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441

GATE Electrical 2018 | Question: 16
A continuous-time input signal $x(t)$ is an eigenfunction of an LTI system, if the output is $k \: x(t)$, where $k$ is an eigenvalue $k \: e^{j \omega t} \: x(t)$, where $k$ is an eigenvalue and $e^{j \omega t}$ is a complex ... $k \: H(\omega)$, where $k$ is an eigenvalue and $H(\omega)$ is a frequency response of the system

A continuous-time input signal $x(t)$ is an eigenfunction of an LTI system, if the output is$k \: x(t)$, where $k$ is an eigenvalue$k \: e^{j \omega t} \: x(t)$, where $k...

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442

GATE Electrical 2018 | Question: 11
Let $f$ be a real-valued function of a real variable defined as $f(x)=x^2$ for $x \geq 0$, and $f(x)=-x^2$ for $x<0$. Which one of the following statements is true? $f(x)$ is discontinuous at $x=0$ $f(x)$ ... is differentiable but its first derivative is not continuous at $x=0$ $f(x)$ is differentiable but its first derivative is not differentiable at $x=0$

Let $f$ be a real-valued function of a real variable defined as $f(x)=x^2$ for $x \geq 0$, and $f(x)=-x^2$ for $x<0$. Which one of the following statements is true?$f(x)$...

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443

GATE Electrical 2018 | Question: 8
In the figure, the voltages are $v_1(t)=100 \cos (\omega t)$, $v_2(t)=100 \cos (\omega t + \pi /18)$ and $v_3(t)=100 \cos (\omega t + \pi / 36)$. The circuit is in sinusoidal steady state, and $R< < \omega L$. $P_1$, $P_2$ and $P_3$ are the ... $P_1 <0$, $P_2>0$, $P_3>0$ $P_1 <0$, $P_2>0$, $P_3<0$ $P_1 > 0$, $P_2<0$, $P_3>0$

In the figure, the voltages are $v_1(t)=100 \cos (\omega t)$, $v_2(t)=100 \cos (\omega t + \pi /18)$ and $v_3(t)=100 \cos (\omega t + \pi / 36)$. The circuit is in sinuso...

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444

GATE Electrical 2018 | Question: 9
Match the transfer functions of the second-order systems with the nature of the systems given below. ... P-I, Q-II, R-III P-II, Q-I, R-III P-III, Q-II, R-I P-III, Q-I, R-II

Match the transfer functions of the second-order systems with the nature of the systems given below.$\begin{array} {} \underline{\textit{Transfer functions}} & \underline...

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445

GATE Electrical 2018 | Question: 10
A positive charge of $1$ nC is placed at $(0,0,0.2)$ where all dimensions are in meters. Consider the $x-y$ plane to be a conducting ground plane. Take $\epsilon_0 = 8.85 \times 10^{-12}$ F/m. The $Z$ component of the E field at $(0,0,0.1)$ is closest to $899.18$ V/m $-899.18$ V/m $999.09$ V/m $-999.09$ V/m

A positive charge of $1$ nC is placed at $(0,0,0.2)$ where all dimensions are in meters. Consider the $x-y$ plane to be a conducting ground plane. Take $\epsilon_0 = 8.85...

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446

GATE Electrical 2018 | Question: 12
The value of the directional derivative of the function $\Phi (x,y,z) = xy^2 +yz^2+zx^2$ at the point $(2,-1,1)$ in the direction of the vector $\textbf{p}= \textbf{i} +2 \textbf{j} + 2 \textbf{k}$ is $1$ $0.95$ $0.93$ $0.9$

The value of the directional derivative of the function $\Phi (x,y,z) = xy^2 +yz^2+zx^2$ at the point $(2,-1,1)$ in the direction of the vector $\textbf{p}= \textbf{i} +2...

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447

GATE Electrical 2018 | Question: 13
The value of the integral $\oint _c \frac{z+1}{z^2-4} dz$ in counter clockwise direction around a circle $C$ of radius $1$ with center at the point $z=-2$ is $\frac{\pi i}{2} \\ $ $2 \pi i\\$ $ – \frac{\pi i}{2}\\$ $-2 \pi i$

The value of the integral $\oint _c \frac{z+1}{z^2-4} dz$ in counter clockwise direction around a circle $C$ of radius $1$ with center at the point $z=-2$ is$\frac{\pi i}...

