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GATE201211
A twophase load draws the following phase currens: $i_1(t)=I_m \sin(\omega t – \phi_1), i_2(t) = I_m \cos(\omega t – \phi_2)$. These currents are balanced if $\phi_1$ is equal to $ \phi_2$ $\phi_2$ $\pi/2  \phi_2$ $\pi/2 + \phi_2$
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GATE201210
The slip of an induction motor normally does not depend on rotor speed synchronous speed shaft torque coreloss component
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GATE20129
The bus admittance matrix of a threebus threeline system is $Y=j \begin{bmatrix} 13 & 10 & 5 \\ 10 & 18 & 10 \\ 5 & 10 & 13 \end{bmatrix}$ If each transmission line between the two buses is represented by an equivalent $\pi$network, the magnitude of the shunt susceptance of the line connecting bus $1$ and $2$ is $4$ $2$ $1$ $0$
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GATE20128
If $x[n]=(1/3)^{\mid n \mid} – (1/2)^n \: u[n]$, then the region of convergence (ROC) of its $Z$transform in the $Z$plane will be $\frac{1}{3} < \mid z \mid < 3$ $\frac{1}{3} < \mid z \mid < \frac{1}{2}$ $\frac{1}{2} < \mid z \mid < 3$ $\frac{1}{3} < \mid z \mid $
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GATE20127
In the sum of products function $f(X,Y,Z) = \Sigma(2,3,4,5)$, the prime implicants are $\overline{X}Y, X \overline{Y}$ $\overline{X}Y, X \overline{Y}\overline{Z}, X \overline{Y}Z$ $\overline{X} Y \overline{Z}, \overline{X}YZ, X \overline{Y}$ $\overline{X} Y \overline{Z}, \overline{X}YZ, X \overline{Y} \overline{Z}, X \overline{Y}Z$
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GATE20126
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 steadystate output of the system is zero at $\omega = 1$ \rad/s $\omega = 2$ \rad/s $\omega = 3$ \rad/s $\omega = 4$ \rad/s
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GATE20125
The impedance looking into nodes $1$ and $2$ in the given circuit is $50 \: \Omega$ $100 \: \Omega$ $5 \: \Omega$ $10.1 \: \Omega$
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GATE20124
In the circuit shown below, the current through the inductor is $\frac{2}{1+j} \\ $ A $\frac{1}{1+j} \\$ A $\frac{1}{1+j} \\$ A $0$ A
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GATE20123
Given $f(z) = \frac{1}{z+1} – \frac{2}{z+3}$. If $C$ is a counterclockwise path in the $z$plane such that $\mid z+1 \mid =1$, the value of $\frac{1}{2 \pi \: j} \oint_c f(z) dz$ is $2$ $1$ $1$ $2$
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GATE20122
If $x=\sqrt{1}$, then the value of $x^x$ is $e^{ \pi/2}$ $e^{\pi/2}$ $x$ $1$
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GATE20121
Two independent random variables $X$ and $Y$ are uniformly distributed in he interval $[1,1]$. The probability that $\text{max}[X,Y]$ is less than $1/2$ is $3/4$ $9/16$ $1/4$ $2/3$
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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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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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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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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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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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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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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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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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GATE2017227
The value of the contour integral in the complex plane $\oint \frac{z^{3}2z+3}{z2} dz$ along the contour $\mid z \mid =3$, taken counter clockwise is $18 \pi i$ $0$ $14 \pi i$ $48 \pi i$
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GATE2017226
Let $ g(x)= \begin{cases} x & \ x \leq 1 \\ x+1 & \ x \geq 1 \end{cases}$ and $ f(x)= \begin{cases} 1x & \ x \leq 0 \\ x^{2} & \ x > 0 \end{cases}$. Consider the composition of $f$ and $g$, i.e., $(f {\circ} g) (x) = f (g(x))$. The number of discontinuities in $(f {\circ} g) (x)$ present in the interval $(\infty, 0)$ is: $0$ $1$ $2$ $4$
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GATE2017213
A threephase voltage source inverter with ideal devices operating in $180^{\circ}$ conduction mode is feeding a balanced starconnected resistive load. The $DC$ voltage input is $V_{dc}$. The peak of the fundamental component of the phase voltage is $\frac{V_{dc}}{\pi} \\$ $\frac{2V_{dc}}{\pi} \\$ $\frac{3V_{dc}}{\pi} \\$ $\frac{4V_{dc}}{\pi} $
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GATE2017211
