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1

GATE2019 EC: GA-6
Four people are standing in a line facing you. They are Rahul, Mathew, Seema and Lohit. One is an engineer, one is a doctor, one a teacher and another a dancer. You are told that: Mathew is not standing next to Seema There are two people standing ... Seema is turning to her right to speak to the doctor standing next to her Who among them is an engineer? Seema Lohit Rahul Mathew

asked Feb 12 in Numerical Ability by Arjun (1.4k points)

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2

GATE2019 EC: GA-7
The bar graph in panel (a) shows the proportion of male and female illiterates in $2001$ and $2011.$ The proportions of males and females in $2001$ and $2011$ are given in Panel (b) and (c), respectively. The total population did not change during this period. The percentage increase in the total number of literates from $2001$ to $2011$ is ______. $30.43$ $33.43$ $34.43$ $35.43$

asked Feb 12 in Numerical Ability by Arjun (1.4k points)

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3

GATE2019 EC: GA-8
"Indian history was written by British historians-extremely well documented and researched, but not always impartial. History had to serve its purpose: Everything was made subservient to the glory of the Union Jack. Latter-day Indian scholars ... biased was well documented and researched but was sometimes biased was not well documented and researched and was sometimes biased

asked Feb 12 in Verbal Ability by Arjun (1.4k points)

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4

GATE2019 EC: GA-9
Two design consultants, $P$ and $Q,$ started working from $8$ AM for a client. The client budgeted a total of USD $3000$ for the consultants. $P$ stopped working when the hour hand moved by $210$ degrees on the clock. $Q$ stopped working when the hour ... . After paying the consultants, the client shall have USD _______ remaining in the budget. $000.00$ $166.67$ $300.00$ $433.33$

asked Feb 12 in Numerical Ability by Arjun (1.4k points)

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5

GATE2019 EC: 1
Which of the following functions is analytic over the entire complex plane? $\ln(z)$ $e^{1/z}$ $\frac{1}{1-z}$ $cos(z)$

asked Feb 12 in Others by Arjun (1.4k points)

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6

GATE2019 EC: 2
The families of curves represented by the solution of the equation $\frac{dy}{dx}= – (\frac{x}{y})^n$ for $n=-1$ and $n= +1,$ respectively, are Parabolas and Circles Circles and Hyperbolas Hyperbolas and Circles Hyperbolas and Parabolas

asked Feb 12 in Others by Arjun (1.4k points)

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7

GATE2019 EC: 3
Let $H(z)$ be the $z-$ transform of a real-valued discrete-time signal $h[n].$ If $P(z) = H(z) H(\frac{1}{z})$ has a zero at $z= \frac{1}{2}+\frac{1}{2}j,$ and $P(z)$ has a total of four zeros, which one of the following plots represents all the zeros correctly?

asked Feb 12 in Others by Arjun (1.4k points)

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8

GATE2019 EC: 4
Consider the two-port resistive network shown in the figure. When an excitation of $5$V is applied across Port $1$, and Port $2$ is shorted, the current through the short circuit at Port $2$ is measured to be $1$ A (see (a) in the figure). Now, if an excitation of $5$ V is ... the current through the short circuit at Port $1$? $\text{0.5 A}$ $\text{1 A}$ $\text{2 A}$ $\text{2.5 A}$

asked Feb 12 in Others by Arjun (1.4k points)

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9

GATE2019 EC: 5
Let $Y(s)$ be the unit-step response of a causal system having a transfer function $G(s)= \frac{3-s}{(s+1)(s+3)}$ that is ,$Y(s)=\frac{G(s)}{s}.$ The forced response of the system is $u(t)-2e^{-t}u(t)+e^{-3t}u(t)$ $2u(t)-2e^{-t}u(t)+e^{-3t}u(t)$ $2u(t)$ $u(t)$

asked Feb 12 in Others by Arjun (1.4k points)

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10

GATE2019 EC: 6
For an LTI system, the Bode plot for its gain is as illustrated in the figure shown. The number of system poles $N_{p}$ and the number of system zeros $N_{z}$ in the frequency range $1 Hz \leq f\leq 10^{7} Hz$ is $N_{p}=5, N_{z}=2$ $N_{p}=6, N_{z}=3$ $N_{p}=7, N_{z}=4$ $N_{p}=4, N_{z}=2$

asked Feb 12 in Others by Arjun (1.4k points)