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448

GATE Electrical 2018 | Question: 15
The op-amp shown in the figure is ideal. The input impedance $\frac{v_{\text{in}}}{i_{\text{in}}}$ is given by $Z \frac{R_1}{R_2}$ $ – Z \frac{R_2}{R_1}$ $Z$ $ – Z \frac{R_1}{R_1 + R_2}$

The op-amp shown in the figure is ideal. The input impedance $\frac{v_{\text{in}}}{i_{\text{in}}}$ is given by$Z \frac{R_1}{R_2}$$ – Z \frac{R_2}{R_1}$$Z$$ – Z \frac{...

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449

GATE Electrical 2018 | Question: 7
The graph of a network has $8$ nodes and $5$ independent loops. The number of branches of the graph is $11$ $12$ $13$ $14$

The graph of a network has $8$ nodes and $5$ independent loops. The number of branches of the graph is$11$$12$$13$$14$

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450

GATE Electrical 2018 | Question: 6
Consider a lossy transmission line with $V_1$ and $V_2$ as the sending and receiving end voltages, respectively. $Z$ and $X$ are the series impedance and reactance of the line, respectively. The steady-state stability limit for the transmission line will be greater ... $ \begin{vmatrix} \frac{V_1V_2}{Z} \end{vmatrix} \\ $

Consider a lossy transmission line with $V_1$ and $V_2$ as the sending and receiving end voltages, respectively. $Z$ and $X$ are the series impedance and reactance of the...

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451

GATE Electrical 2018 | Question: 5
Two wattmeter method is used for measurement of power in a balanced three-phase load supplied from a balanced three-phase system. If one of the wattmeters reads half of the other (both positive), then the power factor of the load is $0.532$ $0.632$ $0.707$ $0.866$

Two wattmeter method is used for measurement of power in a balanced three-phase load supplied from a balanced three-phase system. If one of the wattmeters reads half of t...

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452

GATE Electrical 2018 | Question: 4
Four power semiconductor devices are shown in the figure along with their relevant terminals. The device(s) that can carry dc current continuously in the direction shown when gated appropriately is (are) Triac only Triac and MOSFET Triac and GTO Thyristor and Triac

Four power semiconductor devices are shown in the figure along with their relevant terminals. The device(s) that can carry dc current continuously in the direction shown ...

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453

GATE Electrical 2018 | Question: 3
A single phase fully controlled rectifier is supplying a load with an anti-parallel diode as shown in the figure. All switches and diodes are ideal. Which one of the following is true for instantaneous load voltage and current? $v_o \geq 0$ & $i_o<0$ $v_o < 0$ & $i_o <0$ $v_o \geq 0$ & $i_o \geq 0$ $v_0 < 0$ & $i_o\geq 0$

A single phase fully controlled rectifier is supplying a load with an anti-parallel diode as shown in the figure. All switches and diodes are ideal. Which one of the foll...

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454

GATE Electrical 2018 | Question: 2
In a salient pole synchronous motor, the developed reluctance torque attains the maximum value when the load angle in electrical degrees is $0$ $45$ $60$ $90$

In a salient pole synchronous motor, the developed reluctance torque attains the maximum value when the load angle in electrical degrees is$0$$45$$60$$90$

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455

GATE Electrical 2018 | Question: 1
A single-phase $100$ kVA, $1000$ V / $100$ V, $50$ Hz transformer has a voltage has a voltage drop of $5 \%$ across its series impedance at full load. Of this, $3\%$ is due to resistance. The percentage regulation of the transformer at full load with $0.8$ lagging power factor is $4.8$ $6.8$ $8.8$ $10.8$

A single-phase $100$ kVA, $1000$ V / $100$ V, $50$ Hz transformer has a voltage has a voltage drop of $5 \%$ across its series impedance at full load. Of this, $3\%$ is d...

