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1

GATE2019 EC: GA-3
It would take one machine $4$ hours to complete a production order and another machine $2$ hours to complete the same order. If both machines work simultaneously at their respective constant rates, the time taken to complete the same order is ________ hours. $2/3$ $3/4$ $4/3$ $7/3$

answered Jul 23 in Numerical Ability by Debdeep1998 (180 points)

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GATE2019 EC: GA-1
The strategies that the company ________ to sell its products _______ house-to-house marketing. use, includes uses, include used, includes uses, including

answered Jul 23 in Verbal Ability by sudoankit (220 points)

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GATE2019 EC: GA-5
When he did not come home, she _______ him lying dead on the roadside somewhere. concluded looked notice pictured

answered Jul 23 in Verbal Ability by sudoankit (220 points)

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GATE2019 EC: GA-2
The boat arrived ______ dawn. in at on under

answered Jul 23 in Verbal Ability by sudoankit (220 points)

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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 ____________.

answered Jul 23 in Others by yuviabhi (140 points)

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GATE2017 EC-1: GA-10
A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at $25$ m intervals in this plot. The path from $P$ to $Q$ is best described by Up-Down-Up-Down Down-Up-Down-Up Down-Up-Down Up-Down-Up

answered Jul 23 in Numerical Ability by Debdeep1998 (180 points)

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7

GATE2017 EC-1: 1
Consider the 5X 5 matrix $\begin{bmatrix} 1&2&3&4&5\\ 5&1 &2& 3 &4\\ 4&5&1&2&3\\ 3&4&5&1&2\\ 2&3&4&5&1 \end{bmatrix}$ It is given that A has only one real eigenvalue. Then the real eigenvalue of A is -2.5 0 15 25

edited Jun 2 in Linear Algebra by srestha (100 points)

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8

GATE2015-2-GA-8
A tiger is $50$ leaps of its own behind a tree. The tiger takes $5$ leaps per minute to the deer's $4.$ If the tiger and the deer cover $8$ meter and $5$ meter per leap respectively, what distance in meters will the tiger have to run before it catches the deer?

edited Jun 1 in Numerical Ability by Lakshman Patel RJIT (130 points)

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9

GATE2015-2-GA-10
Lamenting the gradual sidelining of the arts in school curricula, a group of prominent artists wrote to the chief minister last year, asking him to allocate more funds to support art education in schools. However, no such increase has been announced in this year's budget. The artists ... arts education these nowadays (iii) and (iv) (i) and (ii) (i),(ii) and (iii) (i) and (ii)

edited Jun 1 in Verbal Ability by Lakshman Patel RJIT (130 points)

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10

GATE2015-1-GA-4
Operators $\square,$ $\Diamond$ and $\rightarrow$ are defined by: $a\,\square\,b=\frac{a+b}{a-b};\, a\,\Diamond, b=\frac{a+b}{a-b};$ $a\,\rightarrow\, b=ab.$ Find the value of $(66\,\square\, 6)\rightarrow(66\,\Diamond, 6).$ $-2$ $-1$ $1$ $2$

edited Jun 1 in Numerical Ability by Lakshman Patel RJIT (130 points)

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11

GATE2015-1-GA-5
If $\log_{x}{(\frac{5}{7})}=\frac{-1}{3},$ then the value of $x$ is $343/125$ $25/343$ $-25/49$ $-49/25$

edited Jun 1 in Numerical Ability by Lakshman Patel RJIT (130 points)

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12

GATE2019 EC: 55
In the circuit shown, $V_{1}=0$ and $V_{2}=V_{dd}.$ The other relevant parameters are mentioned in the figure. Ignoring the effect of channel length modulation and the body effect, the value of $I_{out}$ is _________ $mA$ (rounded off to $1$ decimal place.)

edited May 31 in Others by Pooja Khatri (100 points)

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GATE2019 EC: 54
In the circuit shown, the threshold voltages of the pMOS $(|V_{tp}|)$ and nMOS $(V_{tn})$ transistors are both equal to $1V.$ All the transistors have the same output resistance $r_{ds}$ of $6M\Omega.$ ... . Ignoring the effect of channel length modulation and body bias, the gain of the circuit is ______ (rounded off to $1$ decimal place.)

edited May 31 in Others by Pooja Khatri (100 points)

