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1
GATE2020EC: 14
Which one of the following polezero plots corresponds to the transfer function of an $\text{LTI}$ system characterized by the inputoutput difference equation given below? $y\left [ n \right ]=\sum ^{3}_{k=0}\left ( 1 \right )^{k}x\left [ nk \right ]$
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gate2020ec
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2
GATE2020EC: 55
Consider the following closed loop control system where $G\left ( s \right )=\dfrac{1}{s\left ( s+1 \right )}$ and $C\left ( s \right )=K\dfrac{s+1}{s+3}$. If the steady state error for a unit ramp input is $0.1$, then the value of $K$ is ______________.
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gate2020ec
numericalanswers
networksolutionmethods
steadystateerror
0
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3
GATE2020EC: 54
$X$ is a random variable with uniform probability density function in the interval $[2,\:10]$. For $Y=2X6$, the conditional probability $P\left ( Y\leq 7\mid X\geq 5 \right )$ (rounded off to three decimal places) is __________.
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gate2020ec
numericalanswers
0
answers
4
GATE2020EC: 53
The transfer function of a stable discretetime $\text{LTI}$ system is $H\left ( z \right )=\dfrac{K\left ( z\alpha \right )}{z+0.5}$, where $K$ and $\alpha$ are real numbers. The value of $\alpha$ (rounded off to one decimal place) with $\mid \alpha \mid > 1$, for which the magnitude response of the system is constant over all frequencies, is ___________.
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gate2020ec
numericalanswers
networksolutionmethods
networks
transferfunction
0
answers
5
GATE2020EC: 52
$X\left ( \omega \right )$ is the Fourier transform of $x(t)$ shown below. The value of $\int_{\infty }^{\infty }\mid X \left ( \omega \right ) \mid ^{2}d \omega$ (rounded off to two decimal places) is ____________
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gate2020ec
numericalanswers
continuoustimesignals
signalsandsystems
fouriertransform
0
answers
6
GATE2020EC: 51
For the solid $S$ shown below, the value of $\underset{S}{\iiint} xdxdydz$ (rounded off to two decimal places) is _______________.
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gate2020ec
numericalanswers
engineeringmathematics
0
answers
7
GATE2020EC: 50
For the components in the sequential circuit shown below, $t_{pd}$ is the propagation delay, $t_{\text{setup}}$ is the setuptime, and $t_{\text{hold}}$ is the hold time. The maximum clock frequency (rounded off to the nearest integer), at which the given circuit can operate reliably, is _________$\text{MHz}$.
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gate2020ec
numericalanswers
electromagnetics
propagationdelay
0
answers
8
GATE2020EC: 49
A system with transfer function $G\left ( s \right )=\dfrac{1}{\left ( s+1 \right )\left ( s+a \right )},\:\:a> 0$ is subjected to an input $5 \cos3t$. The steady state output of the system is $\dfrac{1}{\sqrt{10}}\cos\left ( 3t1.892 \right )$. The value of $a$ is _______.
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gate2020ec
numericalanswers
networksolutionmethods
networks
transferfunction
0
answers
9
GATE2020EC: 48
In a digital communication system, a symbol $S$ randomly chosen from the set $\left \{ s_{1},s_{2},s_{3},s_{4} \right \}$ is transmitted. It is given that $s_{1}=3,s_{2}=1,s_{3}=+1$ and $s_{4}=+2$ ... $S=s_{i}$. The index $i$ for which the conditional symbol error probability $P_{i}$ is the highest is ___________.
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gate2020ec
numericalanswers
digitalcommunications
0
answers
10
GATE2020EC: 47
$S_{PM}(t)$ and $S_{FM}(t)$ as defined below, are the phase modulated and the frequency modlated waveforms, respectively, corresponding to the message signal $m(t)$ ... of $S_{PM}(t)$ and $S_{FM}(t)$ are same, then the value of the ratio $\dfrac{K_{p}}{K_{f}}$ is ________ seconds.
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gate2020ec
numericalanswers
communications
modulatedwaveforms
0
answers
11
GATE2020EC: 46
For a $2$port network consisting of an ideal lossless transformer, the parameter $S_{21}$ (rounded off to two decimal places) for a reference impedance of $10 \Omega$, is __________.
