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1
GATE2020EC: 1
If $v_{1},v_{2}, \dots ,v_{6}$ are six vectors in $\mathbb{R}^{4}$ , which one of the following statements is $\text{FALSE}$? It is not necessary that these vectors span $\mathbb{R}^{4}$ ... $\mathbb{R}^{4}$ , then it forms a basis for $\mathbb{R}^{4}$.
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gate2020ec
vectoranalysis
engineeringmathematics
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2
GATE2020EC: 2
For a vector field $\overrightarrow{A}$, which one of the following is $\text{FALSE}$? $\overrightarrow{A}$ is solenoidal if $\triangledown \cdot \overrightarrow{A}=0.$ $\triangledown \times \overrightarrow{A}$ ...
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gate2020ec
engineeringmathematics
vectors
overrightarrow
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3
GATE2020EC: 3
The partial derivative of the function $f(x, y, z) = e^{1x\cos y} + xze^{1/(1+y^{2})}$ with respect to $x$ at the point $(1,0,e)$ is $1$ $0$ $1 \\$ $\dfrac{1}{e}$
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gate2020ec
partialdifferentialequations
engineeringmathematics
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4
GATE2020EC: 4
The general solution of $\dfrac{\mathrm{d^{2}} y}{\mathrm{d} x^{2}}6\dfrac{\mathrm{d} y}{\mathrm{d} x}+9y=0$ is $y=C_{1}e^{3x}+C_{2}e^{3x}$ $y=(C_{1}+C_{2}x)e^{3x}$ $y=(C_{1}+C_{2}x)e^{3x}$ $y=C_{1}e^{3x}$
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gate2020ec
engineeringmathematics
0
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5
GATE2020EC: 5
The output $y[n]$ of a discretetime system for an input $x[n]$ is $y\left [ n \right ]=\underset{\infty \leq k\leq n}{\text{max}} \mid x\left [ k \right ] \mid$ The unit impulse response of the system is $0$ for all $n$. $1$ for all $n$. unit step signal $u\left [ n \right ].$ unit impulse signal $\delta \left [ n \right ].$
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Feb 13
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gate2020ec
continuoustimesignals
signalsandsystems
discretetimesignals
impulseresponse
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0
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6
GATE2020EC: 6
A single crystal intrinsic semiconductor is at a temperature of $300$ $\text{K}$ with effective density of states for holes twice that of electrons. The thermal voltage is $26$ mV. The intrinsic Fermi level is shifted from midbandgap energy level by $18.02 \: meV$ $9.01 \: meV$ $13.45 \: meV$ $26.90 \: meV$
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Feb 13
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gate2020ec
digitalcircuits
semiconductors
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0
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7
GATE2020EC: 7
Consider the recombination process via bulk traps in a forward biased $pn$ homojunction diode. The maximum recombination rate is $U_{\text{max}}$ ... applied bias. With all other parameters unchanged, $U_{\text{max}}$ increases if the thermal velocity of the carriers increases.
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Feb 13
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gate2020ec
electronicdevices
0
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0
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8
GATE2020EC: 8
The components in the circuit shown below are ideal. If the opamp is in positive feedback and the input voltage $V_{i}$ is a sine wave of amplitude $1$ $\text{V}$, the output voltage $V_{o}$ is a noninverted sine wave of $2$ $\text{V}$ amplitude. an inverted sine wave ... amplitude. a square wave of $5$ $\text{V}$ amplitude. a constant of either $+5$ $\text{V}$ or $5$ $\text{V}$.
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Feb 13
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gate2020ec
communications
amplitude
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0
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9
GATE2020EC: 9
In the circuit shown below, the Thevenin voltage $V_{TH}$is $2.4\:V$ $2.8\:V$ $3.6\:V$ $4.5\:V$
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Feb 13
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1.4k
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gate2020ec
networksolutionmethods
networks
theveninvoltage
0
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0
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10
GATE2020EC: 10
The figure below shows a multiplexer where $S_{1}$ and $S{2}$ are the select lines, $I_{0}$ to $I_{3}$ are the input data lines, $\text{EN}$ is the enable line, and $\text{F(P, Q, R)}$ is the output. $\text{F}$ is $PQ+\overline{Q}R.$ $PQ+Q\overline{R}.$ $P\overline{Q}R+\overline{P}Q.$ $\overline{Q}+PR.$
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Feb 13
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gate2020ec
digitalcircuits
multiplexers
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0
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11
GATE2020EC: 11
The polezero map of a rational function $G(s)$ is shown below. When the closed contour $\Gamma$ is mapped into the $G(s)$plane, then the mapping encircles the origin of the $G(s)$plane once in the counterclockwise direction. the origin of the $G(s)$ ... $1 + j0$ of the $G(s)$plane once in the clockwise direction.