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GATE2019 EC: 53
A CMOS inverter, designed to have a mid-point voltage $V_{1}$ equal to half of $V_{dd}.$ as shown in the figure, has the following parameters: $V_{dd}=3V$ $\mu_{n} C_{ox}=100 \mu A/V^{2}; V_{tn}=0.7V $ for nMOS $\mu_{p} C_{ox}=40 \mu A/V^{2}; V_{tp}=0.9V $ for pMOS The ration of $(\frac{W}{L})_{n}$ to $(\frac{W}{L})_{p}$ is equal to _______ (rounded off to 3 decimal places).

edited May 31 in Others by Pooja Khatri (100 points)

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15

GATE2019 EC: 52
In the circuit shown. $V_{s}$ is a $10V$ square wave of period, $T=4 ms$ with $R=500 \Omega$ and $C= 10\mu F.$ The capacitor is initially uncharged at $t=0,$ and the diode is assumed to be ideal. The voltage across the capacitor $(V_{c})$ at $3ms$ is equal to _____ volts (rounded off to one decimal place)

edited May 31 in Others by Pooja Khatri (100 points)

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16

GATE2019 EC: 51
A rectangular waveguide of width $w$ and height $h$ has cut-off frequencies for $TE_{10}$ and $TE_{11}$ modes in the ration $1:2$ . The aspect ratio $w/h$, rounded off to two decimal places , is ____________________.

edited May 31 in Others by Pooja Khatri (100 points)

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17

GATE2019 EC: 50
Consider a long-channel MOSFET with a channel length $1\mu m$ and width $10 \mu m.$ The device parameters are acceptor concentration $N_{A}=5 \times 10^{16} cm^{-3},$ electron mobility $\mu_{n}=800 cm^{2}/V-s,$ ... is _______ $mA$ (rounded off to two decimal places.). $[\varepsilon_{0}=8.854 \times 10^{-14}F/cm, \varepsilon_{si=11.9}]$

edited May 31 in Others by Pooja Khatri (100 points)

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18

GATE2019 EC: 49
In an ideal $pn$ junction with an ideality factor of $1$ at $T=300K,$ the magnitude of the reverse-bias voltage required to reach $75\%$ of its reverse saturation current, rounded off to $2$ decimal places, is ______ $mV.$ $[k=1.38 \times 10^{-23} JK^{-1}, h=6.625 \times 10^{-34} J-s, q=1.602 \times 10^{-19}C]$

edited May 31 in Others by Pooja Khatri (100 points)

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19

GATE2019 EC: 48
A Germanium sample of dimensions $1 cm \times 1 cm$ is illuminated with a $20mW,$ $600 nm$ laser light source as shown in the figure. The illuminated sample surface has a $100 nm$ of loss-less Silicon dioxide layer that reflects one-fourth of the incident ... the bandgap is $0.66eV,$ the thickness of the Germanium layer, rounded off to $3$ decimal places, is _____________ $\mu m.$

edited May 31 in Others by Pooja Khatri (100 points)

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20

GATE2019 EC: 47
A random variable $X$ takes values $-1$ and $+1$ with probabilities $0.2$ and $0.8$, respectively. It is transmitted across a channel which adds noise $N,$ so that the random variable at the channel output is $Y=X+N$. The noise $N$ is independent of ... so as to minimize the probability of error $Pr[X \neq X].$ The minimum probability of error, rounded off to $1$ decimal place, is

edited May 30 in Others by Pooja Khatri (100 points)

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21

GATE2019 EC: 46
A voice signal $m(t)$ is in the frequency range $5kHz$ to $15kHz$. The signal is amplitude-modulated to generated an AM signal $f(t)=A(1+m(t))cos 2\pi f_{c}t,$ where $f_{c}=600 kHz.$ The AM signal $f(t)$ is to be digitized and ... required for the encoding. The rate, in Megabits per second (rounded off to $2$ decimal places), of the resulting stream of coded bits is ________ Mbps.

edited May 30 in Others by Pooja Khatri (100 points)

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22

GATE2019 EC: 45
Let a random process $Y(t)$ be described as $Y(t)=h(t)*X(t)+Z(t),$ where $X(t)$ is a white noise process with power spectral density $S_{x}(f)=5$W/Hz. The filter $h(t)$ has a magnitude response given by $|H(f)|=0.5$ ... $Y(t),$ in watts, is equal to _________ W (rounded off to two decimal places).

edited May 30 in Others by Pooja Khatri (100 points)

