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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
Jun 20
in
Vector Analysis
by
Divyanshu Shukla
(
140
points)

55
views
gate2016ec3
vectoranalysis
+1
vote
1
answer
2
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 $4$ $5$ $6$ $7$
edited
Apr 23
in
Numerical Ability
by
Lakshman Patel RJIT
(
3.8k
points)

146
views
gateec2021
numericalability
datainterpretation
bargraph
+1
vote
2
answers
3
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 _______. $8 : 23$ $23 : 8$ $23 : 31$ $31 : 23$
edited
Apr 22
in
Numerical Ability
by
Lakshman Patel RJIT
(
3.8k
points)

649
views
gate2020ec
numericalability
datainterpretation
bargraph
+1
vote
1
answer
4
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
answer edited
Apr 12
in
Analytical Aptitude
by
Arjun
(
4.5k
points)

442
views
gateec2021
analyticalaptitude
logicalreasoning
statementsfollow
+1
vote
1
answer
5
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 ... $\text{(ii) and (iv)}$ $\text{(i), (iii) and (iv)}$ $\text{(i) and (iii)}$
recategorized
Apr 11
in
Verbal Ability
by
Lakshman Patel RJIT
(
3.8k
points)

101
views
gateec2021
verbalability
verbalreasoning
passagereading
+2
votes
1
answer
6
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? $9,92,500$ $9,95,006$ $10,00,000$ $12,51,506$
recategorized
Apr 11
in
Numerical Ability
by
Lakshman Patel RJIT
(
3.8k
points)

116
views
gateec2021
numericalability
simplecompoundinterest
+1
vote
2
answers
7
GATE ECE 2021  GA Question: 2
$p$ and $q$ are positive integers and $\dfrac{p}{q}+\dfrac{q}{p}=3,$ then, $\dfrac{p^{2}}{q^{2}}+\dfrac{q^{2}}{p^{2}}=$ $3$ $7$ $9$ $11$
recategorized
Apr 11
in
Numerical Ability
by
Lakshman Patel RJIT
(
3.8k
points)

110
views
gateec2021
numericalability
algebra
+1
vote
1
answer
8
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 ____________ $4$ $3$ $6$ $7$
recategorized
Apr 11
in
Spatial Aptitude
by
Lakshman Patel RJIT
(
3.8k
points)

140
views
gateec2021
spatialaptitude
patternsintwodimensions
+1
vote
1
answer
9
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
recategorized
Apr 11
in
Verbal Ability
by
Lakshman Patel RJIT
(
3.8k
points)

102
views
gateec2021
verbalability
wordpairs
+1
vote
1
answer
10
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 $\text{CORRECT}$? $\text{(i) and (ii)}$ $\text{(i) and (iii)}$ $\text{(ii) and (iii)}$ $\text{(i) and (iv)}$
recategorized
Apr 11
in
Verbal Ability
by
Lakshman Patel RJIT
(
3.8k
points)

115
views
gateec2021
verbalability
englishgrammar
tense
0
votes
0
answers
11
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 __________
recategorized
Apr 11
in
Vector Analysis
by
Lakshman Patel RJIT
(
3.8k
points)

45
views
gateec2021
numericalanswers
vectoranalysis
vectorinplanes
0
votes
0
answers
12
GATE ECE 2021  Question: 31
The propagation delays of the $\text{XOR}$ gate, $\text{AND}$ gate and multiplexer $\text{(MUX)}$ in the circuit shown in the figure are $4\:ns$, $2\:ns$ and $1\:ns$, respectively. If all the inputs $\text{P, Q, R, S and T}$ are applied simultaneously and held constant, the maximum propagation delay of the circuit is $3\:ns$ $5\:ns$ $6\:ns$ $7\:ns$
recategorized
Apr 11
in
Digital Circuits
by
Lakshman Patel RJIT
(
3.8k
points)

67
views
gateec2021
digitalcircuits
combinationalcircuits
multiplexers
0
votes
0
answers
13
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 $\frac{2}{5}$ $\frac{1}{3}$ $\frac{1}{2}$ $\frac{2}{3}$
recategorized
Apr 11
in
Probability and Statistics
by
Lakshman Patel RJIT
(
3.8k
points)

64
views
gateec2021
probabilityandstatistics
probability
conditionalprobability
0
votes
0
answers
14
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 $\frac{\pi }{8}\sin\left ( 2i \right )$ $\frac{\pi }{8}\sin\left ( 2i \right )$ $\frac{\pi }{4}\sin\left ( 2i \right )$ $\frac{\pi }{4}\sin\left ( 2i \right )$
recategorized
Apr 11
in
Complex Analysis
by
Lakshman Patel RJIT
(
3.8k
points)

147
views
gateec2021
complexanalysis
0
votes
0
answers
15
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 _________________
recategorized
Apr 11
in
Vector Analysis
by
Lakshman Patel RJIT
(
3.8k
points)

