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1

GATE2020-EC: 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 $\mathbb{R}^{4}$.

asked Feb 13, 2020 in Vector Analysis by jothee (1.4k points)

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2

GATE2020-EC: 2
For a vector field $\overrightarrow{A}$, which one of the following is $\text{FALSE}$? $\overrightarrow{A}$ is solenoidal if $\triangledown \cdot \overrightarrow{A}=0.$ $\triangledown \times \overrightarrow{A}$ ...

asked Feb 13, 2020 in Vector Analysis by jothee (1.4k points)

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3

GATE2020-EC: 3
The partial derivative of the function $f(x, y, z) = e^{1-x\cos y} + xze^{-1/(1+y^{2})}$ with respect to $x$ at the point $(1,0,e)$ is $-1$ $0$ $1 \\$ $\dfrac{1}{e}$

asked Feb 13, 2020 in Differential Equations by jothee (1.4k points)

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4

GATE2020-EC: 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 $y=C_{1}e^{3x}+C_{2}e^{-3x}$ $y=(C_{1}+C_{2}x)e^{-3x}$ $y=(C_{1}+C_{2}x)e^{3x}$ $y=C_{1}e^{3x}$

asked Feb 13, 2020 in Engineering Mathematics by jothee (1.4k points)

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5

GATE2020-EC: 5
The output $y[n]$ of a discrete-time 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 $\delta \left [ n \right ].$

asked Feb 13, 2020 in Continuous-time Signals by jothee (1.4k points)

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6

GATE2020-EC: 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 mid-bandgap energy level by $18.02 \: meV$ $9.01 \: meV$ $13.45 \: meV$ $26.90 \: meV$

asked Feb 13, 2020 in Digital Circuits by jothee (1.4k points)

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7

GATE2020-EC: 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.

asked Feb 13, 2020 in Electronic Devices by jothee (1.4k points)

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8

GATE2020-EC: 8
The components in the circuit shown below are ideal. If the op-amp 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 non-inverted 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 $-5$ $\text{V}$.

asked Feb 13, 2020 in Communications by jothee (1.4k points)

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9

GATE2020-EC: 9
In the circuit shown below, the Thevenin voltage $V_{TH}$is $2.4\:V$ $2.8\:V$ $3.6\:V$ $4.5\:V$

asked Feb 13, 2020 in Network Solution Methods by jothee (1.4k points)

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10

GATE2020-EC: 11
The pole-zero 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 counter-clockwise direction. the origin of the $G(s)$- ... $-1 + j0$ of the $G(s)$-plane once in the clockwise direction.

asked Feb 13, 2020 in Continuous-time Signals by jothee (1.4k points)

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11

GATE2020-EC: 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 ... $\alpha ^{N}$ $1-\alpha ^{N}$ $1-\left ( 1-\alpha \right )^{N}$

asked Feb 13, 2020 in Communications by jothee (1.4k points)

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12

GATE2020-EC: 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 $(0.5, 0)$.

asked Feb 13, 2020 in Electromagnetics by jothee (1.4k points)

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13

GATE2020-EC: 14
Which one of the following pole-zero plots corresponds to the transfer function of an $\text{LTI}$ system characterized by the input-output difference equation given below? $y\left [ n \right ]=\sum ^{3}_{k=0}\left ( -1 \right )^{k}x\left [ n-k \right ]$

asked Feb 13, 2020 in Continuous-time Signals by jothee (1.4k points)

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14

GATE2020-EC: 15
In the given circuit, the two-port 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 _____________$\Omega$.

asked Feb 13, 2020 in Network Solution Methods by jothee (1.4k points)

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15

GATE2020-EC: 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 _______ $\text{H}$.

asked Feb 13, 2020 in Network Solution Methods by jothee (1.4k points)

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16

GATE2020-EC: 17
In the circuit shown below, all the components are ideal and the input voltage is sinusoidal. The magnitude of the steady-state output $V_{o}$ ( rounded off to two decimal places) is ______ $V$.

asked Feb 13, 2020 in Network Solution Methods by jothee (1.4k points)

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17

GATE2020-EC: 18
In the circuit shown below, all the components are ideal. If $V_{i}$ is $+2\:V$, the current $I_{o}$ sourced by the op-amp is __________ $\text{mA}$.

asked Feb 13, 2020 in Analog Circuits by jothee (1.4k points)

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18

GATE2020-EC: 19
In an $8085$ microprocessor, the number of address lines required to access a $16$ K byte memory bank is ____________ .

asked Feb 13, 2020 in Digital Circuits by jothee (1.4k points)

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19

GATE2020-EC: 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 __________ $V$.

asked Feb 13, 2020 in Digital Circuits by jothee (1.4k points)

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20

GATE2020-EC: 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 __________ $\Omega$.

asked Feb 13, 2020 in Electromagnetics by jothee (1.4k points)

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21

GATE2020-EC: 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 __________.

asked Feb 13, 2020 in Communications by jothee (1.4k points)

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22

GATE2020-EC: 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 ___________.

