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GATE ECE 2016 Set 3  Question: 27
If the vectors $e_1=(1,0,2)$, $e_2=(0,1,0)$ and $e_3=(2,0,1)$ form an orthogonal basis of the threedimensional real space $\mathbb{R}^3$, then the vector $\textbf{u}=(4,3,3)\in \mathbb{R}^3 $ can be expressed as $\textbf{u}=$ ... \frac{2}{5}$e_1+3e_2+$\large\frac{11}{5}$e_3 \\$ $\textbf{u}=$\large\frac{2}{5}$e_1+3e_2$\large\frac{11}{5}$e_3$
answered
22 hours
ago
in
Vector Analysis
by
Divyanshu Shukla
(
140
points)

34
views
gate2016ec3
vectoranalysis
+1
vote
1
answer
2
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 ... $\text{(ii) and (iv)}$ $\text{(i), (iii) and (iv)}$ $\text{(i) and (iii)}$
answered
Apr 11
in
Verbal Ability
by
Arjun
(
4.5k
points)

74
views
gateec2021
verbalability
verbalreasoning
passagereading
+1
vote
1
answer
3
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 $\text{CORRECT}$? $\text{(i) and (ii)}$ $\text{(i) and (iii)}$ $\text{(ii) and (iii)}$ $\text{(i) and (iv)}$
answered
Apr 11
in
Verbal Ability
by
Arjun
(
4.5k
points)

78
views
gateec2021
verbalability
englishgrammar
tense
+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
answered
Apr 11
in
Verbal Ability
by
Dhruov
(
480
points)

74
views
gateec2021
verbalability
wordpairs
+1
vote
2
answers
5
GATE ECE 2020  GA Question: 4
The Canadian constitution requires that equal importance be given to English and French. Last year, Air Canada lost a lawsuit, and had to pay a sixfigure fine to a Frenchspeaking couple after they filed complaints about formal in ... the French ones. the English announcements being longer than the French ones. equal importance being given to English and French.
answered
Apr 11
in
Verbal Ability
by
Arjun
(
4.5k
points)

163
views
gate2020ec
verbalability
verbalreasoning
passagereading
+1
vote
2
answers
6
GATE ECE 2020  GA Question: 6
The global financial crisis in $2008$ is considered to be the most serious worldwide financial crisis, which started with the subprime lending crisis in $\text{USA}$ in $2007$. The subprime lending crisis led to the ... $\rightarrow$ East Asian crisis$\rightarrow$ banking crisis$\rightarrow$ subprime lending crisis.
answered
Apr 10
in
Verbal Ability
by
Arjun
(
4.5k
points)

166
views
gate2020ec
verbalability
verbalreasoning
passagereading
+1
vote
2
answers
7
GATE ECE 2020  GA Question: 2
He was not only accused of theft _____ of conspiracy. rather but also but even rather than
answered
Apr 10
in
Verbal Ability
by
Arjun
(
4.5k
points)

364
views
gate2020ec
verbalability
englishgrammar
+1
vote
2
answers
8
GATE ECE 2020  GA Question: 5
A superadditive function $f(\cdot)$ satisfies the following property $f\left ( x_{1} +x_{2}\right )\geq f\left ( x_{1} \right ) + f\left ( x_{2} \right )$ Which of the following functions is a superadditive function for $x > 1$? $e^{x}$ $\sqrt{x}$ $1/x$ $e^{x}$
answered
Apr 10
in
Numerical Ability
by
Lakshman Patel RJIT
(
3.8k
points)

328
views
gate2020ec
numericalability
functions
+1
vote
2
answers
9
GATE ECE 2020  GA Question: 10
The following figure shows the data of students enrolled in $5$ years $(2014\;\text{to}\; 2018)$ for two schools $P$ and $Q$. During this period, the ratio of the average number of the students enrolled in school $P$ to the average of the difference of the number of students enrolled in schools $P$ and $Q$ is _______. $8 : 23$ $23 : 8$ $23 : 31$ $31 : 23$
answered
Mar 31
in
Numerical Ability
by
Lakshman Patel RJIT
(
3.8k
points)

567
views
gate2020ec
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 $2:3$ $3:4$ $4:5$ $5:6$
answered
Mar 22
in
Numerical Ability
by
Lakshman Patel RJIT
(
3.8k
points)