61
views
gateec2021
numericalanswers
vectoranalysis
vectorinplanes
+1
vote
1
answer
16
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 $2:3$ $3:4$ $4:5$ $5:6$
recategorized
Apr 11
in
Numerical Ability
by
Lakshman Patel RJIT
(
3.8k
points)

121
views
gateec2021
numericalability
geometry
triangles
area
0
votes
0
answers
17
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 $\frac{G_{1}+G_{2}+G_{1}G_{2}H}{1+G_{1}H}$ $\frac{G_{1}+G_{2}}{1+G_{1}H+G_{2}H}$ $\frac{G_{1}+G_{2}}{1+G_{1}H}$ $\frac{G_{1}+G_{2}+G_{1}G_{2}H}{1+G_{1}H+G_{2}H}$
recategorized
Apr 11
in
Control Systems
by
Lakshman Patel RJIT
(
3.8k
points)

33
views
gateec2021
controlsystems
0
votes
0
answers
18
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 $2^{8}$ $2^{32}$ $2^{15}$ $2^{19}$
recategorized
Apr 11
in
Digital Circuits
by
Lakshman Patel RJIT
(
3.8k
points)

50
views
gateec2021
digitalcircuits
combinationalcircuits
decoders
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 $\sigma ^{2}_{Y}=2 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=4 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=5 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=25 \sigma ^{2}_{X}$
recategorized
Apr 11
in
Probability and Statistics
by
Lakshman Patel RJIT
(
3.8k
points)

38
views
gateec2021
probabilityandstatistics
randomvariable
variance
0
votes
0
answers
20
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 $\left ( 1x^{2} \right )^{3/4}$ $\left ( 1x^{2} \right )^{1/4}$ $\left ( 1x^{2} \right )^{3/2}$ $\left ( 1x^{2} \right )^{1/2}$
recategorized
Apr 11
in
Differential Equations
by
Lakshman Patel RJIT
(
3.8k
points)

43
views
gateec2021
differentialequations
firstorderdifferentialequation
0
votes
0
answers
21
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 $\frac{1}{2}$ $\frac{1}{4}$ $\frac{1}{6}$ $\frac{1}{3}$
recategorized
Apr 11
in
Vector Analysis
by
Lakshman Patel RJIT
(
3.8k
points)

67
views
gateec2021
vectoranalysis
vectorinplanes
0
votes
0
answers
22
GATE ECE 2021  Question: 37
For a vector field $D=\rho\cos^{2}\:\varphi \:a_{\rho }+z^{2}\sin^{2}\:\varphi \:a_{\varphi }$ in a cylindrical coordinate system $\left ( \rho ,\varphi ,z \right )$ with unit vectors $a_{\rho },a_{\varphi }$ and $a_{z}$, the ... $\left ( \rho =3, 0\leq z\leq 2 \right )$ (rounded off to two decimal places) is ________________
recategorized
Apr 11
in
Vector Analysis
by
Lakshman Patel RJIT
(
3.8k
points)

25
views
gateec2021
numericalanswers
vectoranalysis
0
votes
0
answers
23
GATE ECE 2021  Question: 36
A real $2\times2$ nonsingular matrix $A$ with repeated eigenvalue is given as $A=\begin{bmatrix} x & 3.0\\ 3.0 & 4.0 \end{bmatrix}$ where $x$ is a real positive number. The value of $x$ (rounded off to one decimal place) is ________________
recategorized
Apr 11
in
Linear Algebra
by
Lakshman Patel RJIT
(
3.8k
points)

32
views
gateec2021
numericalanswers
linearalgebra
eigenvalues
0
votes
0
answers
24
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 $y\:=\:7$
recategorized
Apr 11
in
Digital Circuits
by
Lakshman Patel RJIT
(
3.8k
points)

87
views
gateec2021
digitalcircuits
numbersystem
numberrepresentation
+1
vote
1
answer
25
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 ____________ $\frac{\pi }{3}$ $\frac{2\pi }{3}$ $\frac{3\pi }{2}$ $3\pi$
recategorized
Apr 11
in
Numerical Ability
by
Lakshman Patel RJIT
(
3.8k
points)

350
views
gateec2021
numericalability
mensuration
cones
0
votes
0
answers
26
GATE ECE 2021  Question: 46
The propagation delay of the exclusive$\text{OR}$ ($\text{XOR}$) gate in the circuit in the figure is $3\:ns$. The propagation delay of all the flipflops is assumed to be zero. The clock ($\text{Clk}$ ... of triggering clock edges after which the flipflop outputs $Q_{2}Q_{1}Q_{0}$ becomes $1\; 0\; 0$ (in integer) is
recategorized
Apr 11
in
Digital Circuits
by
Lakshman Patel RJIT
(
3.8k
points)

