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GATE201255
The transfer function of a compensator is given as $G_c(s) = \frac{s+a}{s+b}$ The phase of the above lead compensator is maximum at $\sqrt{2}$ rad/s $\sqrt{3}$ rad/s $\sqrt{6}$ rad/s $1 / \sqrt{3}$ rad/s
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GATE201256
One of the parts (A, B, C, D) in the sentence given below contains an ERROR. Which one of the following is $\textbf{INCORRECT}$? $\textbf{I requested that he should be given the driving test today instead of tomorrow.}$ requested that should be given the driving test instead of tomorrow
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GATE201243
The feedback system shown below oscillates at $2$ rads /s when $K=2$ and $a=0.75$ $K=3$ and $a=0.75$ $K=4$ and $a=0.5$ $K=2$ and $a=0.5$
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GATE201244
The input $x(t)$ and output $y(t)$ of a system are related as $y(t)= \int_ { \infty}^t x(\tau) \cos(3 \tau) d \tau$. The system is timeinvariant and stable stable and not timeinvariant timeinvariant and not stable not timeinvariant and not stable
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GATE201245
An analog voltmeter uses external multiplier settings. With a multiplier setting of $20 \: k \Omega$, it reads $440$ V and with a multiplier setting of $80 \: k \Omega$, it reads $352$ V. For a multiplier setting of $40 \: k \Omega$, the voltmeter reads $371$ V $383$ V $394$ V $406$ V
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GATE201246
The locked rotor current in a $3$phase, star connected $15$ kW, $4$pole, $230$ V, $50$ Hz induction motor at rated conditions is $50$ A. Neglecting losses and magnetizing current, the approximate locked rotor line current drawn when the motor is connected to a $236$ V, $57$ Hz supply is $58.5$ A $45.0$ A $42.7$ A $55.6$ A
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GATE201247
A single phase $10$ kVA, $50$ Hz transformer with $1$ kV primary winding draws $0.5$ A and $55$ W, at rated voltage and frequency, on no load. A second transformer has a core with all its linear dimensions $\sqrt{2}$ times the corresponding dimensions of the first transformer. The core material and lamination ... , are $0.7$ A, $77.8$ W $0.7$ A, $155.6$ W $1$ A, $110$ W $1$ A, $220$ W
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GATE201248
In the $3$phase inverter circuit shown, the load is balanced and the gating scheme is $180^{\circ}$conduction mode. All the switching devices are ideal. The rms value of load phase voltage is $106.1$ V $141.4$ V $212.2$ V $282.8$ V
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GATE201249
In the $3$phase inverter circuit shown, the load is balanced and the gating scheme is $180^{\circ}$conduction mode. All the switching devices are ideal. If the dc bus voltage $V_d=300$ V, the power consumed by $3$phase load is $1.5$ kW $2.0$ kW $2.5$ kW $3.0$ kW
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GATE201236
A $220$ V, $15$ kW, $1000$ rpm shunt motor with armature resistance of $0.25 \: \Omega$, has a rated line current of $68$ A and a rated field current of $2.2$ A. The change on field flux required to obtain a speed of $1600$ rpm while drawing a line current of $52.8$ A and a field current of $1.8$ A is $18.18 \%$ increase $18.18 \%$ decrease $36.36 \%$ increase $36.36 \%$ decrease
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GATE201237
A fair coin is tossed till a head appears for the first ime. The probability that the number of required tosses is odd, is $1/3$ $1/2$ $2/3$ $3/4$
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GATE201238
The direction of vector $\textbf{A}$ is radically outward from the origin, with $\mid \textbf{A} \mid k r ^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of $n$ for which $\nabla \cdot \textbf{A} = 0$ is $2$ $2$ $1$ $0$
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GATE201239
Consider the differential equation $\frac{d^2y(t)}{dt^2} + 2 \frac{dy(t)}{dt} + y(t)=\delta (t)$ with $y(t) \mid_{t=0^}= 2$ and $\frac{dy}{dt} \mid _{t=0^} =0$. The numerical value of $\frac{dy}{dt} \mid _{t=0^+}$ is $2$ $1$ $0$ $1$
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GATE201240
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 $0.8 \: \Omega$ $1.4 \: \Omega$ $2 \: \Omega$ $2.8 \: \Omega$
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GATE201241
The state variable description of an LTI system is given by ... $a_1 = 0, \: a_2 \neq 0, \: a_3 = 0$ $a_1 \neq 0, \: a_2 \neq 0, \: a_3 = 0$
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GATE201242
The Fourier transform of a signal $h(t)$ is $H(j \omega) = (2 \cos \omega) (\sin 2 \omega )/ \omega$. The value of $h(0)$ is $1/4$ $1/2$ $1$ $2$
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GATE201229
The voltage gain $A_V$ of the circuit shown below is $\mid A_V \mid \approx 200$ $\mid A_V \mid \approx 100$ $\mid A_V \mid \approx 20$ $\mid A_V \mid \approx 10$
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GATE201230
The state transition diagram for the logic circuit shown is
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GATE201231
Let $y[n]$ denote the convolution of $h[n]$ and $g[n]$, where $h[n]=(1/2)^n u[n]$ and $g[n]$ is a casual sequence. If $y[0]=1$ and $y[1]=1/2$, then $g[1]$ equals $0$ $1/2$ $1$ $3.2$
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GATE201232
