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1

GATE EE 2021 | GA Question: 1
The people _______________ were at the demonstration were from all sections of society. whose which who whom

asked Feb 20 in Analytical Aptitude by Arjun (6.7k points)

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2

GATE EE 2021 | GA Question: 2
A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ________________.

asked Feb 20 in Analytical Aptitude by Arjun (6.7k points)

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3

GATE EE 2021 | GA Question: 3
For a regular polygon having $10$ sides, the interior angle between the sides of the polygon, in degrees, is: $396$ $324$ $216$ $144$

asked Feb 20 in Analytical Aptitude by Arjun (6.7k points)

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4

GATE EE 2021 | GA Question: 4
Which one of the following numbers is exactly divisible by $\left ( 11^{13} +1\right )$? $11^{26} +1$ $11^{33} +1$ $11^{39} -1$ $11^{52} -1$

asked Feb 20 in Analytical Aptitude by Arjun (6.7k points)

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5

GATE EE 2021 | GA Question: 5
$\textit{Oasis}$ is to $\textit{sand}$ as $\textit{island}$ is to _____________ Which one of the following options maintains a similar logical relation in the above sentence? Stone Land Water Mountain

asked Feb 20 in Analytical Aptitude by Arjun (6.7k points)

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6

GATE EE 2021 | GA Question: 6
The importance of sleep is often overlooked by students when they are preparing for exams. Research has consistently shown that sleep deprivation greatly reduces the ability to recall the material learnt. Hence, cutting down on sleep to study longer hours can be ... , he needs little or no sleep. To do well in an exam, adequate sleep must be part of the preparation.

asked Feb 20 in Analytical Aptitude by Arjun (6.7k points)

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7

GATE EE 2021 | GA Question: 7
In the figure shown above, each inside square is fomed by joining the midpoints of the sides of the next larger square. The area of the smallest square (shaded) as shown, in $cm^{2}$ is: $12.50$ $6.25$ $3.125$ $1.5625$

asked Feb 20 in Analytical Aptitude by Arjun (6.7k points)

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8

GATE EE 2021 | GA Question: 8
Let $X$ be a continuous random variable denoting the temperature measured. The range of temperature is $[0, 100]$ degree Celsius and let the probability density function of $X$ be $f\left ( x \right )=0.01$ for $0\leq X\leq 100$. The mean of $X$ is __________ $2.5$ $5.0$ $25.0$ $50.0$

asked Feb 20 in Analytical Aptitude by Arjun (6.7k points)

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9

GATE EE 2021 | GA Question: 9
The number of students passing or failing in an exam for a particular subject is presented in the bar chart above. Students who pass the exam cannot appear for the exam again. Students who fail the exam in the first attempt must appear for the exam in the following year. ... $3$ respectively, are ______________. $65$ and $53$ $60$ and $50$ $55$ and $53$ $55$ and $48$

asked Feb 20 in Analytical Aptitude by Arjun (6.7k points)

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10

GATE EE 2021 | GA Question: 10
Seven cars $\text{P, Q. R, S, T, U and V}$ are parked in a row not necessarily in that order. The cars $T$ and $U$ should be parked next to each other. The cars $S$ and $V$ also should be parked next to each other, whereas $P$ and $Q$ cannot ... and $R$ are not parked together. $V$ is the only car parked in between $S$ and $R$. Car $P$ is parked at the extreme end.

asked Feb 20 in Analytical Aptitude by Arjun (6.7k points)

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11

GATE EE 2021 | Question: 1
Let $p$ and $q$ be real numbers such that $p^{2}+q^{2}=1$ . The eigenvalues of the matrix $\begin{bmatrix} p & q\\ q& -p \end{bmatrix}$are $1$ and $1$ $1$ and $-1$ $j$ and $-j$ $pq$ and $-pq$

asked Feb 20 in new by Arjun (6.7k points)

