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1
GATE ECE 2021  GA Question: 1
The current population of a city is $11,02,500$ . If it has been increasing at the rate of $5\%$ per annum, what was its population $2$ years ago? $9,92,500$ $9,95,006$ $10,00,000$ $12,51,506$
asked
Feb 20
in
Numerical Ability
by
Arjun
(
4.5k
points)

116
views
gateec2021
numericalability
simplecompoundinterest
+1
vote
2
answers
2
GATE ECE 2021  GA Question: 2
$p$ and $q$ are positive integers and $\dfrac{p}{q}+\dfrac{q}{p}=3,$ then, $\dfrac{p^{2}}{q^{2}}+\dfrac{q^{2}}{p^{2}}=$ $3$ $7$ $9$ $11$
asked
Feb 20
in
Numerical Ability
by
Arjun
(
4.5k
points)

110
views
gateec2021
numericalability
algebra
+1
vote
1
answer
3
GATE ECE 2021  GA Question: 3
The least number of squares that must be added so that the line $PQ$ becomes the line of symmetry is ____________ $4$ $3$ $6$ $7$
asked
Feb 20
in
Spatial Aptitude
by
Arjun
(
4.5k
points)

140
views
gateec2021
spatialaptitude
patternsintwodimensions
+1
vote
1
answer
4
GATE ECE 2021  GA Question: 4
$\textit{Nostalgia}$ is to $\textit{anticipation}$ as ____________ is to _____________ Which one of the following options maintains a similar logical relation in the above sentence? Present, past Future, past Past, future Future, present
asked
Feb 20
in
Verbal Ability
by
Arjun
(
4.5k
points)

102
views
gateec2021
verbalability
wordpairs
+1
vote
1
answer
5
GATE ECE 2021  GA Question: 5
Consider the following sentences: I woke up from sleep. I woked up from sleep. I was woken up from sleep. I was wokened up from sleep. Which of the above sentences are grammatically $\text{CORRECT}$? $\text{(i) and (ii)}$ $\text{(i) and (iii)}$ $\text{(ii) and (iii)}$ $\text{(i) and (iv)}$
asked
Feb 20
in
Verbal Ability
by
Arjun
(
4.5k
points)

115
views
gateec2021
verbalability
englishgrammar
tense
+1
vote
1
answer
6
GATE ECE 2021  GA Question: 6
Given below are two statements and two conclusions. $\text{Statement 1}$: All purple are green. $\text{Statement 2}$: All black are green. $\text{Conclusion I}$: Some black are purple. $\text{Conclusion II}$: No black is purple. Based on the above ... correct Either conclusion $\text{I}$ or $\text{II}$ is correct Both conclusion $\text{I}$ and $\text{II}$ are correct
asked
Feb 20
in
Analytical Aptitude
by
Arjun
(
4.5k
points)

442
views
gateec2021
analyticalaptitude
logicalreasoning
statementsfollow
+1
vote
1
answer
7
GATE ECE 2021  GA Question: 7
Computers are ubiquitous. They are used to improve efficiency in almost all fields from agriculture to space exploration. Artificial intelligence $\text{(AI)}$ is currently a hot topic. $\text{Al}$ enables computers to learn, given enough training data. For humans, sitting in front of a ... $\text{(ii) and (iv)}$ $\text{(i), (iii) and (iv)}$ $\text{(i) and (iii)}$
asked
Feb 20
in
Verbal Ability
by
Arjun
(
4.5k
points)

101
views
gateec2021
verbalability
verbalreasoning
passagereading
+1
vote
1
answer
8
GATE ECE 2021  GA Question: 8
Consider a square sheet of side $1$ unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step. one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in cubic units, is ____________ $\frac{\pi }{3}$ $\frac{2\pi }{3}$ $\frac{3\pi }{2}$ $3\pi$
asked
Feb 20
in
Numerical Ability
by
Arjun
(
4.5k
points)

350
views
gateec2021
numericalability
mensuration
cones
+1
vote
1
answer
9
GATE ECE 2021  GA Question: 9
The number of minutes spent by two students, $X$ and $Y$, exercising every day in a given week are shown in the bar chart above. The number of days in the given week in which one of the students spent a minimum of $10\%$ more than the other student, on a given day, is $4$ $5$ $6$ $7$
asked
Feb 20
in
Numerical Ability
by
Arjun
(
4.5k
points)

