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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 $4$ $5$ $6$ $7$
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Numerical Ability
Apr 23, 2021
293
views
gateec-2021
numerical-ability
data-interpretation
bar-graph
2
answers
2
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 _______. $8 : 23$ $23 : 8$ $23 : 31$ $31 : 23$
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Numerical Ability
Apr 22, 2021
911
views
gate2020-ec
numerical-ability
data-interpretation
bar-graph
1
answer
3
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 ... $\text{(ii) and (iv)}$ $\text{(i), (iii) and (iv)}$ $\text{(i) and (iii)}$
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Verbal Ability
Apr 11, 2021
197
views
gateec-2021
verbal-ability
verbal-reasoning
passage-reading
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
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Analytical Aptitude
Apr 11, 2021
552
views
gateec-2021
analytical-aptitude
logical-reasoning
statements-follow
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 $\text{CORRECT}$? $\text{(i) and (ii)}$ $\text{(i) and (iii)}$ $\text{(ii) and (iii)}$ $\text{(i) and (iv)}$
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Verbal Ability
Apr 11, 2021
274
views
gateec-2021
verbal-ability
english-grammar
tense
1
answer
6
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
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Verbal Ability
Apr 11, 2021
278
views
gateec-2021
verbal-ability
word-pairs
1
answer
7
GATE ECE 2021 | GA Question: 3
The least number of squares that must be added so that the line $P-Q$ becomes the line of symmetry is ____________ $4$ $3$ $6$ $7$
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Spatial Aptitude
Apr 11, 2021
237
views
gateec-2021
spatial-aptitude
patterns-in-two-dimensions
2
answers
8
GATE ECE 2021 | GA Question: 2
$p$ and $q$ are positive integers and $\dfrac{p}{q}+\dfrac{q}{p}=3,$ then, $\dfrac{p^{2}}{q^{2}}+\dfrac{q^{2}}{p^{2}}=$ $3$ $7$ $9$ $11$
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Numerical Ability
Apr 11, 2021
202
views
gateec-2021
numerical-ability
algebra
1
answer
9
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? $9,92,500$ $9,95,006$ $10,00,000$ $12,51,506$
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Numerical Ability
Apr 11, 2021
210
views
gateec-2021
numerical-ability
simple-compound-interest
0
answers
10
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 counter-clockwise oriented circle defined as $\left | x-i \right |=2$. The value of the integral is $-\frac{\pi }{8}\sin\left ( 2i \right )$ $\frac{\pi }{8}\sin\left ( 2i \right )$ $-\frac{\pi }{4}\sin\left ( 2i \right )$ $\frac{\pi }{4}\sin\left ( 2i \right )$
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Complex Analysis
Apr 11, 2021
184
views
gateec-2021
complex-analysis
0
answers
11
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 $\sigma ^{2}_{Y}=2 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=4 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=5 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=25 \sigma ^{2}_{X}$
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Probability and Statistics
Apr 11, 2021
68
views
gateec-2021
probability-and-statistics
random-variable
variance
0
answers
12
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 $\frac{1}{2}$ $\frac{1}{4}$ $\frac{1}{6}$ $\frac{1}{3}$
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Vector Analysis
Apr 11, 2021
177
views
gateec-2021
vector-analysis
vector-in-planes
0
answers
13
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 $y\:=\:7$
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Digital Circuits
Apr 11, 2021
166
views
gateec-2021
digital-circuits
number-system
number-representation
0
answers
14
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 $2^{8}$ $2^{32}$ $2^{15}$ $2^{19}$
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Digital Circuits
Apr 11, 2021
87
views
gateec-2021
digital-circuits
combinational-circuits
decoders
0
answers
15
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 $\frac{G_{1}+G_{2}+G_{1}G_{2}H}{1+G_{1}H}$ $\frac{G_{1}+G_{2}}{1+G_{1}H+G_{2}H}$ $\frac{G_{1}+G_{2}}{1+G_{1}H}$ $\frac{G_{1}+G_{2}+G_{1}G_{2}H}{1+G_{1}H+G_{2}H}$
