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1
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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Mar 24, 2018
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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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Mar 24, 2018
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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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Mar 24, 2018
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4
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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Mar 24, 2018
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5
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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Mar 24, 2018
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6
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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Mar 24, 2018
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7
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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Mar 24, 2018
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8
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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Mar 24, 2018
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9
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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Mar 24, 2018
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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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Mar 24, 2018
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11
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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Mar 24, 2018
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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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Mar 24, 2018
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13
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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Mar 24, 2018
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14
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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Mar 24, 2018
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15
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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Mar 24, 2018
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16
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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Mar 24, 2018
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17
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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Mar 24, 2018
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18
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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Mar 24, 2018
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19
GATE201210
The slip of an induction motor normally does not depend on rotor speed synchronous speed shaft torque coreloss component
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Mar 24, 2018
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20
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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Mar 24, 2018
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21
GATE201212
A periodic voltage waveform observed on an oscilloscope across a load is shown. A permane magnet moving coil (PMMC) meter connected across the same load reads $4$V $5$ V $8$ V $10$ V
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Mar 24, 2018
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22
GATE201213
The bridge method commonly used for finding mutual inductance is Heaviside Campbell bridge Schering bridge De Sauty bridge Wien bridge
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Mar 24, 2018
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23
GATE201214
With initial condition $x(1)=0.5$, the solution of the differential equation $t\frac{dx}{dt}+x=t$ is $x=t\frac{1}{2} \\ $ $x=t^2\frac{1}{2} \\ $ $x=\frac{t^2}{2} \\$ $x=\frac{t}{2}$
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Mar 24, 2018
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24
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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Mar 24, 2018
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25
GATE20122
If $x=\sqrt{1}$, then the value of $x^x$ is $e^{ \pi/2}$ $e^{\pi/2}$ $x$ $1$
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Mar 24, 2018
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26
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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Mar 24, 2018
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27
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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28
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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29
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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Mar 24, 2018
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30
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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31
GATE201854
The equivalent circuit of a single phase induction motor is shown in the figure, where the parameters are $R_1 =R_2=X_{l1}=X_{l2} = 12 \Omega$, $X_M=240 \: \Omega$ and $S$ is the slip. At noload, the motor speed can be approximated to the synchronous speed. The noload lagging power factor of the motor is __________ (up to $3$ decimal places).
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Feb 19, 2018
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32
GATE201855
The voltage $v(t)$ across the terminals $a$ and $b$ as shown in the figure, is a sinusoidal voltage having a frequency $\omega = 100 \text{ radian/s}$. When the inductor current $i(t)$ is in phase with the voltage $v(t)$, the magnitude of the impedance $Z$ (in $\Omega$) seen between the terminals $a$ and $b$ is __________ (up to $2$ decimal places)
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Feb 19, 2018
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33
GATE201846
The unit step response $y(t)$ of a unity feedback system with open loop transfer function $G(s)H(s)= \frac{K}{(s+1)^2(s+2)}$ is shown in the figure. The value of $K$ is ___________ (up to $2$ decimal places).
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34
GATE201847
A threephase load is connected to a threephase balanced supply as shown in the figure. If $V_{\text{an}} = 100 \angle 0^{\circ} \: V$, $V_{\text{bn}}=100 \angle  120 ^{\circ} \: V$ ... positive in the anticlockwise direction), the value of $R$ for zero current in the neutral wire is __________ $\Omega$ (up to $2$ decimal places).
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35
GATE201848
The voltage across the circuit in the figure, and the current through it, are given by the following expressions: $v(t)=510 \cos (\omega t+ 60^{\circ}) \: V$ $i(t)=5 + X \cos (\omega t) \: A$ where $\omega =100 \: \pi \text{ radian}/s$. If the average power delivered to the circuit is zero, then the value of $X$ (in Ampere) is _______ (up to $2$ decimal places)
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36
GATE201849
A phase controlled single phase rectifier, supplied by an AC source, feeds power to an $RLE$ load as shown in the figure. The rectifier output voltage has an average value given by $V_{\text{o}}= \frac{V_m}{2 \pi} (3+\cos \alpha)$ ... firing angle. If the power delivered to the lossless battery is $1600$ W, $\alpha$ in degree is ___________ (up to $2$ decimal places).
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Feb 19, 2018
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37
GATE201850
The figure shows two buck converters connected in parallel. The common input dc voltage for the converters has a value of $100 \: V$. The converters have inductors of identical value. The load resistance is $1 \: \Omega$. The capacitor voltage has negligible ripple. Both ... average value of $i_{s1}$, the current of switch $S1$ (in Ampere), is ____________ (up to $2$ decimal places).
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Feb 19, 2018
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38
GATE201851
A $3$phase $900$ kVA, $3 \: kV/ \sqrt{3} kV$ ( $\Delta/$), $50$ Hz transformer has primary (high voltage side) resistance per phase of $0.3 \: \Omega$ and secondary (low voltage side) resistance per phase of $0.02 \: \Omega$. Iron loss of the transformer is $10 \: kW$. The full load $\%$ efficiency of the transformer operated at unity power factor is _______ (up to $2$ decimal places)
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39
GATE201852
A $200$ V DC series motor, when operating from rated voltage while driving a certain load, draws $10$ A current and runs at $1000$ r.p.m. The total series resistance is $1 \: \Omega$. The magnetic circuit is assumed to be linear. At the same supply voltage, the load torque is increased by $44 \%$. The speed of the motor in r.p.m (rounded to the nearest integer) is _____________
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40
GATE201853
A dc to dc converter shown in the figure is charging a battery bank, $B2$ whose voltage is constant at $150 \: V$. $B1$ is another battery bank whose voltage is constant at $50 \: V$. The value of the inductor, $L$ is $5$ ... state and assuming the diode D to be ideal, the power transferred from $B1$ to $B2$ (in Watt) is ___________ (up to $2$ decimal places)
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Feb 19, 2018
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