146
views
gateec2021
numericalability
datainterpretation
bargraph
+1
vote
1
answer
10
GATE ECE 2021  GA Question: 10
Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above. The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is $2:3$ $3:4$ $4:5$ $5:6$
asked
Feb 20
in
Numerical Ability
by
Arjun
(
4.5k
points)

121
views
gateec2021
numericalability
geometry
triangles
area
0
votes
0
answers
11
GATE ECE 2021  Question: 1
The vector function $F\left ( r \right )=x\hat{i}+y\hat{j}$ is defined over a circular arc $C$ shown in the figure. The line integral of $\int _{C} F\left ( r \right ).dr$ is $\frac{1}{2}$ $\frac{1}{4}$ $\frac{1}{6}$ $\frac{1}{3}$
asked
Feb 20
in
Vector Analysis
by
Arjun
(
4.5k
points)

67
views
gateec2021
vectoranalysis
vectorinplanes
0
votes
0
answers
12
GATE ECE 2021  Question: 2
Consider the differential equation given below. $\frac{dy}{dx}+\frac{x}{1x^{2}}y=x\sqrt{y}$ The integrating factor of the differential equation is $\left ( 1x^{2} \right )^{3/4}$ $\left ( 1x^{2} \right )^{1/4}$ $\left ( 1x^{2} \right )^{3/2}$ $\left ( 1x^{2} \right )^{1/2}$
asked
Feb 20
in
Differential Equations
by
Arjun
(
4.5k
points)

43
views
gateec2021
differentialequations
firstorderdifferentialequation
0
votes
0
answers
13
GATE ECE 2021  Question: 3
Two continuous random variables $X$ and $Y$ are related as $Y=2X+3$ Let $\sigma ^{2}_{X}$ and $\sigma ^{2}_{Y}$denote the variances of $X$ and $Y$, respectively. The variances are related as $\sigma ^{2}_{Y}=2 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=4 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=5 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=25 \sigma ^{2}_{X}$
asked
Feb 20
in
Probability and Statistics
by
Arjun
(
4.5k
points)

38
views
gateec2021
probabilityandstatistics
randomvariable
variance
0
votes
0
answers
14
GATE ECE 2021  Question: 4
Consider a realvalued baseband signal $x(t)$, band limited to $\text{10 kHz}$. The Nyquist rate for the signal $y\left ( t \right )=x\left ( t \right )x\left ( 1+\dfrac{t}{2} \right )$ is $\text{15 kHz}$ $\text{30 kHz}$ $\text{60 kHz}$ $\text{20 kHz}$
asked
Feb 20
in
Others
by
Arjun
(
4.5k
points)

39
views
gateec2021
0
votes
0
answers
15
GATE ECE 2021  Question: 5
Consider two $16$point sequences $x\left [ n \right ]$ and $h\left [ n \right ]$. Let the linear convolution of $x\left [ n \right ]$ and $h\left [ n \right ]$ be denoted by $y\left [ n \right ]$, while $z\left [ n \right ]$ denotes the $16$point inverse discrete Fourier ... $k=0,1,2,,15$ $k=0$ $k=15$ $\text{k=0 and k=15}$
asked
Feb 20
in
Others
by
Arjun
(
4.5k
points)

43
views
gateec2021
0
votes
0
answers
16
GATE ECE 2021  Question: 6
A bar of silicon is doped with boron concentration of $10^{16} \text{cm}^{3}$ and assumed to be fully ionized. It is exposed to light such that electronhole pairs are generated throughout the volume of the bar at the rate of $10^{20} \text{cm}^{3} s^{1}$. If the ... $2 \times 10^{20} \text{cm}^{6}$ $10^{32} \text{cm}^{6}$ $2 \times 10^{32} \text{cm}^{6}$
asked
Feb 20
in
Others
by
Arjun
(
4.5k
points)

47
views
gateec2021
0
votes
0
answers
17
GATE ECE 2021  Question: 7
The energy band diagram of a $\text{ptype}$ semiconductor bar of length $L$ under equilibrium condition (i.e.. the Fermi energy level $E_{F}$ is constant) is shown in the figure. The valance band $E_{V}$ is sloped since doping is nonuniform along the bar. The difference ... bar is $\frac{\Delta }{qL}$ $\frac{2\Delta }{qL}$ $\frac{\Delta }{2qL}$ $\frac{3\Delta }{2qL}$
asked
Feb 20
in
Others
by
Arjun
(
4.5k
points)