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12

GATE EE 2021 | Question: 2
Let $p\left ( z\right )=z^{3}+\left ( 1+j \right )z^{2}+\left ( 2+j \right )z+3$, where $z$ ... $p\left ( z \right )=0$ come in conjugate pairs All the roots cannot be real

asked Feb 20 in new by Arjun (6.7k points)

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13

GATE EE 2021 | Question: 3
Let $f\left ( x \right )$ be a real-valued function such that ${f}'\left ( x_{0} \right )=0$ for some $x _{0} \in\left ( 0,1 \right ),$ and ${f}''\left ( x \right )> 0$ for all $x \in \left ( 0,1 \right )$. Then $f\left ( x \right )$ has no local minimum in $(0,1)$ one local maximum in $(0,1)$ exactly one local minimum in $(0,1)$ two distinct local minima in $(0,1)$

asked Feb 20 in new by Arjun (6.7k points)

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14

GATE EE 2021 | Question: 4
For the network shown, the equivalent Thevenin voltage and Thevenin impedance as seen across terminals ‘$\text{ab}$’ is $\text{10 V}$ in series with $12\:\Omega$ $\text{65 V}$ in series with $15\:\Omega$ $\text{50 V}$ in series with $2\:\Omega$ $\text{35 V}$ in series with $2\:\Omega$

asked Feb 20 in new by Arjun (6.7k points)

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15

GATE EE 2021 | Question: 5
Which one of the following vector functions represents a magnetic field $\overrightarrow{B}$? $\text{($\hat{X}, \hat{Y}$ and $\hat{Z}$ are unit vectors along x-axis, y-axis, and z-axis, respectively)}$ $10x\hat{X}+20y\hat{Y}-30z\hat{Z}$ $10y\hat{X}+20x\hat{Y}-10z\hat{Z}$ $10z\hat{X}+20y\hat{Y}-30x\hat{Z}$ $10x\hat{X}-30z\hat{Y}+20y\hat{Z}$

asked Feb 20 in new by Arjun (6.7k points)

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16

GATE EE 2021 | Question: 6
If the input $x(t)$ and output $y(t)$ of a system are related as $y\left ( t \right )=\text{max}\left ( 0,x\left ( t \right ) \right ),$ then the system is linear and time-variant linear and time-invariant non-linear and time-variant non-linear and time-invariant

asked Feb 20 in new by Arjun (6.7k points)

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17

GATE EE 2021 | Question: 7
Two discrete-time linear time-invariant systems with impulse responses $h_{1}\left [ n \right ]=\delta \left [ n-1 \right ]+\delta \left [ n+1 \right ]$ and $h_{2}\left [ n \right ]=\delta \left [ n\right ]+\delta \left [ n-1 \right ]$ are connected in cascade ... $\delta \left [ n\right ]\delta \left [ n-1\right ]+\delta \left [ n-2\right ]\delta \left [ n+1 \right ]$

asked Feb 20 in new by Arjun (6.7k points)

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18

GATE EE 2021 | Question: 8
Consider the table given: ... $\text{P-T-Y, Q-V-Z, R-S-X}$ $\text{P-U-X, Q-V-Y, R-T-Z}$

asked Feb 20 in new by Arjun (6.7k points)

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19

GATE EE 2021 | Question: 9
Consider a power system consisting of $N$ number of buses. Buses in this power system are categorized into slack bus, $PV$ buses and $PQ$ buses for load flow study. The number of $PQ$ buses is $N_{L}$. The balanced Newton-Raphson method is used to carry out load flow study in ... $\left ( N-1 \right )\times \left ( N-1+N_{L} \right )$

asked Feb 20 in new by Arjun (6.7k points)

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20

GATE EE 2021 | Question: 10
Two generators have cost functions $F_{1}$ and $F_{2}$ . Their incremental-cost characteristics are $\dfrac{dF_{1}}{dP_{1}}=40+0.2P_{1}$ $\dfrac{dF_{2}}{dP_{2}}=32+0.4P_{2}$ They need to deliver a combined load of $260$ $\text{MW}$. Ignoring the network losses, for economic ... are $P_{1}=P_{2}=130$ $P_{1}=160, P_{2}=100$ $P_{1}=140, P_{2}=120$ $P_{1}=120, P_{2}=140$

asked Feb 20 in new by Arjun (6.7k points)