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11

GATE2019 EC: 7
A linear Hamming code is used to map $4-bit$ message to $7-bit$ codewords. The encoder mapping is linear. If the message $0001$ is mapped to the codeword $0000111$, and the message $0011$ is mapped to the codeword $1100110$, then the message $0010$ is mapped to $0010011$ $1100001$ $1111000$ $1111111$

asked Feb 12 in Others by Arjun (1.4k points)

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12

GATE2019 EC: 8
Which one of the following options describes correctly the equilibrium band diagram at $T=300$K of a Silicon $pnn^{+}$ $p^{++}$ configuration shown in the figure?

asked Feb 12 in Others by Arjun (1.4k points)

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13

GATE2019 EC: 9
The correct circuit representation of the structure shown in the figure is

asked Feb 12 in Others by Arjun (1.4k points)

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14

GATE2019 EC: 10
The figure shows the high-frequency C-V curve of a MOS capacitor (at $T=300$K) with $Φ_{ms}=0 V$ and no oxide charges. The flat-band, inversion, and accumulation conditions are represented, respectively, by the points $P,Q,R$ $Q,R,P$ $R,P,Q$ $Q,P,R$

asked Feb 12 in Others by Arjun (1.4k points)

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15

GATE2019 EC: 11
What is the electric flux $(\int \vec{E}.d \hat{a})$ through a quarter-cylinder of height $H$(as shown in the figure) due to an infinitely long line charge along the axis of the cylinder with a charge density of $Q$ ? $\frac{HQ}{\varepsilon_{0}}$ $\frac{HQ}{4\varepsilon_{0}}$ $\frac{H\varepsilon}{4Q}$ $\frac{4H}{Q\varepsilon_{0}}$

asked Feb 12 in Others by Arjun (1.4k points)

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16

GATE2019 EC: 12
In the table shown, List I and List II, respectively, contain terms appearing on the left-hand side and the right-hand side of Maxwell's equations (in their standard form). Match the left-hand side with the corresponding right-hand side. ... $\text{1-Q,2-S,3-P,4-R}$ $\text{1-R,2-Q,3-S,4-P}$

asked Feb 12 in Others by Arjun (1.4k points)

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17

GATE2019 EC: 13
A standard CMOS inverter is designed with equal rise and fall times $(\beta_{n}=\beta_{p}).$ If the width of the pMOS transistor in the inverter is increased what would be the effect on the LOW noise margin $NM_{L}$ and the HIGH noise margin $NM_{H}$ ... decreases. $NM_{L}$ decreases and $NM_{H}$ increases. Both $NM_{L}$ and $NH_{H}$ increases. No change in the noise margins.

asked Feb 12 in Others by Arjun (1.4k points)

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18

GATE2019 EC: 14
In the circuit shown, what are the values of $F$ for $EN=0$ and $EN=1$, respectively? $\text{0 and D}$ $\text{Hi-Z and D}$ $\text{0 and 1}$ $\text{Hi-Z and}$ $ \overline{D}$

asked Feb 12 in Others by Arjun (1.4k points)

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19

GATE2019 EC: 15
In the circuit shown, $A$ and $B$ are the inputs and $F$ is the output. What is the functionality of the circuit? Latch XNOR SRAM Cell XOR

asked Feb 12 in Others by Arjun (1.4k points)

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20

GATE2019 EC: 16
The value of the contour integral $\frac{1}{2\pi j} \oint(z+\frac{1}{z})^{2}dz$ evaluated over the unit circle $|z|=1$ is_______.

asked Feb 12 in Others by Arjun (1.4k points)

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21

GATE2019 EC: 18
If $X$ and $Y$ are random variable such that $E[2X+Y]=0$ and $E[X+2Y]=33$, then $E[X]+E[Y]=$__________________.

asked Feb 12 in Others by Arjun (1.4k points)

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22

GATE2019 EC: 19
The value of the integral $\int_{0}^{\pi} \int_{y}^{\pi}\frac{sinx}{x}dx dy ,$ is equal to _____________.

asked Feb 12 in Others by Arjun (1.4k points)

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23

GATE2019 EC: 20
Let $Z$ be an exponential random variable with mean $1$. That is, the cumulative distribution function of $Z$is given by $F_{z}(x)=$\begin{Bmatrix} 1-e^{-x}& if x\geq 0 \\ 0& if x< 0 \end{Bmatrix}$ Then Pr$(z>2|z>1)$, rounded off to two decimal places, is equal to ___________.

