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GATE2020EE4
Consider a signal $x\left [ n \right ]=\left ( \frac{1}{2} \right )^{n}1\left [ n \right ],$ where $1\left [ n \right ]=0$ if $n< 0$, and $1\left [ n \right ]= 1$ if $n \geq 0.$ ... $\left  z \right > 2$ $\left  z \right < \frac{1}{2}$ $\left  z \right > \frac{1}{2}$
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GATE2020EE5
The value of the following complex integral, with $\text{C}$ representing the unit circle centered at origin in the counterclockwise sense, is: $\int _{C}\frac{z^{2}+1}{z^{2}2z}\:dz$ $8\pi i$ $8\pi i$ $\pi i$ $\pi i$
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GATE2020EE12
Thyristor $T_{1}$ is triggered at an angle $\alpha$ (in degree), and $T_{2}$ at angle $180^{\circ}+\alpha$, in each cycle of the sinusoidal input voltage. Assume both thyristors to be ideal. To control the load power over the range $0$ to $\text{2 k W}$, the minimum range of ... $0^{\circ}\:to\:120^{\circ}$ $60^{\circ}\:to\:120^{\circ}$ $60^{\circ}\:to\:180^{\circ}$
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GATE2020EE21
A singlephase, $\text{4 kVA}$, $\text{200 V/100 V}$, $\text{50 Hz}$ transformer with laminated $\text{CRGO}$ steel core has rated noload loss of $\text{450 W}$. When the highvoltage winding is excited with $\text{160 V}$, $\text{40 Hz}$ ... $\text{25 Hz}$ sinusoidal ac source, the noload losses will be _____________________$\text{W}$ (rounded off to $2$ decimal places).
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GATE2020EE24
Consider a negative unity feedback system with forward path transfer function $G\left ( s \right )=\frac{K}{\left ( s+a \right )\left ( sb \right )\left ( s+c \right )}$, where $\text{K, a, b, c}$ are positive real numbers. For a Nyquist path enclosing the ... $\frac{G\left ( s \right )}{1+G\left ( s \right )}$ lying in the open right half of the $\text{s}$plane is__________.
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6
GATE2020EE10
Consider a linear timeinvariant system whose input $\text{r(t)}$ and output $\text{y(t)}$ are related by the following differential equation: $\frac{d^{2}y\left ( t \right )}{dt^{2}}+4y\left ( t \right )=6r\left ( t \right )$ The poles of this system are at $+2j,2j$ $+2,2$ $+4,4$ $+4j,4j$
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GATE2020EE14
A commonsource amplifier with a drain resistance, $R_{D}=4.7\:k\Omega$, is powered using a $10\:V$ power supply. Assuming that the transconductance, $_{m}$, is $520\:\mu A/V$, the voltage gain of the amplifier is closest to: $2.44$ $1.22$ $1.22$ $2.44$
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GATE2020EE15
A sequence detector is designed to detect precisely 3 digital inputs, with overlapping sequences detectable. For the sequence $\text{(1,0,1)}$ and input data $\text{(1,1,0,1,0,0,1,1,0,1,0,1,1,0)}$, what is the output of this detector? $1,1,0,0,0,0,1,1,0,1,0,0$ $0,1,0,0,0,0,0,1,0,1,0,0$ $0,1,0,0,0,0,0,1,0,1,1,0$ $0,1,0,0,0,0,0,0,1,0,0,0$
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GATE2020EE18
Currents through ammeters $\text{A2}$ and $\text{A3}$ in the figure are $1\angle 10^{\circ}\:and\:1\angle 70^{\circ}$, respectively. The reading of the ammeter $\text{A1}$ (rounded off to $3$ decimal places) is_______$\text{A}$.
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GATE2020EE19
The Thevenin equivalent voltage, $V_{TH}$, in $\text{V}$ (rounded off to $2$ decimal places) of the network shown below, is _______
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GATE2020EE26
For real numbers, $\text{x}$ and $\text{y}$, with $y=3x^{2}+3x+1$, the maximum and minimum value of $\text{y}$ for $\text{x}$ $\epsilon\left [ 2,0 \right ]$ are respectively, ______. $\text{7 and 1/4}$. $\text{7 and 1}$. $\text{2 and 1/2}$. $\text{1 and 1/4}$.
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GATE2020EE28
A $\text{250 V}$ dc shunt motor has an armature resistance of $0.2\:\Omega$ and a field resistance of $100\:\Omega$. When the motor is operated on noload at rated voltage, it draws an armature current of $\text{5 A}$ and runs at $\text{1200 rpm}$ ... operating conditions. The speed of the motor, in $\text{rpm}$ under this loaded condition, is closest to: $1200$ $1000$ $1220$ $900$
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GATE2020EE30
Consider the diode circuit shown below. The diode, D, obeys the currentvoltage characteristic $I_{D}=I_{S}\left ( exp\left ( \frac{V_{D}}{nV_{T}} \right )1 \right )$, where $n> 1, V_{T}> 0, V_{D}$ is the voltage across the diode and $I_{D}$ is the current through it. ... $\text{Large}$ $R_{1}$ and $\text{small}$ $R_{2}$. $\text{Small}$ $R_{1}$ and $\text{large}$ $R_{2}$.
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GATE2020EE9
Out of the following options, the most relevant information needed to specify the real power $\text{(P)}$ at the $\text{PV}$ buses in a load flow analysis is solution of economic load dispatch rated power output of the generator rated voltage of the generator base power of the generator
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15
GATE2020EE11
A singlephase, fullbridge diode rectifier fed from a $230$ $\text{V}$, $50$ $\text{Hz}$ sinusoidal source supplies a series combination of finite resistance, $\text{R}$, and a very large inductance, $\text{L}$. The two most dominant frequency components in the source current are: $50\:Hz,\:0\:Hz$ $50\:Hz,\:100\:Hz$ $50\:Hz,\:150\:Hz$ $150\:Hz,\:250\:Hz$
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16
GATE2020EE16
Consider the initial value problem below. The value of y at $x=\ln{2}$, (rounded off to $3$ decimal places) is_____________________. $\frac{\mathrm{d} y}{\mathrm{d} x}=2xy,\:\:y\left ( 0 \right )=1$
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GATE2020EE2
Which of the following is true for all possible nonzero choices of integers $m,n;m\neq n,$ or all possible nonzero choices of real numbers $p,q;p\neq q,$ as applicable? $\frac{1}{\pi }\int_{0}^{\pi }\sin m\theta \:\sin n\theta d\theta =0$ ... $\lim_{\alpha \rightarrow \infty }\frac{1}{2\alpha }\int_{\alpha }^{\alpha }\sin p\theta \:\sin q\theta d\theta =0$
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18
GATE2020EE6
$x_{R}$ and $x_{A}$ are, respectively, the rms and average values of $x\left ( t \right )=x\left ( tT \right ),$ and similarly, $y_{R}$ and $y_{A}$ are, respectively, the rms and average values of $y\left ( t \right )=kx\left ( t \right ).\:k,T$ are independent of $\text{t}$. ... $y_{A}\neq kx_{A} ;\:y_{R}= kx_{R}$ $y_{A}\neq kx_{A} ;\:y_{R}\neq kx_{R}$
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GATE2020EE29
Two buses, $\text{i and j}$, are connected with a transmission line admittance $\text{y}$ ...
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GATE2020EE13
Which of the options is an equivalent representation of the signal flow graph shown here?
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