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23

GATE2019 EC: 44
Let $h[n]$ be a length$-7$ discrete-time finite impluse response filter, given by $h[0]=4, \quad h[1]=3,\quad h[2]=2,\quad h[3]=1,$ $\quad h[-1]=-3, \quad h[-2]=-2, \quad h[-3]=-1,$ and $h[n]$ is zero for $|n|\geq4.$ A length $-3$ ... $g[n],$ respectively. For the filter that minimizes $E(h,g),$ the value of $10g[-1]+g[1],$ rounded off to $2$ decimal places, is _____________.

edited May 30 in Others by Pooja Khatri (100 points)

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24

GATE2019 EC: 43
Consider the homogenous ordinary differential equation $x^{2}\frac{d^{2}y}{dx^{2}}-3x\frac{dy}{dx}+3y=0, \quad x>0$ with $y(x)$ as a general solution. Given that $y(1)=1 \quad and \quad y(2)=14$ the value of $y(1.5),$ rounded off to two decimal places, is_______________.

edited May 30 in Others by Pooja Khatri (100 points)

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25

GATE2019 EC: 42
Consider a unity feedback system, as in the figure shown, with an integral compensator $\frac{K}{s}$ and open-loop transfer function $G(s)=\frac{1}{s^{2}+3s+2}$ where $K>0.$ The positive value of $K$ for which there are exactly two poles of the unity feedback system on the $j\omega$ axis is equal to ________ (rounded off to two decimal places.)

edited May 30 in Others by Pooja Khatri (100 points)

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26

GATE2019 EC: 41
The RC circuit shown below has a variable resistance $R(t)$ given by the following expression: $R(t)=R_{0}(1-\frac{t}{T}) for \quad 0 \leq t < T$ where $R_{0}=1 \Omega,$ and $C=1F.$ We are also given that $T=3 R_{0}C$ ... time $t=0$ is $1 A,$ then the current $I(t)$, in amperes, at time $t=T/2$ is __________ (rounded off to $2$ decimal places).

edited May 30 in Others by Pooja Khatri (100 points)

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27

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 $1.2$

edited May 30 in Others by Pooja Khatri (100 points)

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28

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

edited May 30 in Others by Pooja Khatri (100 points)

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29

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 $28 V$

edited May 30 in Others by Pooja Khatri (100 points)

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30

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 $1.5 \times 10^{8} m/s$ $2 \times 10^{8} m/s$ $3 \times 10^{8} m/s$ $4.5 \times 10^{8} m/s$

edited May 30 in Others by Pooja Khatri (100 points)

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31

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 $r$ ... $\frac{5\mu_{0}I}{6\pi r}$ $\frac{\mu_{0}^{2}I^{2}}{2\pi r^{2}}$

edited May 30 in Others by Pooja Khatri (100 points)

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32

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 $R= \frac{\eta \times \lambda}{1.24}$ $R= \frac{\lambda}{\eta \times 1.24}$ $R= \frac{1.24 \times\lambda}{\eta}$ $R= \frac{1.24}{\eta \times \lambda}$

edited May 30 in Others by Pooja Khatri (100 points)

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33

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 $P_{b}$? $0$ $1$ $2$ $3$

edited May 30 in Others by Pooja Khatri (100 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 $B=[0\quad0\quad1]^{T}$ ... $A=\begin{bmatrix} 0&1&0\\ 0&0&1\\-3&-2&-1 \\\end{bmatrix} \text{and} \quad C=\begin{bmatrix} 0&0&1 \end{bmatrix}$

edited May 30 in Others by Pooja Khatri (100 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 $H(s)=\frac{s^{2}+1}{s^{3}+s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{s^{3}+2s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{2s^{2}+1}$

edited May 30 in Others by Pooja Khatri (100 points)

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36

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 $5.25$ $4.50$ $3.89$ $2.81$

edited May 30 in Others by Pooja Khatri (100 points)

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37

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 $\text{sin(1000 t)+ cos(1000 t)}$ $\text{2 sin(1000 t) +2 cos(1000t)}$ $\text{3 sin(1000 t) + cos(1000t)}$ $\text{sin(1000 t) +3 cos(1000t)}$

edited May 30 in Others by Pooja Khatri (100 points)

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38

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 ? $a=1,b=1$ $a=0,b=-1$ $a=-1,b=1$ $a=0,b=1$

edited May 30 in Others by Pooja Khatri (100 points)

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39

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 ... $a_{1}=1,a_{2}=W_{6},a_{3}=W_{6}^{2}$ $a_{1}=-1,a_{2}=W_{6}^{2},a_{3}=W_{6}$

edited May 30 in Others by Pooja Khatri (100 points)

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40

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

edited May 30 in Others by Pooja Khatri (100 points)

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