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456

GATE Electrical 2017 Set 2 | GA Question: 10
An air pressure contour line joins locations in a region having the same atmospheric pressure. The following is an air pressure contour plot of a geographical region. Contour lines are shown at $0.05$ bar intervals in this plot. If a possibility of a ... over a region, which of the following regions is most likely to have a thunderstorm? $P$ $Q$ $R$ $S$

An air pressure contour line joins locations in a region having the same atmospheric pressure. The following is an air pressure contour plot of a geographical region. Con...

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457

GATE Electrical 2017 Set 2 | GA Question: 9
The number of roots of $e^{x}+0.5x^{2}-2=0$ in the range $[-5, 5]$ is $0$ $1$ $2$ $3$

The number of roots of $e^{x}+0.5x^{2}-2=0$ in the range $[-5, 5]$ is$0$$1$$2$$3$

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458

GATE Electrical 2017 Set 2 | GA Question: 8
$X$ is a $30$ digit number starting with the digit $4$ followed by the digit $7$. Then the number $X^{3}$ will have $90$ digits $91$ digits $92$ digits $93$ digits

$X$ is a $30$ digit number starting with the digit $4$ followed by the digit $7$. Then the number $X^{3}$ will have$90$ digits$91$ digits$92$ digits$93$ digits

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459

GATE Electrical 2017 Set 2 | GA Question: 7
There are three boxes. One contains apples, another contains oranges and the last one contains both apples and oranges. All three are known to be incorrectly labelled. If you are permitted to open just one box and then pull ... 'Apples'. The box labelled 'Apples and Oranges'. The box labelled 'Oranges'. Cannot be determined.

There are three boxes. One contains apples, another contains oranges and the last one contains both apples and oranges. All three are known to be incorrectly labelled. If...

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460

GATE Electrical 2017 Set 2 | GA Question: 5
There are $3$ red socks, $4$ green socks and $3$ blue socks. You choose $2$ socks. The probability that they are of the same colour is $1/5$ $7/30$ $1/4$ $4/15$

There are $3$ red socks, $4$ green socks and $3$ blue socks. You choose $2$ socks. The probability that they are of the same colour is$1/5$$7/30$$1/4$$4/15$

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461

GATE Electrical 2017 Set 2 | GA Question: 4
A test has twenty questions worth $100$ marks in total. There are two types of questions. Multiple choice questions are worth $3$ marks each and essay questions are worth $11$ marks each. How many multiple choice questions does the exam have? $12$ $15$ $18$ $19$

A test has twenty questions worth $100$ marks in total. There are two types of questions. Multiple choice questions are worth $3$ marks each and essay questions are worth...

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462

GATE Electrical 2017 Set 2 | GA Question: 3
There are five buildings called $V, W, X, Y$ and $Z$ in a row (not necessarily in that order). $V$ is to the West of $W . Z$ is to the East of $X$ and the West of $V$. $W$ is to the West of $Y$. Which is the building in the middle? $V$ $W$ $X$ $Y$

There are five buildings called $V, W, X, Y$ and $Z$ in a row (not necessarily in that order). $V$ is to the West of $W . Z$ is to the East of $X$ and the West of $V$. $W...

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463

GATE Electrical 2017 Set 2 | GA Question: 2
Saturn is _______ to be seen on a clear night with the naked eye. Enough bright Bright enough As enough bright Bright as enough

Saturn is _______ to be seen on a clear night with the naked eye.Enough brightBright enoughAs enough brightBright as enough

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464

GATE Electrical 2017 Set 2 | Question: 55
A thin soap bubble of radius $R=1$ cm, and thickness $a=3.3 \mu m (a << R)$, is at a potential of $1$ V with respect to a reference point at infinity. The bubble bursts and becomes a single spherical drop ... resulting single spherical drop with respect to the same reference point at infinity is _________. (Give the answer up to two decimal places.)

A thin soap bubble of radius $R=1$ cm, and thickness $a=3.3 \mu m (a << R)$, is at a potential of $1$ V with respect to a reference point at infinity. The bubble bursts a...

