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1

GATE2012-36
A fair coin is tossed till head appears for the first time. The probability that the number of required tosses is odd, is $\frac{1}{3}$ $\frac{1}{2}$ $\frac{2}{3}$ $\frac{3}{4}$

answered Nov 26, 2019 in Others by Naveen Kumar 3 (150 points)

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2

GATE2019 EC: 17
The number of distinct eigenvalues of the matrix $A=\begin{bmatrix} 2&2&3&3\\0&1&1&1\\0&0&3&3\\0&0&0&2 \end{bmatrix}$ is equal to ____________.

answered Jul 23, 2019 in Others by yuviabhi (140 points)

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3

GATE2019 EC: 1
Which one 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, 2019 in Others by Arjun (1.4k points)

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4

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

asked Feb 12, 2019 in Others by Arjun (1.4k points)

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5

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, 2019 in Others by Arjun (1.4k points)

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6

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 $1\: A$ ... figure), what is the current through the short circuit at Port $1?$ $0.5\: A$ $1\: A$ $2\: A$ $2.5\: A$

asked Feb 12, 2019 in Others by Arjun (1.4k points)

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7

GATE2019 EC: 5
Let $Y(s)$ be the unit-step response of a causal system having a transfer function $G(s)= \dfrac{3-s}{(s+1)(s+3)}$ that is ,$Y(s)=\dfrac{G(s)}{s}.$ 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, 2019 in Others by Arjun (1.4k points)

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8

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, 2019 in Others by Arjun (1.4k points)

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9

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, 2019 in Others by Arjun (1.4k points)

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10

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, 2019 in Others by Arjun (1.4k points)

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11

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

asked Feb 12, 2019 in Others by Arjun (1.4k points)

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12

GATE2019 EC: 10
The figure shows the high-frequency C-V curve of a MOS capacitor $(\text{at}\: T=300\: K)$ with $\Phi_{ms}= 0\: V$ 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, 2019 in Others by Arjun (1.4k points)

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13

GATE2019 EC: 11
What is the electric flux $\left(\int \vec{E}.d \hat{a}\right)$ 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 $Q?$ $\frac{HQ}{\varepsilon_{0}}$ $\frac{HQ}{4\varepsilon_{0}}$ $\frac{H\varepsilon_{0}}{4Q}$ $\frac{4H}{Q\varepsilon_{0}}$

asked Feb 12, 2019 in Others by Arjun (1.4k points)

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14

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. ... $1-Q,2-R,3-P,4-S$ $1-Q,2-S,3-P,4-R$ $1-R,2-Q,3-S,4-P$

asked Feb 12, 2019 in Others by Arjun (1.4k points)

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15

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 $NM_{H}$ increases. No change in the noise margins.

asked Feb 12, 2019 in Others by Arjun (1.4k points)

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16

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, 2019 in Others by Arjun (1.4k points)

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17

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, 2019 in Others by Arjun (1.4k points)

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18

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

asked Feb 12, 2019 in Others by Arjun (1.4k points)

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19

GATE2019 EC: 18
If $X$ and $Y$ are random variables such that $E\left[2X+Y\right]=0$ and $E\left[X+2Y\right]=33$, then $E\left[X\right]+E\left[Y\right]=$___________.

asked Feb 12, 2019 in Others by Arjun (1.4k points)

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20

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

asked Feb 12, 2019 in Others by Arjun (1.4k points)

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21

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

asked Feb 12, 2019 in Others by Arjun (1.4k points)

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22

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

asked Feb 12, 2019 in Others by Arjun (1.4k points)

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23

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 ... the 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, 2019 in Others by Arjun (1.4k points)

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24

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, 2019 in Others by Arjun (1.4k points)

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25

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, 2019 in Others by Arjun (1.4k points)

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26

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

asked Feb 12, 2019 in Others by Arjun (1.4k points)

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27

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

asked Feb 12, 2019 in Others by Arjun (1.4k points)

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28

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 $6+ \dfrac{\pi}{2}$ $8+\pi$ $12+\pi$ $16+2\pi$

asked Feb 12, 2019 in Others by Arjun (1.4k points)

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29

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 $W_{6}=exp\left(-\:\dfrac{j2\pi}{6}\right).$ In the figure, what should be the values of the coefficients $a_{1},a_{2},a_{3}$ in terms ... $a_{1}=1,a_{2}=W_{6},a_{3}=W_{6}^{2}$ $a_{1}=-1,a_{2}=W_{6}^{2},a_{3}=W_{6}$

asked Feb 12, 2019 in Others by Arjun (1.4k points)

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30

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 $x[n]= c_{1}exp\left(-\dfrac{j\pi n}{2}\right)+c_{2}\left(\dfrac{j\pi n}{2}\right),$ where $c_{1}$ and $c_{2}$ ... $n$, 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, 2019 in Others by Arjun (1.4k points)

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31

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

asked Feb 12, 2019 in Others by Arjun (1.4k points)

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32

GATE2019 EC: 31
Consider a causal second-order system with the transfer function $G(s)=\dfrac{1}{1+2s+s^{2}}$ with a unit-step $R(s)=\dfrac{1}{s}$ 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 $\underset{t\rightarrow \infty}{\lim}\:c(t),$ rounded off to two decimal places, is $5.25$ $4.50$ $3.89$ $2.81$

asked Feb 12, 2019 in Others by Arjun (1.4k points)

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33

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 $H(s)=\dfrac{Y(s)}{X(s)}$ is $H(s)=\frac{s^{2}+1}{s^{3}+s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{s^{3}+2s^{2}+s+1}$ $H(s)=\frac{s+1}{s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{2s^{2}+1}$

asked Feb 12, 2019 in Others by Arjun (1.4k points)

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34

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, 2019 in Others by Arjun (1.4k points)

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35

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 $\textbf{same}$ bit-error probability $P_{b}$? $0$ $1$ $2$ $3$

asked Feb 12, 2019 in Others by Arjun (1.4k points)

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36

GATE2019 EC: 35
The quantum efficiency $(\eta)$ and responsivity $(R)$ at wavelength $\lambda \:(\text{in}\: \mu m)$ 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, 2019 in Others by Arjun (1.4k points)

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37

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, 2019 in Others by Arjun (1.4k points)

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38

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

asked Feb 12, 2019 in Others by Arjun (1.4k points)

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39

GATE2019 EC: 38
In the circuit shown, the breakdown voltage and the maximum current of the Zener diode are $20\:V$ and $60\:mA$, respectively. The values of $R_{1}$ and $R_{L}$ are $200\: \Omega$ and $1\:k\Omega,$ respectively. What is the range of $V_{i}$ that will maintain the Zener diode in the ‘on’ state? $22\: V$ to $34\: V$ $24\: V$ to $36\: V$ $18\: V$ to $24\: V$ $20\: V$ to $28\: V$

asked Feb 12, 2019 in Others by Arjun (1.4k points)

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40

GATE2019 EC: 39
The state transition diagram for the circuit shown is

asked Feb 12, 2019 in Others by Arjun (1.4k points)