36
views
gateec2021
numericalanswers
digitalcircuits
sequentialcircuit
counters
+1
vote
2
answers
27
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.
answer selected
Apr 11
in
Verbal Ability
by
Lakshman Patel RJIT
(
3.8k
points)

201
views
gate2020ec
verbalability
verbalreasoning
passagereading
+1
vote
2
answers
28
GATE ECE 2020  GA Question: 2
He was not only accused of theft _____ of conspiracy. rather but also but even rather than
answer selected
Apr 11
in
Verbal Ability
by
Lakshman Patel RJIT
(
3.8k
points)

406
views
gate2020ec
verbalability
englishgrammar
+1
vote
2
answers
29
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 $x > 1$? $e^{x}$ $\sqrt{x}$ $1/x$ $e^{x}$
commented
Apr 11
in
Numerical Ability
by
Arjun
(
4.5k
points)

386
views
gate2020ec
numericalability
functions
+1
vote
2
answers
30
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.
answer selected
Apr 11
in
Verbal Ability
by
Lakshman Patel RJIT
(
3.8k
points)

193
views
gate2020ec
verbalability
verbalreasoning
passagereading
+1
vote
1
answer
31
GATE ECE 2020  GA Question: 3
Select the word that fits the analogy: Explicit: Implicit :: Express: _______ Impress Repress Compress Suppress
answer selected
Apr 10
in
Verbal Ability
by
Arjun
(
4.5k
points)

343
views
gate2020ec
verbalability
wordpairs
+1
vote
1
answer
32
GATE ECE 2020  GA Question: 7
It is quarter past three in your watch. The angle between the hour hand and the minute hand is ________. $0^{\circ}$ $7.5^{\circ}$ $15^{\circ}$ $22.5^{\circ}$
answer selected
Apr 10
in
Numerical Ability
by
Arjun
(
4.5k
points)

202
views
gate2020ec
numericalability
clocktime
+1
vote
1
answer
33
GATE ECE 2020  GA Question: 9
$a, b, c$ are real numbers. The quadratic equation $ax^{2}bx+c=0$ has equal roots, which is $\beta$, then $\beta =b/a$ $\beta^{2} =ac$ $\beta^{3} =bc/\left ( 2a^{2} \right )$ $\beta^{2} \neq 4ac$
answer edited
Apr 8
in
Numerical Ability
by
Arjun
(
4.5k
points)

212
views
gate2020ec
numericalability
quadraticequations
+1
vote
1
answer
34
GATE ECE 2020  GA Question: 8
A circle with centre $\text{O}$ is shown in the figure. A rectangle $\text{PQRS}$ of maximum possible area is inscribed in the circle. If the radius of the circle is $a$, then the area of the shaded portion is _______. $\pi a^{2}a^{2}$ $\pi a^{2}\sqrt{2}a^{2}$ $\pi a^{2}2a^{2}$ $\pi a^{2}3a^{2}$
answer edited
Apr 8
in
Numerical Ability
by
Lakshman Patel RJIT
(
3.8k
points)

1k
views
gate2020ec
numericalability
geometry
circle
area
+1
vote
1
answer
35
GATE ECE 2020  GA Question: 1
The untimely loss of life is a cause of serious global concern as thousands of people get killed ____ accidents every year while many other die ____ diseases like cardio vascular disease, cancer, etc. in, of from, of during, from from, from
answer selected
Apr 8
in
Verbal Ability
by
Arjun
(
4.5k
points)

288
views
gate2020ec
verbalability
mostappropriateword
0
votes
0
answers
36
GATE ECE 2021  Question: 33
The electrical system shown in the figure converts input source current $i_{s}(t)$ to output voltage $v_{o}(t)$ Current i $i_{L}(t)$ in the inductor and voltage $v_{c}(t)$ across the capacitor ... as well as completely observable completely state controllable but not observable completely observable but not state controllable neither state controllable nor observable
edited
Mar 19
in
Others
by
soujanyareddy13
(
100
points)

29
views
gateec2021
0
votes
0
answers
37
GATE ECE 2021  Question: 32
The content of the registers are $R_{1} = 25H, R_{2} = 30H$ and $R_{3} = 40H$. The following machine instructions are executed. $\text{PUSH } \{R_{1}\}$ $\text{PUSH } \{R_{2}\}$ $\text{PUSH } \{R_{3}\}$ $\text{POP } \{R_{1}\}$ $\text{POP } \{R_{2}\}$ ... $R_{1}=30H,\:R_{2}=40H,\:R_{3}=25H$ $R_{1}=40H,\:R_{2}=25H,\:R_{3}=30H$
edited
Mar 17
in
Others
by
soujanyareddy13
(
100
points)

22
views
gateec2021
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 ______________
edited
Mar 17
in
Others
by
soujanyareddy13
(
100
points)

48
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 _____ $\text{kHz}$.
edited
Mar 17
in
Others
by
soujanyareddy13
(
100
points)

68
views
gateec2021
numericalanswers
0
votes
0
answers
40
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
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