asked Feb 12 in Others by Arjun (1.4k points)

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24

GATE2019 EC: 21
Consider the signal $f(t)=1+2 cos(\pi t)+3 sin (\frac{2\pi}{3}t)+4 cos (\frac{\pi}{2}t+\frac{\pi}{4})$, where $t$ is in seconds. Its fundamental time period, in seconds, is _____________________.

asked Feb 12 in Others by Arjun (1.4k points)

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25

GATE2019 EC: 22
The baseband signal $m(t)$ shown in the figure is phase-modulated to generate the $PM$ signal $\varphi(t)=cos(2\pi f_{c}t+ k m(t)).$ The time $t$ on the $x-$ axis in the figure is in milliseconds. If the carrier ... ratio of the minimum instantaneous frequency (in kHz) to the maximum instantaneous frequency (in kHz) is ___________________ (rounded off to $2$ decimal places).

asked Feb 12 in Others by Arjun (1.4k points)

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26

GATE2019 EC: 23
Radiation resistance of a small dipole current element of length $l$ at a frequency of $3$ GHz is $3$ ohms. If the length is changed by $1\%$, then the percentage change in the radiation resistance, rounded off to two decimal places, is ______________ $\%.$

asked Feb 12 in Others by Arjun (1.4k points)

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27

GATE2019 EC: 24
In the circuit shown, $V_{s}$ is square wave of period $T$ with maximum and minimum values of $8 V$ and $-10 V$, respectively. Assume that the diode is ideal and $R_{1}=R_{2}=50 \Omega.$ The average value of $V_{L}$ is _______ volts (rounded off to $1$ decimal place.)

asked Feb 12 in Others by Arjun (1.4k points)

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28

GATE2019 EC: 25
In the circuit shown, the clock frequency, i.e., the frequency of the ClK signal, is $12kHz$. The frequency of the signal at $Q_{2}$ is _____________ kHz.

asked Feb 12 in Others by Arjun (1.4k points)

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29

GATE2019 EC: 26
Consider a differentiable function $f(x)$ on the set of real numbers, such that $f(-1)=0$ and $|f’(x)| \leq2.$ Given these conditions, which one of the following inequalities is necessarily true for all $x \in[-2,2]?$ $f(x)\leq \frac{1}{2}|x+1|$ $f(x)\leq 2|x+1|$ $f(x)\leq \frac{1}{2}|x|$ $f(x)\leq 2|x|$

asked Feb 12 in Others by Arjun (1.4k points)

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30

GATE2019 EC: 27
Consider the line integral $\int_{c} (xdy-ydx)$ the integral being taken in a counterclockwise direction over the closed curve $C$ that forms the boundary of the region $R$ shown in the figure below. The region $R$ is the area enclosed by the union of a $2 \times 3$ rectangle and ... -circle of radius $1$. The line integral evaluates to $6+ \frac{\pi}{2}$ $8+\pi$ $12+\pi$ $16+2\pi$

asked Feb 12 in Others by Arjun (1.4k points)

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31

GATE2019 EC: 28
Consider a six-point decimation-in-time Fast Fourier Transform (FFT) algorithm, for which the signal-flow graph corresponding to $X[1]$ is shown in the figure. Let $W_{6}=exp(-\frac{j2\pi}{6}).$ In the figure, what should be the values of the coefficients $a_{1},a_{2},a_{3}$ in terms of $W_{6}$ so ... $a_{1}=1,a_{2}=W_{6},a_{3}=W_{6}^{2}$ $a_{1}=-1,a_{2}=W_{6}^{2},a_{3}=W_{6}$

asked Feb 12 in Others by Arjun (1.4k points)

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32

GATE2019 EC: 29
It is desired to find a three-tap casual filter which gives zero signal as an output to an input of the form $x[n]= c_{1}exp(-\frac{j\pi n}{2})+c_{2}(\frac{j\pi n}{2}),$ where $c_{1}$ and $c_{2}$ ... $y[n]=0$ for all $n$, when $x[n]$ is as given above ? $a=1,b=1$ $a=0,b=-1$ $a=-1,b=1$ $a=0,b=1$

asked Feb 12 in Others by Arjun (1.4k points)

