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GATE2020ECGA: 1
The untimely loss of life is a cause of serious global concern as thousands of people get killed______accidents every year while many other die______diseases like cardio vascular disease, cancer, etc. in, of from, of during, from from, from
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GATE2020ECGA: 2
He was not only accused of theft_______of conspiracy. rather but also but even rather than
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GATE2020ECGA: 3
Select the word that fits the analogy: Explicit: Implicit :: Express: _______ Impress Repress Compress Suppress
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GATE2020ECGA: 4
The Canadian constitution requires that equal importance be given to English and French. Last year, Air Canada lost a lawsuit, and had to pay a sixfigure fine to a Frenchspeaking couple after they filed complaints about formal inflight ... the French ones. the English announcements being longer than the French ones. equal importance being given to English and French.
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GATE2020ECGA: 5
A superadditive function $\text{f(.)}$ satisfies the following property $f\left ( x_{1} +x_{2}\right )\geq f\left ( x_{1} \right ) + f\left ( x_{2} \right )$ Which of the following functions is a superadditive function for $x > 1$? $e^{x}$ $\sqrt{x}$ $1/x$ $e^{x}$
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GATE2020ECGA: 6
The global financial crisis in $2008$ is considered to be the most serious worldwide financial crisis, which started with the subprime lending crisis in $\text{USA}$ in $2007$. The sub prime lending crisis led to the banking ... $\rightarrow$ East Asian crisis$\rightarrow$ banking crisis$\rightarrow$ subprime lending crisis.
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GATE2020ECGA: 7
It is quarter past three in your watch. The angle between the hour hand and the minute hand is ________. $0^{\circ}$ $7.5^{\circ}$ $15^{\circ}$ $22.5^{\circ}$
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GATE2020ECGA: 8
A circle with centre $\text{O}$ is shown in the figure. A rectangle $\text{PQRS}$ of maximum possible area is inscribed in the circle. If the radius of the circle is $\text{a}$, then the area of the shaded portion is _______. $\pi a^{2}a^{2}$ $\pi a^{2}\sqrt{2}a^{2}$ $\pi a^{2}2a^{2}$ $\pi a^{2}3a^{2}$
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GATE2020ECGA: 9
$\text{a, b, c}$ are real numbers. The quadratic equation $ax^{2}bx+c=0$ has equal roots, which is $\beta ,$ then $\beta =b/a$ $\beta^{2} =ac$ $\beta^{3} =bc/\left ( 2a^{2} \right )$ $\beta^{2} \neq 4ac$
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GATE2020ECGA: 10
The following figure shows the data of students enrolled in $5$ years $\text{(2014 to 2018)}$ for two schools $\text{p}$ and $\text{Q}$. During this period, the ratio of the average number of the students enrolled in school $\text{P}$ to the average of the difference of the number ... enrolled in schools $\text{P}$ and $\text{Q}$ is _______. $8 : 23$ $23 : 8$ $23 : 31$ $31 : 23$
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GATE2020EC: 1
If $v_{1},v_{2},...,v_{6}$ 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: 2
For a vector field $\overrightarrow{A}$, which one of the following is $\text{FALSE}$? $\overrightarrow{A}$ is solenoidal if $\triangledown .\overrightarrow{A}=0.$ $\triangledown \times \overrightarrow{A}$ ...
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GATE2020EC: 3
The partial derivative of the function $\text{f(x, y, z)} = e^{1x\cos y} + xze^{1/(1+y^{2})}$ $1$ $0$ $1$ $\frac{1}{e}$
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GATE2020EC: 4
The general solution of $\frac{\mathrm{d^{2}} y}{\mathrm{d} x^{2}}6\frac{\mathrm{d} y}{\mathrm{d} x}+9y=0$ 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: 5
The output $\text{y[n]}$ of a discretetime system for an input $\text{x[n]}$ is $y\left [ n \right ]=max_{\infty \leq k\leq n}\left  x\left [ k \right ] \right .$ The unit impluse 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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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 $\text{26 mV}$. The intrinsic Fermi level is shifted from midbandgap energy level by $\text{18.02 meV.}$ $\text{9.01 meV.}$ $\text{13.45 meV.}$ $\text{26.90 meV.}$
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GATE2020EC: 7
Consider the recombination process via bulk traps in a forward biased $\text{pn}$ homojunction diode. The maximum recombination rate is $U_{max}$ ... on the applied bias. With all other parameters unchanged, $U_{max}$ increases if the thermal velocity of the carriers increases.