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21

GATE EE 2021 | Question: 11
For the closed-loop system shown, the transfer function $\dfrac{E\left ( s \right )}{R\left ( s \right )}$ is $\frac{G}{1+GH}$ $\frac{GH}{1+GH}$ $\frac{1}{1+GH}$ $\frac{1}{1+G}$

asked Feb 20 in new by Arjun (6.7k points)

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22

GATE EE 2021 | Question: 12
Inductance is measured by Schering bridge Maxwell bridge Kelvin bridge Wien bridge

asked Feb 20 in new by Arjun (6.7k points)

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23

GATE EE 2021 | Question: 13
Suppose the circles $x^{2}+y^{2}=1$ and $\left ( x-1\right )^{2}+\left ( y-1 \right )^{2}=r^{2}$ intersect each other orthogonally at the point $\left ( u,v \right )$. Then $u+v=$ _______________.

asked Feb 20 in new by Arjun (6.7k points)

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24

GATE EE 2021 | Question: 14
In the given circuit, the value of capacitor $C$ that makes current $I=0$ is ________________ $\mu F$.

asked Feb 20 in new by Arjun (6.7k points)

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25

GATE EE 2021 | Question: 15
Two single-core power cables have total conductor resistances of $0.7\;\Omega$ and $0.5\;\Omega$, respectively, and their insulation resistances (between core and sheath) are $600\;M\Omega$ and $900\;M\Omega$, respectively. When the two cables are joined in series, the ratio of insulation resistance to conductor resistance is ___________$\times 10^{6}$.

asked Feb 20 in new by Arjun (6.7k points)

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26

GATE EE 2021 | Question: 16
In the given circuit, for voltage $V_y$ to be zero, the value of $\beta$ should be _________. (Round off to $2$ decimal places).

asked Feb 20 in new by Arjun (6.7k points)

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27

GATE EE 2021 | Question: 17
A $1\;\mu C$ point charge is held at the origin of a cartesian coordinate system. If a second point charge of $10\;\mu C$ is moved from $\left ( 0,10,0 \right )$ to $\left ( 5,5,5\right )$ and subsequently to $\left ( 5,0,0\right )$, then the ... $\dfrac{1}{4\pi \varepsilon _{0}}=9\times 10^{9}$ in $\text{SI}$ units. All coordinates are in meters.

asked Feb 20 in new by Arjun (6.7k points)

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28

GATE EE 2021 | Question: 18
The power input to a $\text{500 V, 50 Hz, 6-pole, 3-phase}$ induction motor running at $975 \text{RPM}$ is $40 \text{ kW}$ . The total stator losses are $1 \text{ kW}$. If the total friction and windage losses are $2.025\text{ kW}$, then the efficiency is _____________$\%$.

asked Feb 20 in new by Arjun (6.7k points)

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29

GATE EE 2021 | Question: 19
An alternator with internal voltage of $1\angle \delta _{1}\text{p.u}$ and synchronous reactance of $\text{0.4 p.u}$ is connected by a transmission line of reactance $\text{0.1 p.u}$ ... $2$ decimal places.) (Machines are of non-salient type. Neglect resistances.)

asked Feb 20 in new by Arjun (6.7k points)

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30

GATE EE 2021 | Question: 20
The Bode magnitude plot for the transfer function $\frac{V_{o}\left ( s \right )}{V_{i}\left ( s \right )}$ of the circuit is as shown. The value of $R$ is _____________$\Omega$. (Round off to $2$ decimal places.)

asked Feb 20 in new by Arjun (6.7k points)

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31

GATE EE 2021 | Question: 21
A signal generator having a source resistance of $50\:\Omega$ is set to generate a $\text{1 kHz}$ sinewave. Open circuit terminal voltage is $\text{10 V}$ peak-to-peak. Connecting a capacitor across the terminals reduces the voltage to $\text{8 V}$ peak-to-peak. The value of this capacitor is _____________$\mu F$. (Round off to $2$ decimal places.)

