pu, respectively. The generator is an open ci...

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448

GATE Electrical 2017 Set 1 | Question: 52
The circuit shown in the figure uses matched transistors with a thermal voltage $V_{T}=25$m V. The base currents of the transistors are negligible. The value of the resistance $R$ in $k\Omega$ that is required to provide $1 \mu A$ bias current for the differential amplifier block shown is ________.(Give the answer up to one decimal place.)

The circuit shown in the figure uses matched transistors with a thermal voltage $V_{T}=25$m V. The base currents of the transistors are negligible. The value of the resis...

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449

GATE Electrical 2017 Set 1 | Question: 33
The transfer function of the system $Y(s)/U(s)$ ... $\frac{(s-4)}{(s^{2}+s-4)} \\ $ $\frac{(s+4)}{(s^{2}-s-4)} \\$

The transfer function of the system $Y(s)/U(s)$ whose state-space equations are given below is:$\begin{bmatrix} \dot{x}_{1}(t)\\ \dot{x}_{2}(t) \end{bmatrix}=\begin{bma...

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450

GATE Electrical 2017 Set 1 | Question: 32
In the system whose signal flow graph is shown in the figure, $U_{1}(s)$ and $U_{2}(s)$ are inputs. The transfer function $\frac{Y(s)}{U_{1}(s)}$ is $\frac{k_{1}}{J Ls^{2}+J Rs+k_{1}k_{2}}$ $\frac{k_{1}}{J Ls^{2}-J Rs-k_{1}k_{2}}$ ... $\frac{k_{1}-U_{2}(sL-R)}{J Ls^{2}-(J R+U_{2}L)s-k_{1}k_{2}+U_{2}R}$

In the system whose signal flow graph is shown in the figure, $U_{1}(s)$ and $U_{2}(s)$ are inputs. The transfer function $\frac{Y(s)}{U_{1}(s)}$ is$\frac{k_{1}}{J Ls^{2}...

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451

GATE Electrical 2017 Set 1 | Question: 5
Consider an electron, a neutron and a proton initially at rest and placed along a straight line such that the neutron is exactly at the center of the line joining the electron and proton. At $t=0$, the particles are released ... these will collide first? The particles will never collide. All will collide together. Proton and neutron. Electron and neutron.

Consider an electron, a neutron and a proton initially at rest and placed along a straight line such that the neutron is exactly at the center of the line joining the ele...

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452

GATE Electrical 2017 Set 1 | Question: 6
The transfer function of a system is given by, $\frac{V_{0}(s)}{V_{i}(s)}=\frac{1-s}{1+s}$ Let the output of the system be $v_{0}(t)=V_{m} \sin (\omega t + \varphi )$ for the input, $v_{i}(t)=V_{m} \sin (\omega t )$. Then the minimum and maximum values of ... $\frac{\pi}{2}$ $\frac{-\pi}{2}$ and $0$ $0$ and $\frac{\pi}{2}$ $-\pi$ and $0$

The transfer function of a system is given by,$\frac{V_{0}(s)}{V_{i}(s)}=\frac{1-s}{1+s}$Let the output of the system be $v_{0}(t)=V_{m} \sin (\omega t + \varphi )$ for t...

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453

GATE Electrical 2017 Set 1 | Question: 11
A closed loop system has the characteristic equation given by $s^{3}+Ks^{2}+(K+2)s+3=0$. For this system to be stable, which one of the following conditions should be satisfied? $0 < K < 0.5$ $0.5 < K < 1$ $0 < K < 1$ $K > 1$

A closed loop system has the characteristic equation given by $s^{3}+Ks^{2}+(K+2)s+3=0$. For this system to be stable, which one of the following conditions should be sat...