94
views
gateec2021
numericalability
geometry
triangles
area
+1
vote
1
answer
11
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 $4$ $5$ $6$ $7$
answered
Mar 22
in
Numerical Ability
by
Lakshman Patel RJIT
(
3.8k
points)

114
views
gateec2021
numericalability
datainterpretation
bargraph
+1
vote
1
answer
12
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
answered
Mar 22
in
Analytical Aptitude
by
Lakshman Patel RJIT
(
3.8k
points)

392
views
gateec2021
analyticalaptitude
logicalreasoning
statementsfollow
+1
vote
1
answer
13
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 ____________ $\frac{\pi }{3}$ $\frac{2\pi }{3}$ $\frac{3\pi }{2}$ $3\pi$
answered
Mar 22
in
Numerical Ability
by
Lakshman Patel RJIT
(
3.8k
points)

210
views
gateec2021
numericalability
mensuration
cones
+1
vote
1
answer
14
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 ____________ $4$ $3$ $6$ $7$
answered
Mar 22
in
Spatial Aptitude
by
Lakshman Patel RJIT
(
3.8k
points)

96
views
gateec2021
spatialaptitude
patternsintwodimensions
+2
votes
1
answer
15
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? $9,92,500$ $9,95,006$ $10,00,000$ $12,51,506$
answered
Mar 22
in
Numerical Ability
by
Lakshman Patel RJIT
(
3.8k
points)

89
views
gateec2021
numericalability
simplecompoundinterest
+1
vote
2
answers
16
GATE ECE 2021  GA Question: 2
$p$ and $q$ are positive integers and $\dfrac{p}{q}+\dfrac{q}{p}=3,$ then, $\dfrac{p^{2}}{q^{2}}+\dfrac{q^{2}}{p^{2}}=$ $3$ $7$ $9$ $11$
answered
Mar 22
in
Numerical Ability
by
Lakshman Patel RJIT
(
3.8k
points)

86
views
gateec2021
numericalability
algebra
0
votes
0
answers
17
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)

43
views
gateec2021
vectoranalysis
vectorinplanes
0
votes
0
answers
18
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)

31
views
gateec2021
differentialequations
firstorderdifferentialequation
0
votes
0
answers
19
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)

24
views
gateec2021
probabilityandstatistics
randomvariable
variance
0
votes
0
answers
20
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)

27
views
gateec2021
0
votes
0
answers
21
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)

29
views
gateec2021
0
votes
0
answers
22
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)

33
views
gateec2021
0
votes
0
answers
23
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)

27
views
gateec2021
0
votes
0
answers
24
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)

25
views
gateec2021
0
votes
0
answers
25
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)

28
views
gateec2021
0
votes
0
answers
26
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)

37
views
gateec2021
0
votes
0
answers
27
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)

64
views
gateec2021
digitalcircuits
numbersystem
numberrepresentation
0
votes
0
answers
28
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)

36
views
gateec2021
digitalcircuits
combinationalcircuits
decoders
0
votes
0
answers
29
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)

24
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gateec2021
controlsystems
0
votes
0
answers
30
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)

29
views
gateec2021
0
votes
0
answers
31
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)

28
views
gateec2021
0
votes
0
answers
32
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)

30
views
gateec2021
numericalanswers
vectoranalysis
vectorinplanes
0
votes
0
answers
33
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)

38
views
gateec2021
numericalanswers
vectoranalysis
vectorinplanes
0
votes
0
answers
34
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 ________ $A$.
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Feb 20
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Others
by
Arjun
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4.5k
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gateec2021
numericalanswers
0
votes
0
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35
GATE ECE 2021  Question: 19
Consider the circuit shown in the figure. The value of $v_{0}$ (rounded off to one decimal place) is _________ $V$.
asked
Feb 20
in
Others
by
Arjun
(
4.5k
points)

34
views
gateec2021
numericalanswers
0
votes
0
answers
36
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
in
Others
by
Arjun
(
4.5k
points)

23
views
gateec2021
numericalanswers
0
votes
0
answers
37
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
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27
views
gateec2021
numericalanswers
0
votes
0
answers
38
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)

33
views
gateec2021
numericalanswers
0
votes
0
answers
39
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 _____ $\text{kHz}$.
asked
Feb 20
in
Others
by
Arjun
(
4.5k
points)

54
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gateec2021
numericalanswers
0
votes
0
answers
40
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
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4.5k
points)

30
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gateec2021
numericalanswers
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