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gate2020ec
numericalanswers
impedance
electromagnetics
0
answers
12
GATE2020EC: 45
The magnetic field of a uniform plane wave in vacuum is given by $\overrightarrow{H}\left ( x,y,z,t \right )=(\hat{a_{x}}+2\hat{a_{y}}+b\hat{a_{z}})\cos\left ( \omega t+3xyz\right ).$ The value of $b$ is ___________.
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gate2020ec
numericalanswers
overrightarrow
vectoralgebra
0
answers
13
GATE2020EC: 44
In the voltage regulator shown below, $V_{1}$ is the unregulated imput at $15\:V$. Assume $V_{BE}=0.7\:V$ and the base current is negligible for both the $\text{BJTs}$. If the regulated output $V_{O}$ is $9\:V$, the value of $R_{2}$ is ___________$\Omega$
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gate2020ec
numericalanswers
analogcircuits
bjt
0
answers
14
GATE2020EC: 43
For an infinitesimally small dipole in free space, the electric field $E_{\theta }$ in the far field is proportional to $e^{jkr/r}\sin\theta$, where $k=2\pi /\lambda$. A vertical infinitesimally small electric dipole $\left (\delta l \ll \lambda \right )$ is placed ... far field radiation pattern occurs at $\theta =60^{\circ}$, is $\lambda$ $0.5\lambda$ $0.25\lambda$ $0.75\lambda$
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gate2020ec
electromagnetics
radiationpattern
0
answers
15
GATE2020EC: 42
For the modulated signal $x\left ( t \right )=m\left ( t \right )\cos\left ( 2\pi f_{c}t \right )$, the message signal $m\left ( t \right )=4\cos\left ( 1000\pi t \right )$ and the carrier frequency $f_{c}$ is $1\: MHz$. The signal $x(t)$ is passed through a ... $\cos\left ( 920\pi t \right )$ $\cos\left ( 1000\pi t \right )$ $\cos\left ( 540\pi t \right )$
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gate2020ec
communications
modulator
demodulator
0
answers
16
GATE2020EC: 41
The components in the circuit given below are ideal. If $R=2\:k \Omega$ and $C=1$ $\mu F$, the $3$ dB cutoff frequency of the circuit in Hz is $14.92$ $34.46$ $59.68$ $79.58$
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Aug 13
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gate2020ec
controlsystems
0
answers
17
GATE2020EC: 40
The characteristic equation of a system is $s^{3}+3s^{2}+\left ( K+2 \right )s+3K=0.$ In the root locus plot for the given system, as $K$ varies from $0$ to $\infty$, the breakaway or breakin points(s) lie within $(1, 0)$ $(2, 1)$ $(3, 2)$ $(\infty, 3)$
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Aug 12
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gate2020ec
controlsystems
locusplot
0
answers
18
GATE2020EC: 39
The state diagram of a sequence detector is shown below. State $S_{0}$ is the initial state of the sequence detector. If the output is $1$, then the sequence $01010$ is detected. the sequence $01011$ is detected. the sequence $01110$ is detected. the sequence $01001$ is detected.
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gate2020ec
statediagram
sequencedetector
controlsystems
0
answers
19
GATE2020EC: 38
$P, Q$, and $R$ are the decimal integers corresponding to the $4$bit binary number $1100$ considered in signed magnitude, $1$’s complement, and $2$’s complement representations, respectively. The $6$bit $2$’s complement representation of $(P+Q+R)$ is $110101$ $110010$ $111101$ $111001$
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gate2020ec
controlsystems
0
answers
20
GATE2020EC: 37
Using the incremental low frequency smallsignal model of the $\text{MOS}$ device, the Norton equivalent resistance of the following circuit is $r_{ds}+R+g_{m}r_{ds}R \\$ $\dfrac{r_{ds}+R}{1+g_{m}r_{ds}} \\$ $r_{ds}+\dfrac{1}{g_{m}}+R \\$ $r_{ds}+R$
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gate2020ec
electronicdevices
mos
nortonequivalentresistance
0
answers
21
GATE2020EC: 36
An enhancement $\text{MOSFET}$ of threshold voltage $3\:V$ is being used in the sample and hold circuit given below. Assume that the substrate of the $\text{MOS}$ device is connected to $10\:V$. If the input voltage $V_{1}$ lies between $\pm 10\:V,$ ... $\text{10 V and 10 V}$. $\text{13 V and 7 V}$. $\text{10 V and 13 V}$.