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Feb 13
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1.4k
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gate2020ec
continuoustimesignals
signalsandsystems
polezero
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0
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12
GATE2020EC: 12
A digital communication system transmits a block of $N$ bits. The probability of error in decoding a bit is $\alpha$. The error event of each bit is independent of the error events of the other bits. The received block is declared erroneous if at least one of its bits is decoded wrongly. The ... $\alpha ^{N}$ $1\alpha ^{N}$ $1\left ( 1\alpha \right )^{N}$
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Feb 13
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jothee
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gate2020ec
probability
digitalcommunications
0
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0
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13
GATE2020EC: 13
The impedances $Z=jX,$ for all $X$ in the range $\left ( \infty ,\infty \right )$, map to the Smith chart as a circle of radius $1$ with centre at $(0, 0)$. a point at the centre of the chart. a line passing through the centre of the chart. a circle of radius $0.5$ with centre at $(0.5, 0)$.
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Feb 13
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jothee
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gate2020ec
impedance
electromagnetics
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0
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14
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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Feb 13
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gate2020ec
0
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0
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15
GATE2020EC: 15
In the given circuit, the twoport network has the impedance matrix $\begin{bmatrix} Z \end{bmatrix}=\begin{bmatrix} 40 & 60\\ 60& 120 \end{bmatrix}$. The value of $Z_{L}$ for which maximum power is transferred to the load is _____________$\Omega$.
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Feb 13
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jothee
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1.4k
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gate2020ec
numericalanswers
networks
0
votes
0
answers
16
GATE2020EC: 16
The current in the $\text{RL}$circuit shown below is $i\left ( t \right )=10\cos\left ( 5t\pi /4 \right )A$. The value of the inductor $\text{(rounded off to two decimal places)}$ is _______ $\text{H}$.
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Feb 13
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jothee
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1.4k
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gate2020ec
numericalanswers
networks
inductors
0
votes
0
answers
17
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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Feb 13
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1.4k
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gate2020ec
numericalanswers
networksolutionmethods
steadystate
sinusoidal
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0
answers
18
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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Feb 13
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jothee
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1.4k
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gate2020ec
numericalanswers
opamp
analogcircuits
0
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0
answers
19
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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Feb 13
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jothee
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1.4k
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gate2020ec
numericalanswers
digitalcircuits
microprocessor8085
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0
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20
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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Feb 13
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by
jothee
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1.4k
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gate2020ec
numericalanswers
digitalcircuits
converters
0
votes
0
answers
21
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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Feb 13
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jothee
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1.4k
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gate2020ec
numericalanswers
impedance
electromagnetics
0
votes
0
answers
22
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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Feb 13
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jothee
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1.4k
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gate2020ec
numericalanswers
probability
engineeringmathematics
0
votes
0
answers
23
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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Feb 13
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jothee
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1.4k
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gate2020ec
numericalanswers
networksolutionmethods
networks
transferfunction
0
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0
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24
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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Feb 13
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jothee
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1.4k
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gate2020ec
numericalanswers
vectoranalysis
engineeringmathematics
gaussstheorem
0
votes
0
answers
25
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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Feb 13
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jothee
(
1.4k
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gate2020ec
numericalanswers
engineeringmathematics
0
votes
0
answers
26
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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Feb 13
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jothee
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1.4k
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gate2020ec
engineeringmathematics
0
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0
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27
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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Feb 13
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jothee
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1.4k
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gate2020ec
differentialequations
engineeringmathematics
0
votes
0
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28
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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Feb 13
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gate2020ec
networks
0
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0
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29
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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Feb 13
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jothee
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1.4k
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gate2020ec
continuoustimesignals
signalsandsystems
discretetimesignals
0
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0
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30
GATE2020EC: 30
For the given circuit, which one of the following is correct state equation? ...
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Feb 13
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jothee
(
1.4k
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gate2020ec
networksolutionmethods
networks
stateequations
0
votes
0
answers
31
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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jothee
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1.4k
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gate2020ec
electronicdevices
junctiondiode
plot
0
votes
0
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32
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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Feb 13
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jothee
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gate2020ec
digitalcircuits
semiconductors
0
votes
0
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33
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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jothee
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gate2020ec
communications
density
doping
0
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0
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34
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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Feb 13
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jothee
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gate2020ec
electronicdevices
solarcell
0
votes
0
answers
35
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
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0
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36
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
votes
0
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37
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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jothee
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1.4k
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gate2020ec
electronicdevices
mos
nortonequivalentresistance
0
votes
0
answers
38
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
votes
0
answers
39
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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jothee
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1.4k
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gate2020ec
statediagram
sequencedetector
controlsystems
0
votes
0
answers
40
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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1.4k
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gate2020ec
controlsystems
locusplot
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