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465

GATE Electrical 2017 Set 2 | Question: 54
A $3$-phase, $2$-pole, $50$Hz, synchronous generator has a rating of $250$ MVA, $0.8$ pf lagging. The kinetic energy of the machine at synchronous speed is $1000$MJ. The machine is running steadily at synchronous speed ... assuming the acceleration is constant for $10$ cycles, the value of the power angle after $5$ cycles is __________ electrical degrees.

A $3$-phase, $2$-pole, $50$Hz, synchronous generator has a rating of $250$ MVA, $0.8$ pf lagging. The kinetic energy of the machine at synchronous speed is $1000$MJ. The ...

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466

GATE Electrical 2017 Set 2 | Question: 53
Two generating units rated $300$MW and $400$MW have governor speed regulation of $6 \%$ and $4 \%$ respectively from no load to full load. Both the generating units are operating in parallel to share a load of $600$MW. Assuming free governor action, the load shared by the larger unit is _________ MW.

Two generating units rated $300$MW and $400$MW have governor speed regulation of $6 \%$ and $4 \%$ respectively from no load to full load. Both the generating units are o...

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467

GATE Electrical 2017 Set 2 | Question: 52
A $3$-phase, $50$Hz generator supplies power of $3$MW at $17.32$kV to a balanced $3$-phase inductive load through an overhead line. The per phase line resistance and reactance are $0.25 \Omega$ and $3.925 \Omega$ respectively. If the voltage at the generator terminal is $17.87$kV, the power factor of the load is ________.

A $3$-phase, $50$Hz generator supplies power of $3$MW at $17.32$kV to a balanced $3$-phase inductive load through an overhead line. The per phase line resistance and reac...

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468

GATE Electrical 2017 Set 2 | Question: 51
Consider an overhead transmission line with $3$-phase, $50$ Hz balanced system with conductors located at the vertices of an equilateral triangle of length $D_{ab}=D_{bc}=D_{ca}=1m$ as shown in figure below. The resistance of the ... of ground, the magnitude of positive sequence reactance in $\Omega/km$ (rounded off to three decimal places) is _________.

Consider an overhead transmission line with $3$-phase, $50$ Hz balanced system with conductors located at the vertices of an equilateral triangle of length $D_{ab}=D_{bc}...

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469

GATE Electrical 2017 Set 2 | Question: 50
In the circuit shown all elements are ideal and the switch $S$ is operated at $10$kHz and $60 \%$ duty ratio. The capacitor is large enough so that the ripple across it is negligible and at steady state acquires a voltage as shown. The peak current in amperes drawn from the $50$ V DC source is _______.(Give the answer up to one decimal place.)

In the circuit shown all elements are ideal and the switch $S$ is operated at $10$kHz and $60 \%$ duty ratio. The capacitor is large enough so that the ripple across it i...

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470

GATE Electrical 2017 Set 2 | Question: 49
For the synchronous sequential circuit shown below, the output $Z$ is zero for the initial conditions $Q_{A}, Q_{B}, Q_{C}= Q'_{A}, Q'_{B}, Q'_{C}=100$ The minimum number of clock cycles after which the output $Z$ would again become zero is _________.

For the synchronous sequential circuit shown below, the output $Z$ is zero for the initial conditions $Q_{A}, Q_{B}, Q_{C}= Q'_{A}, Q'_{B}, Q'_{C}=100$The minimum number ...

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471

GATE Electrical 2017 Set 2 | Question: 48
In the circuit shown in the figure, the diode used is ideal. The input power factor is ________. (Give the answer up to two decimal places).

In the circuit shown in the figure, the diode used is ideal. The input power factor is ________. (Give the answer up to two decimal places).

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472

GATE Electrical 2017 Set 2 | Question: 47
A $10 \frac{1}{2}$ digit timer counter possesses a base clock of frequency $100$ MHz. When measuring a particular input, the reading obtained is the same in: Frequency mode of operation with a gating time of one second and Period mode of operation (in the $\times 10$ns scale). The frequency of the unknown input (reading obtained) in Hz is _______.

A $10 \frac{1}{2}$ digit timer counter possesses a base clock of frequency $100$ MHz. When measuring a particular input, the reading obtained is the same in:Frequency mod...