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gate2020ec
electronicdevices
mosfet
0
answers
22
GATE2020EC: 35
For the $\text{BJT}$ in the amplifier shown below, $V_{BE}=0.7V,\:kT/q=26\:mV$. Assume that $\text{BJT}$ output resistance $(r_{o})$ is very high and the base current is negligible. The capacitors are also assumed to be short circuited at signal frequencies. The input ... . The low frequency voltage gain $v_{o}/v_{i}$ of the amplifier is $89.42$ $128.21$ $178.85$ $256.42$
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gate2020ec
electronicdevices
bjt
0
answers
23
GATE2020EC: 34
A $pn$ junction solar cell of area $1.0\:cm^{2}$, illuminated uniformly with $100\:mW\:cm^{2}$, has the following parameters: Efficiency $= 15\%$, open circuit voltage $= 0.7\:V$, fill factor $= 0.8$, and thickness $=200 \mu m$ ... $0.84\times 10^{19}.$ $5.57\times 10^{19}.$ $1.04\times 10^{19}.$ $83.60\times 10^{19}.$
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gate2020ec
electronicdevices
solarcell
0
answers
24
GATE2020EC: 33
The base of an $\text{npn BJT T1}$ has a linear doping profile $N_{B}\left ( x \right )$ as shown below. The base of another $\text{npn BJT T2}$ has a uniform doping $N_{B}$ of $10^{17}cm^{3}$. All other parameters are identical for both the devices. ... $\text{T1}$. approximately $2.5$ times that of $\text{T1}$. approximately $0.7$ times that of $\text{T1}$.
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gate2020ec
communications
density
doping
0
answers
25
GATE2020EC: 32
The band diagram of a $p$type semiconductor with a bandgap of $1$ eV is shown. Using this semiconductor, a $\text{MOS}$ capacitor having $V_{TH}$ of $0.16 V$, ${C}'_{ox}$ of $100\:nF/cm^{2}$ and a metal work function of $3.87 \: eV$ is fabricated. There is no charge within the ... $C/cm^{2}$) is $1.70\times 10^{8}$ $0.52\times 10^{8}$ $1.41\times 10^{8}$ $0.93\times 10^{8}$
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gate2020ec
digitalcircuits
semiconductors
0
answers
26
GATE2020EC: 31
A onesided abrupt $pn$ junction diode has a depletion capacitance $C_{D}$ of $50$ $\text{pF}$ at a reverse bias of $0.2 V$. The plot of $1/C^{2}_{D}$ versus the applied voltage $V$ for this diode is a straight line as shown in the figure below. The slope of the plot is ___________ $\times 10^{20}F^{2}V^{1}$. $5.7$ $3.8$ $1.2$ $0.4$
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gate2020ec
electronicdevices
junctiondiode
plot
0
answers
27
GATE2020EC: 30
For the given circuit, which one of the following is correct state equation? ...
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gate2020ec
networksolutionmethods
networks
stateequations
0
answers
28
GATE2020EC: 29
A finite duration discretetime signal $x[n]$ is obtained by sampling the continuoustime signal $x\left ( t \right )=\cos\left ( 200\pi t \right )$ at sampling instants $t=n/400, n=0, 1, \dots ,7.$ The $8$point discrete Fourier transform $\text{(DFT)}$ of $x[n]$ is defined ... zero. Only $X[4]$ is nonzero. Only $X[2]$ and $X[6]$ are nonzero. Only $X[3]$ and $X[5]$ are nonzero.