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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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19
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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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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21
GATE2020EC: 11
The polezero map of a rational function $\text{G(s)}$ is shown below. When the closed contour $\Gamma$ is mapped into the $\text{G(s)}$plane, then the mapping encircles the origin of the $\text{G(s)}$plane once in the counterclockwise direction. the ... in the counterclockwise direction. the point $\text{1 + j0}$ of the $\text{G(s)}$plane once in the clockwise direction.
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GATE2020EC: 12
A digital communication system transmits a block of $\text{N}$ 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. ... $\alpha ^{N}$ $1\alpha ^{N}$ $1\left ( 1\alpha \right )^{N}$
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GATE2020EC: 13
The impedances $Z=jX,$ for all $\text{X}$ in the range $\left ( \infty ,\infty \right )$, map to the Smith chart as a circle of radius $1$ with centre at $\text{(0, 0)}$. 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 $\text{(0.5, 0)}$.
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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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25
GATE2020EC: 15
In the given circuit, the twoport network has the impedance matrix $\left [ Z \right ]=\begin{bmatrix} 40 & 60\\ 60& 120 \end{bmatrix}.$ The value of $Z_{L}$ for which maximum power is transferred to the load is _____________$\Omega$.
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26
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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27
GATE2020EC: 17
In the circuit shown below, all the components are ideal and the input voltage is sinsoidial. The magnitude of the steadystate output $V_{o}$ ( rounded off to two decimal places) is ______ $V$.
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28
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: 19
In an $8085$ microprocessor, the number of address lines required to access a $\text{16 K byte}$ memory bank is ____________ .
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GATE2020EC: 20
A $\text{10bit D/A}$ converter is calibrated over the full range from $\text{0 to 10 V}$. If the input to the $\text{D/A}$ converter is $\text{13A}$ (in hex), the output ( rounded off to three decimal places) is __________ $\text{V}$.
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31
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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32
GATE2020EC: 22
A binary random variable $\text{X}$ 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 $\text{X}$ is maximum, is __________.
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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 $\text{K}$, for which the system is marginally stable, is ___________.
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34
GATE2020EC: 24
The random variable $Y=\int_{\infty }^{\infty }W\left ( t \right )\phi \left ( t \right )dt,\:\:\:\:\:\:\:where\:\:\:\phi \left ( t \right )=\left\{\begin{matrix} 1;5\leq t\leq 7 &\\ 0;otherwise \end{matrix}\right.$ and $\text{W(t)}$ ... process with twosided power spectral density $S_{W}\left ( f \right )=3 W/Hz,$ for all $\text{f}$. The variance of $\text{Y}$ is ________.
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GATE2020EC: 25
The two sides of a fair coin are labelled as $0$ to $1$. The coin is tossed two times independently. Let $\text{M}$ and $\text{N}$ denote the labels corresponding to the outcomes of those tosses. For a random variable $\text{X}$, defined as $\text{X = min(M, N),}$ the expected value $E(X)$ (rounded off to two decimal places) is ___________.
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36
GATE2020EC: 26
Consider the following system of linear equations. $x_{1}+2x_{2}=b_{1}$ ; $2x_{1}+4x_{2}=b_{2}$ ; $3x_{1}+7x_{2}=b_{3}$ ; $3x_{1}+9x_{2}=b_{4}$ Which one of the following conditions ensures that a solution exists for the above system? $b_{2}=2b_{1}$ and $6b_{1}3b_{3}=b_{4}=0$ ... $b_{2}=2b_{1}$ 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: 27
Which one of the following options contains two solutions of the differential equation $\frac{\mathrm{d} y}{\mathrm{d} x}=\left ( y1 \right )x?$ $ln\left  y1 \right =0.5x^{2}+C$ and $y=1$ $ln\left  y1 \right =2x^{2}+C$ and $y=1$ $ln\left  y1 \right =0.5x^{2}+C$ and $y=1$ $ln\left  y1 \right =2x^{2}+C$ and $y=1$
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38
GATE2020EC: 28
The current $\text{I}$ in the given network is $\text{0 A}$. $2.38\angle 96.37^{\circ}A.$ $2.38\angle143.63^{\circ}A.$ $2.38\angle23.63^{\circ}A.$
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GATE2020EC: 29
A finite duration discretetime signal $\text{x[n]}$ is obtained by sampling the continuoustime signal $x\left ( t \right )=\cos\left ( 200\pi t \right )$ at sampling instants $t=n/400,$ $n=0, 1, ...,7.$ The $8$point discrete Fourier transform $\text{(DFT)}$ ... zero. Only $\text{X[2]}$ and $\text{X[6]}$ are nonzero. Only $\text{X[3]}$ and $\text{X[5]}$ are nonzero.
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GATE2020EC: 30
For the given circuit, which one of the following is correct state equation? ...
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