A phasecontrolled, singlephase, fullbridge converter is supplying a highly inductive $DC$ load. The converter is fed from a $230$ V, $50$ Hz, AC source. The fundamental frequency in Hz of the voltage ripple on the $DC$ side is $25$ $50$ $100$ $300$
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GATE2017210
For a $3$input logic circuit shown below, the output $Z$ can be expressed as $Q+\overline{R}$ $P\overline{Q}+R$ $\overline{Q}+R$ $P+\overline{Q}+R$
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GATE201726
When a unit ramp input is applied to the unity feedback system having closed loop transfer function $\frac{C(s)}{R(s)}=\frac{Ks+b}{s^{2}+as+b}, (a>0, b>0, K>0)$, the steady state error will be $0 \\ $ $\frac{a}{b} \\$ $\frac{a+K}{b} \\$ $\frac{aK}{b}$
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GATE201721
An urn contains $5$ red balls and $5$ black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a Red ball in the second draw is $\frac{1}{2} \\$ $\frac{4}{9} \\$ $\frac{5}{9} \\$ $\frac{6}{9} $
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GATE2017139
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 $1kVAR \leq Q \leq 2kVAR$ ... case power factor after power factor correction is $0.447 \text{ lag}$ $0.707 \text{ lag}$ $0.894 \text{ lag}$ $1$
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GATE2017136
The output expression for the Karnaugh map shown below is $B \overline{D}+BCD$ $B \overline{D}+AB$ $\overline{B}D+ABC$ $B \overline{D}+ABC$
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GATE2017134
The load shown in the figure is supplied by a $400$V (linetoline), $3$phase source (RYB sequence). The load is balanced and inductive, drawing $3464$ VA. When the switch $S$ is in position $N$, the three wattmeters $W_{1}, W_{2},$ and $W_{3}$ read $577.35$W each. If ... and $W_2=W_3=0$ $W_1=0$; $W_2=1732$; and $W_3=0$ $W_1=866$; $W_2=0$; and $W_3=866$ $W_1=W_2=0$ and $W_3=1732$
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GATE2017133
The transfer function of the system $Y(s)/U(s)$ ... $\frac{(s4)}{(s^{2}+s4)} \\ $ $\frac{(s+4)}{(s^{2}s4)} \\$
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GATE2017132
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 $\frac{k_{1}}{J Ls^{2}+J Rs+k_{1}k_{2}}$ $\frac{k_{1}}{J Ls^{2}J Rsk_{1}k_{2}}$ $\frac{k_{1}U_{2}(R+sL)}{J Ls^{2}+(J RU_{2}L)s+k_{1}k_{2}U_{2}R}$ $\frac{k_{1}U_{2}(sLR)}{J Ls^{2}(J R+U_{2}L)sk_{1}k_{2}+U_{2}R}$
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GATE2017131
Let the signal $x(t)=\sum_{k=\infty }^{+\infty } (1)^{k} \delta (t\frac{k}{2000})$ be passed through an LTI system with frequency response $H(\omega )$ ... $2000+2000\cos (2000 \pi t)+2000\cos (4000 \pi t)$ $4000\cos (2000 \pi t)$ $2000\cos (2000 \pi t)$
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GATE2017128
Consider the line integral $I=\int_{c} (x^{2}+iy^{2})dz$, where $z=x+iy$. The line $c$ is shown in the figure below. The value of $I$ is $\frac{1}{2}i \\ $ $\frac{2}{3}i \\ $ $\frac{3}{4}i \\ $ $\frac{4}{5}i$
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GATE2017127
Consider the differential equation $(t^{2}81)\frac{dy}{dt}+5t y=\sin(t)$ with $y(1)=2 \pi$. There exists a unique solution for this differential equation when $t$ belongs to the interval $(2, 2)$ $(10, 10)$ $(10, 2)$ $(0, 10)$
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GATE2017126
A function $f(x)$ is defined as $f(x)= \begin{cases} e^{x}, & x < 1 \\ \text{In } x+ax^{2}+bx, & x\geq 1 \end{cases}$, where $x \in \mathbb{R}$ Which one of the following statement is TRUE? $f(x)$ is NOT differentiable at $x=1$ for any values of $a$ ... $x=1$ for all values of $a$ and $b$ such that $a+b=e$. $f(x)$ is differentiable at $x=1$ for all values of $a$ and $b$.
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GATE2017114
For the circuit shown in the figure below, assume that diodes $D_{1}, D_{2}$ and $D_{3}$ are ideal. The $DC$ components of voltages $v_{1}$ and $v_{2}$, respectively are $0$V and $1$V $0.5$V and $0.5$V $1$V and $0.5$V $1$V and $1$V
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GATE2017125
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 ________.
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GATE2017124
In the converter circuit shown below, the switches are controlled such that the load voltage $v_{0}(t)$ is a $400$ Hz square wave. The RMS value of the fundamental component of $v_{0}(t)$ in volts is ________.
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GATE2017122
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.)
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GATE2017119
The equivalent resistance between the terminals $A$ and $B$ is __________ $\Omega$.
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