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gate2020ec
continuoustimesignals
signalsandsystems
discretetimesignals
0
answers
29
GATE2020EC: 28
The current $I$ in the given network is $0 \: A$ $2.38\angle 96.37^{\circ}A$ $2.38\angle143.63^{\circ}A$ $2.38\angle23.63^{\circ}A$
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gate2020ec
networks
0
answers
30
GATE2020EC: 27
Which one of the following options contains two solutions of the differential equation $\dfrac{\mathrm{d} y}{\mathrm{d} x}=\left ( y1 \right )x?$ $\ln\mid y1 \mid=0.5x^{2}+C$ and $y=1$ $\ln\mid y1 \mid=2x^{2}+C$ and $y=1$ $\ln\mid y1 \mid=0.5x^{2}+C$ and $y=1$ $\ln\mid y1 \mid=2x^{2}+C$ and $y=1$
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gate2020ec
differentialequations
engineeringmathematics
0
answers
31
GATE2020EC: 26
Consider the following system of linear equations. $\begin{array}{llll} x_{1}+2x_{2}=b_{1} ; & 2x_{1}+4x_{2}=b_{2}; & 3x_{1}+7x_{2}=b_{3} ; & 3x_{1}+9x_{2}=b_{4} \end{array}$ ... $b_{2}=2b_{1}$ and $3b_{1}6b_{3}+b_{4}=0$ $b_{3}=2b_{1}$ and $3b_{1}6b_{3}+b_{4}=0$
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gate2020ec
engineeringmathematics
0
answers
32
GATE2020EC: 25
The two sides of a fair coin are labelled as $0$ to $1$. The coin is tossed two times independently. Let $M$ and $N$ denote the labels corresponding to the outcomes of those tosses. For a random variable $X$, defined as $X = \text{min}(M, N)$, the expected value $E(X)$ (rounded off to two decimal places) is ___________.
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gate2020ec
numericalanswers
engineeringmathematics
0
answers
33
GATE2020EC: 24
The random variable $Y=\int_{\infty }^{\infty }W\left ( t \right )\phi \left ( t \right )dt, \text{ where } \phi \left ( t \right )=\begin{cases} 1; & 5\leq t\leq 7 &\\ 0; & \text{otherwise} \end{cases}$ and $W(t)$ is a real white Gaussian noise process with twosided power spectral density $S_{W}\left ( f \right )=3 W/Hz$, for all $f$. The variance of $Y$ is ________.
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gate2020ec
numericalanswers
vectoranalysis
engineeringmathematics
gaussstheorem
0
answers
34
GATE2020EC: 23
The loop transfer function of a negative feedback system is $G\left ( s \right )H\left ( s \right )=\frac{K(s+11)}{s(s+2)(s+8)}.$ The value of $K$, for which the system is marginally stable, is ___________.
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gate2020ec
numericalanswers
networksolutionmethods
networks
transferfunction
0
answers
35
GATE2020EC: 22
A binary random variable $X$ takes the value $+2$ or $2$. The probability $P(X=+2)=\alpha $. The value of $\alpha$ (rounded off to one decimal place), for which the entropy of $X$ is maximum, is __________.
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gate2020ec
numericalanswers
probability
engineeringmathematics
0
answers
36
GATE2020EC: 21
A transmission line of length $3\lambda /4$ and having a characteristic impedance of $50$ $\Omega$ is terminated with a load of $400 \Omega$. The impedance (rounded off to two decimal places) seen at the input end of the transmission line is __________ $\Omega$.
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gate2020ec
numericalanswers
impedance
electromagnetics
0
answers
37
GATE2020EC: 20
A $10$bit D/A converter is calibrated over the full range from $0$ to $10$ V. If the input to the D/A converter is $13 \:A$ (in hex), the output ( rounded off to three decimal places) is __________ $V$.
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gate2020ec
numericalanswers
digitalcircuits
converters
0
answers
38
GATE2020EC: 19
In an $8085$ microprocessor, the number of address lines required to access a $16$ K byte memory bank is ____________ .
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gate2020ec
numericalanswers
digitalcircuits
microprocessor8085
0
answers
39
GATE2020EC: 18
In the circuit shown below, all the components are ideal. If $V_{i}$ is $+2\:V$, the current $I_{o}$ sourced by the opamp is __________ $\text{mA}$.
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gate2020ec
numericalanswers
opamp
analogcircuits
0
answers
40
GATE2020EC: 17
In the circuit shown below, all the components are ideal and the input voltage is sinusoidal. The magnitude of the steadystate output $V_{o}$ ( rounded off to two decimal places) is ______ $V$.
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gate2020ec
numericalanswers
networksolutionmethods
steadystate
sinusoidal
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