asked Feb 13, 2020 in Network Solution Methods by jothee (1.4k points)

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23

GATE2020-EC: 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 two-sided power spectral density $S_{W}\left ( f \right )=3 W/Hz$, for all $f$. The variance of $Y$ is ________.

asked Feb 13, 2020 in Vector Analysis by jothee (1.4k points)

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24

GATE2020-EC: 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 ___________.

asked Feb 13, 2020 in Engineering Mathematics by jothee (1.4k points)

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25

GATE2020-EC: 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 $3b_{1}-6b_{3}+b_{4}=0$

asked Feb 13, 2020 in Engineering Mathematics by jothee (1.4k points)

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26

GATE2020-EC: 27
Which one of the following options contains two solutions of the differential equation $\dfrac{\mathrm{d} y}{\mathrm{d} x}=\left ( y-1 \right )x?$ $\ln\mid y-1 \mid=0.5x^{2}+C$ and $y=1$ $\ln\mid y-1 \mid=2x^{2}+C$ and $y=1$ $\ln\mid y-1 \mid=0.5x^{2}+C$ and $y=-1$ $\ln\mid y-1 \mid=2x^{2}+C$ and $y=-1$

asked Feb 13, 2020 in Differential Equations by jothee (1.4k points)

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27

GATE2020-EC: 28
The current $I$ in the given network is $0 \: A$ $2.38\angle -96.37^{\circ}A$ $2.38\angle143.63^{\circ}A$ $2.38\angle-23.63^{\circ}A$

asked Feb 13, 2020 in Network Solution Methods by jothee (1.4k points)

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28

GATE2020-EC: 29
A finite duration discrete-time signal $x[n]$ is obtained by sampling the continuous-time 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 non-zero. Only $X[2]$ and $X[6]$ are non-zero. Only $X[3]$ and $X[5]$ are non-zero.

asked Feb 13, 2020 in Continuous-time Signals by jothee (1.4k points)

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29

GATE2020-EC: 30
For the given circuit, which one of the following is correct state equation? ...

asked Feb 13, 2020 in Network Solution Methods by jothee (1.4k points)

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30

GATE2020-EC: 31
A one-sided 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 ___________ $\times 10^{20}F^{-2}V^{-1}$. $-5.7$ $-3.8$ $-1.2$ $-0.4$

asked Feb 13, 2020 in Electronic Devices by jothee (1.4k points)

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31

GATE2020-EC: 32
The band diagram of a $p$-type semiconductor with a band-gap 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 $1.70\times 10^{-8}$ $0.52\times 10^{-8}$ $1.41\times 10^{-8}$ $0.93\times 10^{-8}$

asked Feb 13, 2020 in Digital Circuits by jothee (1.4k points)

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32

GATE2020-EC: 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 $\text{T1}$.

asked Feb 13, 2020 in Analog Circuits by jothee (1.4k points)

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33

GATE2020-EC: 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 $=200 \mu m$ ... $0.84\times 10^{19}.$ $5.57\times 10^{19}.$ $1.04\times 10^{19}.$ $83.60\times 10^{19}.$

asked Feb 13, 2020 in Electronic Devices by jothee (1.4k points)

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34

GATE2020-EC: 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 $-89.42$ $-128.21$ $-178.85$ $-256.42$

asked Feb 13, 2020 in Analog Circuits by jothee (1.4k points)

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35

GATE2020-EC: 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 $\pm 10\:V,$ ... $\text{10 V and -10 V}$. $\text{13 V and -7 V}$. $\text{10 V and -13 V}$.

asked Feb 13, 2020 in Electronic Devices by jothee (1.4k points)

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36

GATE2020-EC: 37
Using the incremental low frequency small-signal model of the $\text{MOS}$ device, the Norton equivalent resistance of the following circuit is $r_{ds}+R+g_{m}r_{ds}R \\$ $\dfrac{r_{ds}+R}{1+g_{m}r_{ds}} \\$ $r_{ds}+\dfrac{1}{g_{m}}+R \\$ $r_{ds}+R$

asked Feb 13, 2020 in Network Solution Methods by jothee (1.4k points)

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37

GATE2020-EC: 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 $110101$ $110010$ $111101$ $111001$

asked Feb 13, 2020 in Control Systems by jothee (1.4k points)

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38

GATE2020-EC: 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.

asked Feb 13, 2020 in Control Systems by jothee (1.4k points)

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39

GATE2020-EC: 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 break-away or break-in points(s) lie within $(-1, 0)$ $(-2, -1)$ $(-3, -2)$ $(-\infty, -3)$

asked Feb 13, 2020 in Control Systems by jothee (1.4k points)

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40

GATE2020-EC: 41
The components in the circuit given below are ideal. If $R=2\:k \Omega$ and $C=1$ $\mu F$, the $-3$ dB cut-off frequency of the circuit in Hz is $14.92$ $34.46$ $59.68$ $79.58$

asked Feb 13, 2020 in Control Systems by jothee (1.4k points)