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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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GATE201251
With $10$ V dc connected at port A in the linear nonreciprocal twoport network shown below, the following were observed: $1 \: \Omega$ connected at port B draws a current of $3$ A $2.5 \: \Omega$ connected at port B draws a current of $2$ A With $10$ V dc connected at port A, the current drawn by $7 \: \Omega$ connected at port B is $3/7$ A $5/7$ A $1$ A $9/7$ A
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GATE201254
The transfer function of a compensator is given as $G_c(s) = \frac{s+a}{s+b}$ $G_c(s)$ is a lead compensator if $a=1, \: b=2$ $a=3, \: b=2$ $a=3, \: b=1$ $a=3, \: b=1$
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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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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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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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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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GATE201250
With $10$ V dc connected at port A in the linear nonreciprocal twoport network shown below, the following were observed: $1 \: \Omega$ connected at port B draws a current of $3$ A $2.5 \: \Omega$ connected at port B draws a current of $2$ A For the same network, with $6$ V dc ... $8$ V dc is connected to port A, the open circuit voltage at port B is $6$ V $7$ V $8$ V $9$ V
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GATE201253
In the circuit shown, the three voltmeter readings are $V_1 =220$ V, $V_2=122$ V, $V_3=136$ V. If $R_L=5 \: \Omega$, the approximate power consumption in the load is $700$ W $750$ W $800$ W $850$ W
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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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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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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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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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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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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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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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GATE201252
In the circuit shown, the three voltmeter readings are $V_1 =220$ V, $V_2=122$ V, $V_3=136$ V. The power factor of the load is $0.45$ $0.50$ $0.55$ $0.60$
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GATE201230
The state transition diagram for the logic circuit shown is
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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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