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Control Systems
Apr 11, 2021
56
views
gateec-2021
control-systems
0
answers
16
GATE ECE 2021 | Question: 17
Consider the vector field $F\:=\:a_{x}\left ( 4y-c_{1}z \right )+a_y\left ( 4x + 2z\right )+a_{z}\left ( 2y +z\right )$ 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 _________________
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Vector Analysis
Apr 11, 2021
97
views
gateec-2021
numerical-answers
vector-analysis
vector-in-planes
0
answers
17
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 $\frac{2}{5}$ $\frac{1}{3}$ $\frac{1}{2}$ $\frac{2}{3}$
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Probability and Statistics
Apr 11, 2021
138
views
gateec-2021
probability-and-statistics
probability
conditional-probability
0
answers
18
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 $3\:ns$ $5\:ns$ $6\:ns$ $7\:ns$
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Digital Circuits
Apr 11, 2021
179
views
gateec-2021
digital-circuits
combinational-circuits
multiplexers
0
answers
19
GATE ECE 2021 | Question: 36
A real $2\times2$ non-singular 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 ________________
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Linear Algebra
Apr 11, 2021
64
views
gateec-2021
numerical-answers
linear-algebra
eigen-values
0
answers
20
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 ________________
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Vector Analysis
Apr 11, 2021
39
views
gateec-2021
numerical-answers
vector-analysis
0
answers
21
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 flip-flops is assumed to be zero. The clock ($\text{Clk}$ ... of triggering clock edges after which the flip-flop outputs $Q_{2}Q_{1}Q_{0}$ becomes $1\; 0\; 0$ (in integer) is
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Digital Circuits
Apr 11, 2021
78
views
gateec-2021
numerical-answers
digital-circuits
sequential-circuit
counters
0
answers
22
GATE ECE 2021 | Question: 2
Consider the differential equation given below. $\frac{dy}{dx}+\frac{x}{1-x^{2}}y=x\sqrt{y}$ The integrating factor of the differential equation is $\left ( 1-x^{2} \right )^{-3/4}$ $\left ( 1-x^{2} \right )^{-1/4}$ $\left ( 1-x^{2} \right )^{-3/2}$ $\left ( 1-x^{2} \right )^{-1/2}$
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Differential Equations
Apr 11, 2021
99
views
gateec-2021
differential-equations
first-order-differential-equation
0
answers
23
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 __________
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Vector Analysis
Apr 11, 2021
103
views
gateec-2021
numerical-answers
vector-analysis
vector-in-planes
1
answer
24
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 $2:3$ $3:4$ $4:5$ $5:6$
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Numerical Ability
Apr 11, 2021
264
views
gateec-2021
numerical-ability
geometry
triangles
area
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 ____________ $\frac{\pi }{3}$ $\frac{2\pi }{3}$ $\frac{3\pi }{2}$ $3\pi$
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Numerical Ability
Apr 11, 2021
1.1k
views
gateec-2021
numerical-ability
mensuration
cones
2
answers
26
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 six-figure fine to a French-speaking 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.
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Verbal Ability
Apr 11, 2021
306
views
gate2020-ec
verbal-ability
verbal-reasoning
passage-reading
2
answers
27
GATE ECE 2020 | GA Question: 2
He was not only accused of theft _____ of conspiracy. rather but also but even rather than
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in
Verbal Ability
Apr 11, 2021
630
views
gate2020-ec
verbal-ability
english-grammar
2
answers
28
GATE ECE 2020 | GA Question: 6
The global financial crisis in $2008$ is considered to be the most serious world-wide financial crisis, which started with the sub-prime lending crisis in $\text{USA}$ in $2007$. The sub-prime lending crisis led to the ... $\rightarrow$ East Asian crisis$\rightarrow$ banking crisis$\rightarrow$ subprime lending crisis.
