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GATE201820
The series impedance matrix of a short threephase transmission line in phase coordinates is $\begin{bmatrix} Z_s & Z_m & Z_m \\ Z_m & Z_s & Z_m \\ Z_m & Z_m & Z_s \end{bmatrix}$. If the positive sequence impedance is $(1+j \: 10) \Omega$, and the ... $(4+j \: 31) \Omega$, then the imaginary part of $Z_m$ (in $\Omega$) is ___________ (up to $2$ decimal places).
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GATE201821
The positive, negative and zero sequence impedances of a $125$ MVA, threephase, $15.5$ kV, stargounded, $50$ Hz generator are $j0.1$ pu, $j0.05$ pu and $j0.01$ pu respectively on the machine rating base. The machine is unloaded and working at the rated ... $b$phase to ground fault (in kA) is __________ (up to $2$ decimal places).
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GATE201822
A $1000 \times 1000$ bus admittance matrix for an electric power system has $8000$ nonzero elements. The minimum number of branches (transmission lines and transformers) in this system are _________ (up to $2$ decimal places).
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GATE201823
The waveform of the current drawn by a semiconverter from a sinusoidal AC voltage source is shown in the figure. If $I_0=20$ A, the rms value of fundamental component of the current is ________ A (up to $2$ decimal places).
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GATE20188
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 average power outputs ... $P_1 <0$, $P_2>0$, $P_3>0$ $P_1 <0$, $P_2>0$, $P_3<0$ $P_1 > 0$, $P_2<0$, $P_3>0$
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GATE20189
Match the transfer functions of the secondorder systems with the nature of the systems given below. ... PI, QII, RIII PII, QI, RIII PIII, QII, RI PIII, QI, RII
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GATE201810
A positive charge of $1$ nC is placed at $(0,0,0.2)$ where all dimensions are in meters. Consider the $xy$ 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
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GATE201811
Let $f$ be a realvalued 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 continuous but not ... $x=0$ $f(x)$ is differentiable but its first derivative is not differentiable at $x=0$
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GATE201812
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 $1$ $0.95$ $0.93$ $0.9$
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GATE201813
The value of the integral $\oint _c \frac{z+1}{z^24} dz$ 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}\\$ $2 \pi i$
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GATE201814
In the logic circuit shown in the figure, $Y$ is given by $Y=ABCD$ $Y=(A+B)(C+D)$ $Y=A+B+C+D$ $Y=AB+CD$
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GATE201815
The opamp 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}$
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GATE20182
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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GATE20183
A single phase fully controlled rectifier is supplying a load with an antiparallel 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? $v_o \geq 0$ & $i_o<0$ $v_o < 0$ & $i_o <0$ $v_o \geq 0$ & $i_o \geq 0$ $v_0 < 0$ & $i_o\geq 0$
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GATE20184
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
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GATE20185
Two wattmeter method is used for measurement of power in a balanced threephase load supplied from a balanced threephase system. If one of the wattmeters reads half of the other (both positive), then the power factor of the load is $0.532$ $0.632$ $0.707$ $0.866$
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GATE20186
Consider a lossy transmission line with $V_1$ and $V_2$ as the sending and receiving end voltages, respectively. $Z$ and $X$ ... $ \begin{vmatrix} \frac{V_1V_2}{Z} \end{vmatrix} \\ $
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GATE20187
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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GATE20181
A singlephase $100$ 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 $4.8$ $6.8$ $8.8$ $10.8$
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GATE2017244
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 shortcircuit condition. For the same field current, the opencircuit voltage is ... to terminal voltage), when the generator delivers the rated load at $0.8$ pf leading, at rated terminal voltage is _________.
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GATE2017245
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 _______.
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GATE2017246
Consider the system described by the following state space representation ... $y(t)$ at $t=1$ sec (rounded off to three decimal places) is ___________.
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GATE2017247
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 _______.
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GATE2017248
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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GATE2017249
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 _________.
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GATE2017250
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.)
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GATE2017251
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 conductors are ... the effect of ground, the magnitude of positive sequence reactance in $\Omega/km$ (rounded off to three decimal places) is _________.
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GATE2017252
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 ________.
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GATE2017253
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.
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GATE2017254
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 and delivering $60$ ... removed, assuming the acceleration is constant for $10$ cycles, the value of the power angle after $5$ cycles is __________ electrical degrees.
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GATE2017255
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 of a soap (assuming ... , of the resulting single spherical drop with respect to the same reference point at infinity is _________. (Give the answer up to two decimal places.)
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GATE2017232
A cascade system having the impulse responses $h_{1}(n)= \{ \underset{\uparrow}{1}1 \}$ and $h_{2}(n)= \{ \underset{\uparrow}{1}1, 1 \}$ is shown in the figure below, where symbol $\uparrow$ denotes the time origin. The input sequence $x(n)$ for which the cascade system produces an ... $x(n)= \{\underset{\uparrow}{1}1, 1, 1, 1 \}$ $x(n)= \{\underset{\uparrow}{1}1, 2, 2, 1 \}$
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GATE2017233
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 rotational losses of the machine, the current drawn by the motor from the $220$V supply is $34.2$ A $30$ A $22$ A $4.84$ A
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GATE2017235
The range of $K$ for which all the roots of the equation $s^{3}+3s^{2}+2s+K=0$ are in the left half of the complex $s$plane is $0 < K < 6$ $0 < K < 16$ $6 < K < 36$ $6 < K < 16$
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GATE2017236
Which of the following systems has maximum peak overshoot due to a unit step input? $\frac{100}{s^{2}+10s+100} \\$ $\frac{100}{s^{2}+15s+100} \\ $ $\frac{100}{s^{2}+5s+100} \\$ $\frac{100}{s^{2}+20s+100}$
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GATE2017238
For the circuit shown below, assume that the $OPAMP$ is ideal. Which one of the following is TRUE? $v_{0}=v_{s}$ $v_{0}=1.5 v_{s}$ $v_{0}=2.5 v_{s}$ $v_{0}=5 v_{s}$
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GATE2017239
The figure below shows a halfbridge voltage source inverter supplying an RLload 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 sinusoidal pulse width ... value of $DC$ source voltage $V_{DC}$ in volts is. $300\sqrt{2}$ $500$ $500\sqrt{2}$ $1000\sqrt{2}$
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GATE2017240
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 $\frac{7}{8} \\$ $\frac{49}{64} \\$ $\frac{7}{64} \\$ $\frac{105}{64}$
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GATE2017242
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 _________.
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GATE2017243
A starconnected, $12.5$kW, $208$ V (line), $3$phase, $60$Hz squirrel cage induction motor has following equivalent circuit parameters per phase referred to the stator: $R_{1}=0.3 \Omega, R_{2}=0.3\Omega, X_{1}=0.41\Omega, X_{2}=0.41\Omega$. Neglect ... . The starting current (in Ampere) for this motor when connected to an $80$ V (line), $20$ Hz, $3$phase AC source is _________.
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