31
views
gateec2021
0
votes
0
answers
18
GATE ECE 2021  Question: 8
In the circuit shown in the figure, the transistors $M_{1}$ and $M_{2}$ are operating in saturation. The channel length modulation coefficients of both the transistors are nonzero. The transconductance of the $\text{MOSFETs}$ $M_{1}$ and $M_{2}$ are $g_{m1}$ ... $g_{m2}\left ( \frac{1}{g_{m1}}\left  \right r_{01}\left  \right r_{02} \right )$
asked
Feb 20
in
Others
by
Arjun
(
4.5k
points)

32
views
gateec2021
0
votes
0
answers
19
GATE ECE 2021  Question: 9
For the circuit with an ideal $\text{OPAMP}$ shown in the figure. $V_{\text{REF}}$ is fixed. If $V_{\text{OUT}}=1$ volt for $V_{\text{IN}}0.1$ volt and $V_{\text{OUT}}=6$ volt for $V_{\text{IN}}=1$ volt, where $V_{\text{OUT}}$ is measured across $R_{L}$ connected at the output of this $\text{OPAMP}$, the value of $R_{F}/R_{\text{IN}}$ is $3.285$ $2.860$ $3.825$ $5.555$
asked
Feb 20
in
Others
by
Arjun
(
4.5k
points)

35
views
gateec2021
0
votes
0
answers
20
GATE ECE 2021  Question: 10
Consider the circuit with an ideal $\text{OPAMP}$ shown in the figure. Assuming $\left  V_{\text{IN}} \right \ll \left  V_{\text{CC}} \right $ and $\left  V_{\text{REF}} \right \ll \left  V_{\text{CC}} \right  $, the condition at which $V_{\text{OUT}}$ equals ... $V_{\text{IN}}\:=\:2\:V_{\text{REF}}$ $V_{\text{IN}}\:=\:2\:+\:V_{\text{REF}}$
asked
Feb 20
in
Others
by
Arjun
(
4.5k
points)

44
views
gateec2021
0
votes
0
answers
21
GATE ECE 2021  Question: 11
If $(1235)_{x}\:=\:(3033)_{y}$, where $x$ and $y$ indicate the bases of the corresponding numbers, then $x\:=\:7$ and $y\:=\:5$ $x\:=\:8$ and $y\:=\:6$ $x\:=\:6$ and $y\:=\:4$ $x\:=\:9$ and $y\:=\:7$
asked
Feb 20
in
Digital Circuits
by
Arjun
(
4.5k
points)

87
views
gateec2021
digitalcircuits
numbersystem
numberrepresentation
0
votes
0
answers
22
GATE ECE 2021  Question: 12
Addressing of a $32K\:\times\:16$ memory is realized using a single decoder. The minimum number of $\text{AND}$ gates required for the decoder is $2^{8}$ $2^{32}$ $2^{15}$ $2^{19}$
asked
Feb 20
in
Digital Circuits
by
Arjun
(
4.5k
points)

50
views
gateec2021
digitalcircuits
combinationalcircuits
decoders
0
votes
0
answers
23
GATE ECE 2021  Question: 13
The block diagram of a feedback control system is shown in the figure The transfer function $\dfrac{Y{\left ( s \right )}}{X {\left ( s \right )}}$ of the system is $\frac{G_{1}+G_{2}+G_{1}G_{2}H}{1+G_{1}H}$ $\frac{G_{1}+G_{2}}{1+G_{1}H+G_{2}H}$ $\frac{G_{1}+G_{2}}{1+G_{1}H}$ $\frac{G_{1}+G_{2}+G_{1}G_{2}H}{1+G_{1}H+G_{2}H}$
asked
Feb 20
in
Control Systems
by
Arjun
(
4.5k
points)

33
views
gateec2021
controlsystems
0
votes
0
answers
24
GATE ECE 2021  Question: 14
The complete Nyquist plot of the openloop transfer function $G(s)H(s)$ of a feedback control system in the figure. If $G(s)H(s)$ has one zero in the righthalf of the $s$plane, the number of poles that the closedloop system will have in the righthalf of the $s$plane is $0$ $1$ $4$ $3$
asked
Feb 20
in
Others
by
Arjun
(
4.5k
points)