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33

GATE2019 EC: 30
In the circuit shown, if $v(t)=2 sin(1000 t)$ volts, $R=1k\Omega$ and $C=1\mu F,$ then the steady-state current $i(t)$, milliamperes(mA). is $\text{sin(1000 t)+ cos(1000 t)}$ $\text{2 sin(1000 t) +2 cos(1000t)}$ $\text{3 sin(1000 t) + cos(1000t)}$ $\text{sin(1000 t) +3 cos(1000t)}$

asked Feb 12 in Others by Arjun (1.4k points)

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34

GATE2019 EC: 31
Consider a casual second-order system with the transfer function $G(s)=\frac{1}{1+2s+2s^{2}}$ with a unit-step $R(s)=\frac{1}{s}$ as an input. Let $C(s)$ be the corresponding output. The time taken by the system output $c(t)$ to reach $94\%$ of its steady-state value $\lim_{t\rightarrow \infty}c(t)$, rounded off to two decimal places, is $5.25$ $4.50$ $3.89$ $2.81$

asked Feb 12 in Others by Arjun (1.4k points)

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35

GATE2019 EC: 32
The block diagram of a system is illustrated in the figure shown, where $X(s)$ is the input and $Y(s)$ is the output. The transfer function $H(s)=\frac{Y(s)}{X(s)}$ is $H(s)=\frac{s^{2}+1}{s^{3}+s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{s^{3}+2s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{2s^{2}+1}$

asked Feb 12 in Others by Arjun (1.4k points)

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36

GATE2019 EC: 33
Let the state-space representation of an LTI system be $x(t)=A x(t)+B u(t), y(t)=Cx(t)+du(t)$ where $A,B,C$ are matrices, $d$ is a scalar, $u(t)$ is the input to the system, and $y(t)$ is its output. Let $B=[0\quad0\quad1]^{T}$ ... $A=\begin{bmatrix} 0&1&0\\ 0&0&1\\-3&-2&-1 \\\end{bmatrix} \text{and} \quad C=\begin{bmatrix} 0&0&1 \end{bmatrix}$

asked Feb 12 in Others by Arjun (1.4k points)

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37

GATE2019 EC: 34
A single bit, equally likely to be $0$ and $1$, is to be sent across an additive white Gaussian noise (AWGN) channel with power spectral density $N_{0}/2.$ Binary signaling with $0 \mapsto p(t),$ and $1 \mapsto q(t),$ is used for the transmission, along with an optimal ... $E$ would we obtain the same bit-error probability $P_{b}$? $0$ $1$ $2$ $3$

asked Feb 12 in Others by Arjun (1.4k points)

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38

GATE2019 EC: 35
The quantum efficiency $\eta$ and responsivity $R$ at wavelength $\lambda$ (in $\mu$m) in a p-i-n photodetector are related by $R= \frac{\eta \times \lambda}{1.24}$ $R= \frac{\lambda}{\eta \times 1.24}$ $R= \frac{1.24 \times\lambda}{\eta}$ $R= \frac{1.24}{\eta \times \lambda}$

asked Feb 12 in Others by Arjun (1.4k points)

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39

GATE2019 EC: 36
Two identical copper wires $W1$ and $W2$ placed in parallel as shown in the figure, carry currents $I$ and $2I$, respectively, in opposite directions. If the two wires are separated by a distance of $4r$, then the magnitude of the magnetic field $\overrightarrow{B}$ between the wires at a distance $r$ ... $\frac{5\mu_{0}I}{6\pi r}$ $\frac{\mu_{0}^{2}I^{2}}{2\pi r^{2}}$

asked Feb 12 in Others by Arjun (1.4k points)

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40

GATE2019 EC: 37
The dispersion equation of a waveguide, which relates the wavenumber $k$ to the frequency $\omega$ is $k(\omega)= (1/c) \sqrt{\omega^{2}-\omega_{0}^{2}}$ where the speed of light $c= 2 \times 10^{8} m/s$ and $\omega_{0}$ is a constant . If the group velocity is $2 \times 10^{8} m/s$, ... is $1.5 \times 10^{8} m/s$ $2 \times 10^{8} m/s$ $3 \times 10^{8} m/s$ $4.5 \times 10^{8} m/s$

asked Feb 12 in Others by Arjun (1.4k points)