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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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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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11
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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14
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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15
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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16
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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17
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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18
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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19
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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20
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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21
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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22
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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23
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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24
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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25
GATE201210
The slip of an induction motor normally does not depend on rotor speed synchronous speed shaft torque coreloss component
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26
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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27
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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28
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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29
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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30
GATE20122
If $x=\sqrt{1}$, then the value of $x^x$ is $e^{ \pi/2}$ $e^{\pi/2}$ $x$ $1$
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31
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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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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33
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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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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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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36
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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GATE2018GA3
The three roots of the equation $f(x) = 0$ are $x = {−2, 0, 3}.$ What are the three values of $ x $ for which $f(x − 3) = 0?$ $−5 , −3 , 0 $ $−2 , 0 , 3$ $0 , 6 , 8$ $1 , 3 , 6$
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Feb 19, 2018
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Numerical Ability
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Arjun
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gate2018ee
generalaptitude
numericalability
quadraticequation
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38
GATE2018GA4
For what values of $k$ given below is $\dfrac{(k + 2)^2}{(k  3)}$ an integer? $4 , 8 , 18 $ $4 , 10 , 16$ $ 4 , 8 , 28 $ $8 , 26 , 28$
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Feb 19, 2018
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Numerical Ability
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generalaptitude
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algebra
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39
GATE2018GA5
Functions $F(a,b)$ and $G(a,b)$ are defined as follows: $F(a,b)=(ab)^{2}$ and $G(a,b)=\mid ab\mid ,$ where $\mid x\mid$ represents the absolute value of $x.$ What would be the value of $G(F(1,3),G(1,3))?$ $2$ $4$ $6$ $36$
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Feb 19, 2018
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Numerical Ability
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gate2018ee
generalaptitude
numericalability
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40
GATE2018GA6
An email password must contain three characters. The password has to contain one numeral from $0$ to $9,$ one upper case and one lower case character from the English alphabet. How many distinct passwords are possible$?$ $6,760$ $13,520$ $40,560$ $1,05,456$
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Feb 19, 2018
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generalaptitude
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