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Verbal Ability
Apr 11, 2021
293
views
gate2020-ec
verbal-ability
verbal-reasoning
passage-reading
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 $x > 1$? $e^{x}$ $\sqrt{x}$ $1/x$ $e^{-x}$
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Numerical Ability
Apr 10, 2021
659
views
gate2020-ec
numerical-ability
functions
1
answer
30
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 _______. $\pi a^{2}-a^{2}$ $\pi a^{2}-\sqrt{2}a^{2}$ $\pi a^{2}-2a^{2}$ $\pi a^{2}-3a^{2}$
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in
Numerical Ability
Apr 8, 2021
1.6k
views
gate2020-ec
numerical-ability
geometry
circle
area
0
answers
31
GATE ECE 2016 Set 2 | GA Question: 8
Two and a quarter hours back, when seen in a mirror, the reflection of a wall clock without umber markings seemed to show $1.30$. What is the actual current time shown by the clock? $8.15$ $11.15$ $12.15$ $12.45$
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Numerical Ability
Mar 17, 2021
38
views
gate2016-ec-2
numerical-ability
clock-time
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 ________. $0^{\circ}$ $7.5^{\circ}$ $15^{\circ}$ $22.5^{\circ}$
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Numerical Ability
Mar 17, 2021
256
views
gate2020-ec
numerical-ability
clock-time
1
answer
33
GATE ECE 2017 Set 2 | GA Question: 7
Each of $P, Q, R, S, W, X, Y$and $Z$ has been married at most once . $X$ and $Y$ are married and have two children $P$ and $Q$. $Z$ is the grandfather of the daughter $S$ of $P$. Further , $Z$ and $W$ are married and are parents of $R$. Which one ... -in-law of $R$ $P$ and $R$ are not married to each other $P$ is a son of $X$ and $Y$ $Q$ cannot be married to $R$
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Analytical Aptitude
Mar 17, 2021
95
views
gate2017-ec-2
analytical-aptitude
family-relationships
1
answer
34
GATE ECE 2016 Set 3 | GA Question: 3
$M$ has a son $Q$ and a daughter $R.$ He has no other children. $E$ is the mother of $P$ and daughter-in-law of $M.$ How is $P$ related to $M?$ $P$ is the son-in-law of $M$ $P$ is the grandchild of $M$ $P$ is the daughter-in-law of $M$ $P$ is the grandfather of $M$
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Analytical Aptitude
Mar 17, 2021
66
views
gate2016-ec-3
analytical-aptitude
family-relationships
0
answers
35
GATE ECE 2014 Set 3 | GA Question: 5
In which of the following options will the expression $P < M$ be definitely true? $M < R > P > S$ $M > S < P < F$ $Q < M < F = P$ $P = A < R < M$
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Analytical Aptitude
Mar 4, 2021
38
views
gate2014-ec-3
analytical-aptitude
logical-reasoning
inequality
0
answers
36
GATE ECE 2014 Set 1 | GA Question: 7
For submitting tax returns, all resident males with annual income below $Rs$ $10$ lakh should fill up Form $P$ and all resident females with income below $Rs$ $8$ lakh should fill up Form $Q.$ All people with incomes above $Rs$ $10$ lakh ... $Rs$ $16$ lakh a non-resident female with annual income $Rs$ $16$ lakh
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Analytical Aptitude
Mar 4, 2021
48
views
gate2014-ec-1
analytical-aptitude
logical-reasoning
passage-reading
0
answers
37
GATE ECE 2016 Set 3 | GA Question: 7
The overwhelming number of people infected with rabies in India has been flagged by the World Health Organization as a source of concern. It is estimated that inoculating $70\%$ of pets and stray dogs against rabies can lead to a significant ... be eradicated in India by vaccinating $70\%$ of stray dogs. Stray dogs are the main source of rabies worldwide.
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Analytical Aptitude
Mar 4, 2021
49
views
gate2016-ec-3
analytical-aptitude
logical-reasoning
passage-reading
0
answers
38
GATE ECE 2016 Set 1 | Question: 3
Given the following statements about a function $f: \Bbb R \rightarrow \Bbb R$, select the right option: P: If $f(x)$ is continuous at $x = x_0$ then it is also differentiable at $x = x_0$. Q: If $f(x)$ is continuous at $x = x_0$ then it may not be ... is false P is false, Q is true, R is true P is false, Q is true, R is false P is true, Q is false, R is true
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Calculus
Mar 3, 2021
35
views
gate2016-ec-1
calculus
continuity-and-differentiability
0
answers
39
GATE ECE 2020 | Question: 54
$X$ is a random variable with uniform probability density function in the interval $[-2,\:10]$. For $Y=2X-6$, the conditional probability $P\left ( Y\leq 7\mid X\geq 5 \right )$ (rounded off to three decimal places) is __________.
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Probability and Statistics
Mar 3, 2021
60
views
gate2020-ec
numerical-answers
probability-and-statistics
probability
probability-density-function
uniform-distribution
0
answers
40
GATE ECE 2020 | Question: 25
The two sides of a fair coin are labelled as $0$ to $1$. The coin is tossed two times independently. Let $M$ and $N$ denote the labels corresponding to the outcomes of those tosses. For a random variable $X$, defined as $X = \text{min}(M, N)$, the expected value $E(X)$ (rounded off to two decimal places) is ___________.
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Probability and Statistics
Mar 3, 2021
124
views
gate2020-ec
numerical-answers
probability-and-statistics
probability
independent-events
random-variable
expectation
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