The circuit shown is a low pass filter with $f_{3dB} = \frac{1}{(R_1+R_2)C}$ \rad/s high pass filter with $f_{3dB} = \frac{1}{R_1C}$ \rad/s low pass filter with $f_{3dB} = \frac{1}{R_1C}$ \rad/s high pass filter with $f_{3dB} = \frac{1}{(R_1+R_2)C}$ \rad/s
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GATE201233
For the system shown below, $S_{D1}$ and $S_{D2}$ are complex power demands at bus $1$ and bus $2$ respectively. If $\mid V_2 \mid =1$ pu, the VAR rating of the capacitor $(Q_{G2})$ connected at bus $2$ is $0.2$ pu $0.268$ pu $0.312$ pu $0.4$ pu
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GATE201234
A cylindrical rotor generator delivers $0.5$ pu power in the steadystate to an infinite bus through a transmission line of reactance $0.5$ pu. The generator noload voltage is $1.5$ pu and the infinite bus voltage is $1$ pu. The inertia constant of the generator is $5$ ... , in degrees, for a threephase dead short circuit fault at the generator terminal is $53.5$ $60.2$ $70.8$ $79.6$
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GATE201235
In the circuit shown, an ideal switch $S$ is operated at $100$ kHz with a duty ratio of $50 \%$. Given that $\Delta i_c$ is $1.6$ A peaktopeak and $I_0$ is $5$ A dc, the peak current in $S$ is $6.6$ A $5.0$ A $5.8$ A $4.2$ A
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GATE201222
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
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25
GATE201223
A halfcontrolled singlephase bridge rectifier is supplying an RL load. It is operated at a firing angle $\alpha$ and the load current is continuous. The fraction of cycle that the freewheeling diode conduct is $1/2$ $\big( 1 \alpha/ \pi \big)$ $\alpha / 2 \pi $ $\alpha/ \pi$
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GATE201224
The typical ratio of latching current to holding current in a $20$ A thyristor is $5.0$ $2.0$ $1.0$ $0.5$
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GATE201225
For the circuit shown in the figure, the voltage and current expressions are $v(t) = E_1 \sin (\omega t) + E_3 \sin (3 \omega t)$ and $i(t)=I_1 \sin (\omega t  \phi _1) + I_3 \sin (3 \omega t  \phi _3) + I_5 \sin (5 \omega t).$ The average power measured by the Wattmeter ... $\frac{1}{2} [E_1 I_1 \cos \phi _1 + E_3 I_1 \cos \phi _1]$
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GATE201226
Given that $\textbf{A}= \begin{bmatrix} 5 & 3 \\ 2 & 0 \end{bmatrix}$ and $\textbf{I} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$, the value of $A^3$ is $15 \: \textbf{A} + 12 \: \textbf{I}$ $19 \: \textbf{A} + 30 \: \textbf{I}$ $17 \: \textbf{A} + 15 \: \textbf{I}$ $17 \: \textbf{A} + 21 \: \textbf{I}$
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GATE201227
The maximum value of $f(x) = x^39x^2+24x+5$ in the interval $[1,6]$ is $21$ $25$ $41$ $46$
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GATE201228
If $V_A – V_B =6$ V, then $V_C – V_D $ is $5$ V $2$ V $3$ V $6$ V
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GATE201215
The unilateral Laplace transform of $f(t)$ is $\frac{1}{s^2+s+1}$. The unilateral Laplace transform of $t f(t)$ is $ – \frac{s}{(s^2+s+1)^2} \\ $ $ – \frac{2s+1}{(s^2+s+1)^2} \\$ $ \frac{s}{(s^2+s+1)^2} \\$ $ \frac{2s+1}{(s^2+s+1)^2}$
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GATE201216
The average power delivered to an impedance $(4j3) \Omega$ by a current $5 \cos (100 \pi \:t +100)$A is $44.2$ W $50$ W $62.5$ W $125$ W
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GATE201217
In the following figure, $C_1$ and $C_2$ are ideal capacitors. $C_1$ has been charged to $12$ V before the ideal switch $S$ is closed at $t=0$. The current $i(t)$ for all $t$ is zero a step function an exponentially decaying function an impulse function
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GATE201218
The $iv$ characteristics of the diode in the circuit given below are $i= \begin{cases} \frac{v0.7}{500}A, & v \geq 0.7 \: V \\ 0 A, & v <0.7 \: V \end{cases}$ The current in the circuit is $10$ mA $9.3$ mA $6.67$ mA $6.2$ mA
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GATE201219
The output $Y$ of a $2$bit comparator is logic $1$ whenever the $2$bit input A is greater than the $2$bit input B. The number of combinations of which the output is logic $1$, is $4$ $6$ $8$ $10$
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GATE201220
Consider the given circuit. In this circuit, the race around does not occur occurs when $\text{CLK}=0$ occurs when $\text{CLK}=1$ and $A=B=1$ occurs when $\text{CLK}=1$ and $A=B=0$
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GATE201221
The figure shows a twogenerator system supplying a load of $P_D = 40$ MW, connected at bus $2$. The fuel cost of generations $G_1$ and $G_2$ are: $C_1(P_{G1})=10,000$ Rs/MWh and $C_2(P_{G2})=12,500$ Rs/MWh and the loss in the line is $P_{\text{loss(pu)}}=0.5 \: P_{G1(pu)}^2$, where ... $P_{G1}=20$, $P_{G2}=22$ $P_{G1}=22$, $P_{G2}=20$ $P_{G1}=20$, $P_{G2}=20$ $P_{G1}=0$, $P_{G2}=42$
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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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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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GATE201210
The slip of an induction motor normally does not depend on rotor speed synchronous speed shaft torque coreloss component
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