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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 ____________.
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GATE2019 EC: 1
Which of the following functions is analytic over the entire complex plane? $\ln(z)$ $e^{1/z}$ $\frac{1}{1z}$ $cos(z)$
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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
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GATE2019 EC: 3
Let $H(z)$ be the $z$ transform of a realvalued discretetime 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?
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GATE2019 EC: 4
Consider the twoport 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 $1$? $\text{0.5 A}$ $\text{1 A}$ $\text{2 A}$ $\text{2.5 A}$
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GATE2019 EC: 5
Let $Y(s)$ be the unitstep response of a causal system having a transfer function $G(s)= \frac{3s}{(s+1)(s+3)}$ that is ,$Y(s)=\frac{G(s)}{s}.$ The forced response of the system is $u(t)2e^{t}u(t)+e^{3t}u(t)$ $2u(t)2e^{t}u(t)+e^{3t}u(t)$ $2u(t)$ $u(t)$
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7
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 $N_{p}=5, N_{z}=2$ $N_{p}=6, N_{z}=3$ $N_{p}=7, N_{z}=4$ $N_{p}=4, N_{z}=2$
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8
GATE2019 EC: 7
A linear Hamming code is used to map $4bit$ message to $7bit$ 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 $0010011$ $1100001$ $1111000$ $1111111$
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9
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?
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GATE2019 EC: 9
The correct circuit representation of the structure shown in the figure is
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GATE2019 EC: 10
The figure shows the highfrequency CV curve of a MOS capacitor (at $T=300$K) with $Φ_{ms}=0 V$ and no oxide charges. The flatband, inversion, and accumulation conditions are represented, respectively, by the points $P,Q,R$ $Q,R,P$ $R,P,Q$ $Q,P,R$
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12
GATE2019 EC: 11
What is the electric flux $(\int \vec{E}.d \hat{a})$ through a quartercylinder 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 $Q$ ? $\frac{HQ}{\varepsilon_{0}}$ $\frac{HQ}{4\varepsilon_{0}}$ $\frac{H\varepsilon}{4Q}$ $\frac{4H}{Q\varepsilon_{0}}$
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13
GATE2019 EC: 12
In the table shown, List I and List II, respectively, contain terms appearing on the lefthand side and the righthand side of Maxwell's equations (in their standard form). Match the lefthand side with the corresponding righthand side. ... $\text{1Q,2S,3P,4R}$ $\text{1R,2Q,3S,4P}$
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14
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.
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15
GATE2019 EC: 14
In the circuit shown, what are the values of $F$ for $EN=0$ and $EN=1$, respectively? $\text{0 and D}$ $\text{HiZ and D}$ $\text{0 and 1}$ $\text{HiZ and}$ $ \overline{D}$
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16
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
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17
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_______.
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18
GATE2019 EC: 18
If $X$ and $Y$ are random variable such that $E[2X+Y]=0$ and $E[X+2Y]=33$, then $E[X]+E[Y]=$__________________.
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19
GATE2019 EC: 19
The value of the integral $\int_{0}^{\pi} \int_{y}^{\pi}\frac{sinx}{x}dx dy ,$ is equal to _____________.
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20
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} 1e^{x}& if x\geq 0 \\ 0& if x< 0 \end{Bmatrix}$ Then Pr$(z>2z>1)$, rounded off to two decimal places, is equal to ___________.
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21
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 _____________________.
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22
GATE2019 EC: 22
The baseband signal $m(t)$ shown in the figure is phasemodulated 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).
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23
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 ______________ $\%.$
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24
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.)
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25
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.
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26
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 $x \in[2,2]?$ $f(x)\leq \frac{1}{2}x+1$ $f(x)\leq 2x+1$ $f(x)\leq \frac{1}{2}x$ $f(x)\leq 2x$
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27
GATE2019 EC: 27
Consider the line integral $\int_{c} (xdyydx)$ 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 $6+ \frac{\pi}{2}$ $8+\pi$ $12+\pi$ $16+2\pi$
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28
GATE2019 EC: 28
Consider a sixpoint decimationintime Fast Fourier Transform (FFT) algorithm, for which the signalflow 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 ... $a_{1}=1,a_{2}=W_{6},a_{3}=W_{6}^{2}$ $a_{1}=1,a_{2}=W_{6}^{2},a_{3}=W_{6}$
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29
GATE2019 EC: 29
It is desired to find a threetap 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 ? $a=1,b=1$ $a=0,b=1$ $a=1,b=1$ $a=0,b=1$
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30
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 steadystate current $i(t)$, milliamperes(mA). is $\text{sin(1000 t)+ cos(1000 t)}$ $\text{2 sin(1000 t) +2 cos(1000t)}$ $\text{3 sin(1000 t) + cos(1000t)}$ $\text{sin(1000 t) +3 cos(1000t)}$
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31
GATE2019 EC: 31
Consider a casual secondorder system with the transfer function $G(s)=\frac{1}{1+2s+2s^{2}}$ with a unitstep $R(s)=\frac{1}{s}$ as an input. Let $C(s)$ be the corresponding output. The time taken by the system output $c(t)$ to reach $94\%$ of its steadystate value $\lim_{t\rightarrow \infty}c(t)$, rounded off to two decimal places, is $5.25$ $4.50$ $3.89$ $2.81$
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32
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 $H(s)=\frac{s^{2}+1}{s^{3}+s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{s^{3}+2s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{2s^{2}+1}$
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33
GATE2019 EC: 33
Let the statespace 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 $B=[0\quad0\quad1]^{T}$ ... $A=\begin{bmatrix} 0&1&0\\ 0&0&1\\3&2&1 \\\end{bmatrix} \text{and} \quad C=\begin{bmatrix} 0&0&1 \end{bmatrix}$
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34
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 biterror probability $P_{b}$? $0$ $1$ $2$ $3$
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35
GATE2019 EC: 35
The quantum efficiency $\eta$ and responsivity $R$ at wavelength $\lambda$ (in $\mu$m) in a pin photodetector are related by $R= \frac{\eta \times \lambda}{1.24}$ $R= \frac{\lambda}{\eta \times 1.24}$ $R= \frac{1.24 \times\lambda}{\eta}$ $R= \frac{1.24}{\eta \times \lambda}$
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36
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 $r$ ... $\frac{5\mu_{0}I}{6\pi r}$ $\frac{\mu_{0}^{2}I^{2}}{2\pi r^{2}}$
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37
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 $1.5 \times 10^{8} m/s$ $2 \times 10^{8} m/s$ $3 \times 10^{8} m/s$ $4.5 \times 10^{8} m/s$
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38
GATE2019 EC: 38
In the circuit shown, the breakdown voltage and the maximum current of the Zener diode are $20V$ and $60mA$, respectively. The values of $R_{1}$ and $R_{L}$ are $200 \Omega$ and $1k\Omega,$ 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 $28 V$
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39
GATE2019 EC: 39
The state transition diagram for the circuit shown is
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40
GATE2019 EC: 40
In the circuits shown the threshold voltage of each nMOS transistor is $0.6V.$ Ignoring the effect of channel length modulation and body bias. the values of Vout1 and Vout2,respectively, in volts, are $1.8$ and $1.2$ $2.4$ and $2.4$ $1.8$ and $2.4$ $2.4$ and $1.2$
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