asked Feb 20 in new by Arjun (6.7k points)

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32

GATE EE 2021 | Question: 22
A $16$-bit synchronous binary up-counter is clocked with a frequency $f_{\text{CLK}}$.The two most significant bits are $\text{OR-ed}$ together to form an output $Y$. Measurements show that $Y$ is periodic, and the duration for which $Y$ remains high in ... $f_{\text{CLK}}$ is ____________$\text{MHz}.$ (Round off to $2$ decimal places.)

asked Feb 20 in new by Arjun (6.7k points)

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33

GATE EE 2021 | Question: 23
In the $\text{BJT}$ circuit shown, beta of the $\text{PNP}$ transistor is $100$. Assume $V_{\text{BE}}=-0.7\;V$. The voltage across $R_{c}$ will be $\text{5 V}$ when $R_{2}$ is __________ $k \Omega$. (Round off to $2$ decimal places.)

asked Feb 20 in new by Arjun (6.7k points)

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34

GATE EE 2021 | Question: 24
In the circuit shown, the input $V_{i}$ is a sinusoidal $\text{AC}$ voltage having an $\text{RMS}$ value of $230\;V\pm 20\%$. The worst-case peak-inverse voltage seen across any diode is ____________$V$. (Round off to $2$ decimal places.)

asked Feb 20 in new by Arjun (6.7k points)

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35

GATE EE 2021 | Question: 25
In the circuit shown, a $\text{5 V}$ Zener diode is used to regulate the voltage across load $R_{0}$. The input is an unregulated $DC$ voltage with a minimum value of $\text{6 V}$ and a maximum value of $\text{8 V}$ ... power dissipation of $\text{2.5 W}$. Assuming the Zener diode to be ideal, the minimum value of $R_{0}$ is _________________ $\Omega$.

asked Feb 20 in new by Arjun (6.7k points)

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36

GATE EE 2021 | Question: 26
In the open interval $\left ( 0,1 \right )$, the polynomial $p\left ( x \right) =x^{4}-4x^{3}+2$ has two real roots one real root three real roots no real roots

asked Feb 20 in new by Arjun (6.7k points)

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37

GATE EE 2021 | Question: 27
Suppose the probability that a coin toss shows "head" is $p$, where $0<p<1$. The coin is tossed repeatedly until the first "head" appears. The expected number of tosses required is $p/\left ( 1-p \right )$ $\left ( 1-p \right )/p$ $1/p$ $1/p^{2}$

asked Feb 20 in new by Arjun (6.7k points)

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38

GATE EE 2021 | Question: 28
Let $\left ( -1 -j \right ), \left ( 3 -j \right ), \left ( 3 + j \right )$ and $\left ( -1+ j \right )$ be the vertices of a rectangle $C$ in the complex plane. Assuming that $C$ is traversed in counter-clockwise direction, the value of the contour integral $\oint _{C}\dfrac{dz}{z^{2}\left ( z-4 \right )}$ is $j\pi /2$ $0$ $-j\pi /8$ $j\pi /16$

asked Feb 20 in new by Arjun (6.7k points)

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39

GATE EE 2021 | Question: 29
In the circuit, switch '$S$' is in the closed position for a very long time. If the switch is opened at time $t = 0$, then in $i_{L} (t)$ amperes, for $t\geq0$ is $8e^{-10t}$ $10$ $8+2e^{-10t}$ $10\left ( 1-e^{-2t} \right )$

asked Feb 20 in new by Arjun (6.7k points)

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40

GATE EE 2021 | Question: 30
The input impedance, $Z_{in}\left ( s \right )$ for the network shown is $\frac{23s^{2}+46s+20}{4s+5}$ $6s+4$ $7s+4$ $\frac{25s^{2}+46s+20}{4s+5}$

asked Feb 20 in new by Arjun (6.7k points)

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