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473

GATE Electrical 2017 Set 2 | Question: 46
Consider the system described by the following state space representation ... $y(t)$ at $t=1$ sec (rounded off to three decimal places) is ___________.

Consider the system described by the following state space representation$\begin{bmatrix}\dot{x}_{1}(t)\\\dot{x}_{2}(t)\end{bmatrix}=\begin{bmatrix}0 &1 \\0 & -2\end{bmat...

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474

GATE Electrical 2017 Set 2 | Question: 45
If the primary line voltage rating is $3.3$kV (Y side) of a $25$kVA, $Y-\Delta$ transformer (the per phase turns ratio is $5:1$), then the line current rating of the secondary side (in Ampere) is _______.

If the primary line voltage rating is $3.3$kV (Y side) of a $25$kVA, $Y-\Delta$ transformer (the per phase turns ratio is $5:1$), then the line current rating of the seco...

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475

GATE Electrical 2017 Set 2 | Question: 44
A $25$ kVA, $400$ V, $\Delta$-connected, $3$-phase, cylindrical rotor synchronous generator requires a field current of $5$ A to maintain the rated armature current under short-circuit condition. For the same field current, the open ... terminal voltage), when the generator delivers the rated load at $0.8$ pf leading, at rated terminal voltage is _________.

A $25$ kVA, $400$ V, $\Delta$-connected, $3$-phase, cylindrical rotor synchronous generator requires a field current of $5$ A to maintain the rated armature current under...

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476

GATE Electrical 2017 Set 2 | Question: 43
A star-connected, $12.5$kW, $208$ V (line), $3$-phase, $60$ ... starting current (in Ampere) for this motor when connected to an $80$ V (line), $20$ Hz, $3$-phase AC source is _________.

A star-connected, $12.5$kW, $208$ V (line), $3$-phase, $60$Hz squirrel cage induction motor has following equivalent circuit parameters per phase referred to the stator: ...

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477

GATE Electrical 2017 Set 2 | Question: 42
A $120$ V DC shunt motor takes $2$A at no load. It takes $7$A on full load while running at $1200$ rpm. The armature resistance is $0.8 \Omega$, and the shunt field resistance is $240 \Omega$. The no load speed, in rpm, is _________.

A $120$ V DC shunt motor takes $2$A at no load. It takes $7$A on full load while running at $1200$ rpm. The armature resistance is $0.8 \Omega$, and the shunt field resis...

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478

GATE Electrical 2017 Set 2 | Question: 41
For the network given in the figure below, the Thevenin's voltage $V_{ab}$ is $-1.5$V $-0.5$V $0.5$V $1.5$V

For the network given in the figure below, the Thevenin's voltage $V_{ab}$ is$-1.5$V$-0.5$V$0.5$V$1.5$V

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479

GATE Electrical 2017 Set 2 | Question: 40
A person decides to toss a fair coin repeatedly until he gets a head. He will make at most $3$ tosses. Let the random variable $Y$ denote the number of heads. The value of $\text{var} \{Y\}$, where $\text{var} \{ \cdot \}$ denotes the variance, equals $\frac{7}{8} \\$ $\frac{49}{64} \\$ $\frac{7}{64} \\$ $\frac{105}{64}$

A person decides to toss a fair coin repeatedly until he gets a head. He will make at most $3$ tosses. Let the random variable $Y$ denote the number of heads. The value o...

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480

GATE Electrical 2017 Set 2 | Question: 39
The figure below shows a half-bridge voltage source inverter supplying an RL-load with $R=40 \Omega$ and $L=(\frac{0.3}{\pi})H$. The desired fundamental frequency of the load voltage is $50$Hz. The switch control signals of the converter are generated using ... $DC$ source voltage $V_{DC}$ in volts is. $300\sqrt{2}$ $500$ $500\sqrt{2}$ $1000\sqrt{2}$

The figure below shows a half-bridge voltage source inverter supplying an RL-load with $R=40 \Omega$ and $L=(\frac{0.3}{\pi})H$. The desired fundamental frequency of the ...

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