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454

GATE Electrical 2017 Set 2 | Question: 33
A $220$ V, $10$ kW, $900$ rpm separately excited $DC$ motor has an armature resistance $R_{a}=0.02 \Omega$. When the motor operates at rated speed and with rated terminal voltage, the electromagnetic torque developed by the motor is $70$Nm. Neglecting the ... the current drawn by the motor from the $220$V supply is $34.2$ A $30$ A $22$ A $4.84$ A

A $220$ V, $10$ kW, $900$ rpm separately excited $DC$ motor has an armature resistance $R_{a}=0.02 \Omega$. When the motor operates at rated speed and with rated terminal...

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455

GATE Electrical 2017 Set 2 | Question: 7
The transfer function $C(s)$ of a compensator is given below. $C(s)=\frac{(1+\frac{s}{0.1})(1+\frac{s}{100})}{(1+s)(1+\frac{s}{10})}$ The frequency range in which the phase (lead) introduced by the compensator reaches the maximum is $0.1 < \omega < 1$ $1 < \omega < 10$ $10 < \omega < 100$ $ \omega > 100$

The transfer function $C(s)$ of a compensator is given below.$C(s)=\frac{(1+\frac{s}{0.1})(1+\frac{s}{100})}{(1+s)(1+\frac{s}{10})}$The frequency range in which the phase...

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456

GATE Electrical 2017 Set 2 | Question: 17
Assume that in traffic junction, the cycle of the traffic signal lights is $2$ minutes of green (Vehicle does not stop) and $3$ minutes of red (Vehicle stops). Consider that the arrival time of vehicles at the junction is uniformly distributed over $5$ minute cycle. The expected waiting time (in minutes) for the vehicle at the junction is ________.

Assume that in traffic junction, the cycle of the traffic signal lights is $2$ minutes of green (Vehicle does not stop) and $3$ minutes of red (Vehicle stops). Consider t...

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457

GATE Electrical 2017 Set 1 | Question: 25
A $3$-phase voltage source inverter is supplied from a $600V$ DC source as shown in the figure below. For a star connected resistive load of $20\Omega$ per phase, the load power for $120^{\circ}$ device conduction, in kW, is ________.

A $3$-phase voltage source inverter is supplied from a $600V$ DC source as shown in the figure below. For a star connected resistive load of $20\Omega$ per phase, the loa...

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458

GATE Electrical 2017 Set 1 | Question: 29
The passive two-port networks are connected in cascade as shown in figure. A voltage source is connected at port $1$. Given $V_{1}=A_{1}V_{2}+B_{1}I_{2}$ $I_{1}=C_{1}V_{2}+D_{1}I_{2}$ $V_{2}=A_{2}V_{3}+B_{2}I_{3}$ $I_{2}=C_{2}V_{3}+D_{2}I_{3}$ ...

The passive two-port networks are connected in cascade as shown in figure. A voltage source is connected at port $1$.Given$V_{1}=A_{1}V_{2}+B_{1}I_{2}$$I_{1}=C_{1}V_{2}+D...

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459

GATE Electrical 2017 Set 1 | Question: 39
A load is supplied by a $230$ V, $50$ Hz source. The active power $P$ and the reactive power $Q$ consumed by the load are such that $1kW \leq P \leq 2kW$ and $1kVAR \leq Q \leq 2kVAR$. A capacitor connected across the load for power factor ... power factor after power factor correction is $0.447 \text{ lag}$ $0.707 \text{ lag}$ $0.894 \text{ lag}$ $1$

A load is supplied by a $230$ V, $50$ Hz source. The active power $P$ and the reactive power $Q$ consumed by the load are such that $1kW \leq P \leq 2kW$ and $1kVAR \leq ...

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GATE Electrical 2017 Set 1 | Question: 3
Let $z(t) = x(t) *y(t)$, where "*" denotes convolution. Let $c$ be a positive real-valued constant. Choose the correct expression for $z(ct)$. $c . x(ct) * y (ct)$ $x (ct) * y (ct)$ $c . x (t) * y(ct)$ $c . x (ct) * y(t)$

Let $z(t) = x(t) *y(t)$, where "*" denotes convolution. Let $c$ be a positive real-valued constant. Choose the correct expression for $z(ct)$.$c . x(ct) * y (ct)$$x (ct) ...

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