51
views
gateec2021
0
votes
0
answers
25
GATE ECE 2021  Question: 15
Consider a rectangular coordinate system $(x,y,z)$ with unit vectors $a_{x}\:a_{y}$ and $a_{z}$. A plane wave traveling in the region $z\geq 0$ with electric field vector $E=10\cos\left ( 2\times 10^{8}t\:+\:\beta z\right )a_{y}$ is incident normally on the ... $\frac{1}{3}$ $\frac{3}{5}$ $\frac{2}{5}$ $\frac{2}{3}$
asked
Feb 20
in
Others
by
Arjun
(
4.5k
points)

38
views
gateec2021
0
votes
0
answers
26
GATE ECE 2021  Question: 16
If the vectors $(1.0,\:1.0,\:2.0)$, $(7.0,\:3.0,\:x)$ and $(2.0,\:3.0,\:1.0)$ in $\mathbb{R}^{3}$ are linearly dependent, the value of $x$ is __________
asked
Feb 20
in
Vector Analysis
by
Arjun
(
4.5k
points)

45
views
gateec2021
numericalanswers
vectoranalysis
vectorinplanes
0
votes
0
answers
27
GATE ECE 2021  Question: 17
Consider the vector field $F\:=\:a_{x}\left ( 4yc_{1}z \right )+a_y\left ( 4x + 2z\right )+a_{z}\left ( 2y +z\right )$ in a rectangular coordinate system $(x,y,z)$ with unit vectors $a_{x},\:a_{y}$ and $a_{z}$. If the field $F$ is irrotational (conservative), then the constant $c_{1}$ (in integer) is _________________
asked
Feb 20
in
Vector Analysis
by
Arjun
(
4.5k
points)

61
views
gateec2021
numericalanswers
vectoranalysis
vectorinplanes
0
votes
0
answers
28
GATE ECE 2021  Question: 18
Consider the circuit shown in the figure. The current $I$ flowing through the $7\:\Omega$ resistor between $P$ and $Q$ (rounded off to one decimal place) is ________ $A$.
asked
Feb 20
in
Others
by
Arjun
(
4.5k
points)

51
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gateec2021
numericalanswers
0
votes
0
answers
29
GATE ECE 2021  Question: 19
Consider the circuit shown in the figure. The value of $v_{0}$ (rounded off to one decimal place) is _________ $V$.
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Feb 20
in
Others
by
Arjun
(
4.5k
points)

46
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gateec2021
numericalanswers
0
votes
0
answers
30
GATE ECE 2021  Question: 20
An $8$bit unipolar (all analog output values are positive) digitaltoanalog converter $\text{(DAC)}$ has a fullscale voltage range from $0\; V$ to $7.68\:V$. If the digital input code is $10010110$ (the leftmost bit is $\text{MSB}$), then the analog output voltage of the $\text{DAC}$ (rounded off to one decimal place) is ___________ $V$.
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Feb 20
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Others
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Arjun
(
4.5k
points)

28
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gateec2021
numericalanswers
0
votes
0
answers
31
GATE ECE 2021  Question: 21
The autocorrelation function $R_{X}\left ( \tau \right )$ of a widesense stationary random process $X(t)$ is shown in the figure. The average power of $X(t)$ is ________________
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Feb 20
in
Others
by
Arjun
(
4.5k
points)

37
views
gateec2021
numericalanswers
0
votes
0
answers
32
GATE ECE 2021  Question: 22
Consider a carrier signal which is amplitude modulated by a singletone sinusoidal message signal with a modulation index of $50\%$. If the carrier and one of the sidebands are suppressed in the modulated signal, the percentage of power saved (rounded off to one decimal place) is ______________
asked
Feb 20
in
Others
by
Arjun
(
4.5k
points)

48
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gateec2021
numericalanswers
0
votes
0
answers
33
GATE ECE 2021  Question: 23
A speech signal, band limited to $4\:\text{kHz}$, is sampled at $1.25$ times the Nyquist rate. The speech samples, assumed to be statistically independent and uniformly distributed in the range $5\:V$ to $+5\:V$, are ... transmission of the signal with arbitrarily small probability of transmission error (rounded off to two decimal places) is _____ $\text{kHz}$.
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Feb 20
in
Others
by
Arjun
(
4.5k
points)

68
views
gateec2021
numericalanswers
0
votes
0
answers
34
GATE ECE 2021  Question: 24
A $4\:kHz$ sinusoidal message signal having amplitude $4\:V$ is fed to a delta modulator ($DM$) operating at a sampling rate of $32\:\text{kHz}$. The minimum step size required to avoid slope overload noise in the $DM$ (rounded off to two decimal places) is _____ $V$.
asked
Feb 20
in
Others
by
Arjun
(
4.5k
points)

45
views
gateec2021
numericalanswers
0
votes
0
answers
35
GATE ECE 2021  Question: 25
The refractive indices of the core and cladding of an optical fiber are $1.50$ and $1.48$, respectively. The critical propagation angle, which is defined as the maximum angle that the light beam makes with the axis of the optical fiber to achieve the total internal reflection, (rounded off to two decimal places) is _____ degree.
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Feb 20
in
Others
by
Arjun
(
4.5k
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51
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gateec2021
numericalanswers
0
votes
0
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36
GATE ECE 2021  Question: 26
Consider the integral $\oint _{c}\frac{sin\left ( x \right )}{x^{2}\left ( x^{2}+4 \right )}dx$ where $C$ is a counterclockwise oriented circle defined as $\left  xi \right =2$. The value of the integral is $\frac{\pi }{8}\sin\left ( 2i \right )$ $\frac{\pi }{8}\sin\left ( 2i \right )$ $\frac{\pi }{4}\sin\left ( 2i \right )$ $\frac{\pi }{4}\sin\left ( 2i \right )$
asked
Feb 20
in
Complex Analysis
by
Arjun
(
4.5k
points)

147
views
gateec2021
complexanalysis
0
votes
0
answers
37
GATE ECE 2021  Question: 27
A box contains the following three coins. A fair coin with head on one face and tail on the other face. A coin with heads on both the faces. A coin with tails on both the faces. A coin is picked randomly from the box and tossed. Out of the two remaining coins in the box, one ... getting a head in the second toss is $\frac{2}{5}$ $\frac{1}{3}$ $\frac{1}{2}$ $\frac{2}{3}$
asked
Feb 20
in
Probability and Statistics
by
Arjun
(
4.5k
points)

64
views
gateec2021
probabilityandstatistics
probability
conditionalprobability
0
votes
0
answers
38
GATE ECE 2021  Question: 28
The switch in the circuit in the figure is in position $P$ for a long time and then moved to position $Q$ at time $t=0$. The value of $\dfrac{dv\left ( t \right )}{dt}$ at $t=0^{+}$ is $0\:V/s$ $3\:V/s$ $3\:V/s$ $5\:V/s$
asked
Feb 20
in
Others
by
Arjun
(
4.5k
points)

33
views
gateec2021
0
votes
0
answers
39
GATE ECE 2021  Question: 29
Consider the twoport network shown in the figure. The admittance parameters, in siemens, are $y_{11}=2,\:y_{12}=4,\:y_{21}=4,\:y_{22}=2$ $y_{11}=1,\:y_{12}=2,\:y_{21}=1,\:y_{22}=3$ $y_{11}=2,\:y_{12}=4,\:y_{21}=1,\:y_{22}=2$ $y_{11}=2,\:y_{12}=4,\:y_{21}=4,\:y_{22}=3$
asked
Feb 20
in
Others
by
Arjun
(
4.5k
points)

36
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gateec2021
0
votes
0
answers
40
GATE ECE 2021  Question: 30
For an $n$channel silicon $\text{MOSFET}$ with $10\:nm$ gate oxide thickness, the substrate sensitivity $\left ( \partial V_{T}/\partial \left  V_{BS} \right  \right )$ is found to be $50\:mV/V$ at a substrate voltage $\left  V_{BS} \right =2V$, where $V_{T}$ is the ... $4.37\times 10^{15}\:cm^{3}$ $2.37\times 10^{15}\:cm^{3}$ $9.37\times 10^{15}\:cm^{3}$
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Feb 20
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Others
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Arjun
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29
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