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Recent questions and answers in Quantitative Aptitude
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1
TIFR ECE 2015 | Question: 11
For $x>0$, for which range of values of $\alpha$ is the following inequality true? \[ x \log _{e}(x) \geq x-\alpha \] $\alpha \geq 1 / 2$ $\alpha \geq 0$ $\alpha \leq 2$ $\alpha \geq 1$ None of the above
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Quantitative Aptitude
Dec 15, 2022
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tifr2015
quantitative-aptitude
logarithms
inequality
1
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0
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2
TIFR ECE 2010 | Question: 18
Under what conditions is the following inequality true for $a, b>0$ $ \log _e(a+b) \geq \lambda \log _e(a / \lambda)+(1-\lambda) \log _e(b /(1-\lambda)) $ $\lambda=0.5$ $0<a / \lambda \leq 1, b /(1-\lambda)>0$ $a / \lambda>0,0<b /(1-\lambda) \leq 1$ All of the above None of the above
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tifr2010
quantitative-aptitude
inequality
1
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0
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3
TIFR ECE 2010 | Question: 19
Let us define an interval $A(n)$ as a function of $n$ as $A(n)=(-1 / n, 1 / n)$. Then the set of points that lie in the intersection of $A_{n}{ }^{\prime} s, n=1, \ldots, \infty$ is an interval is a single point is an empty set cannot be determined has two disjoint intervals
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Dec 1, 2022
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tifr2010
quantitative-aptitude
sets
1
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0
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4
TIFR ECE 2021 | Question: 2
Given a fixed perimeter of $1,$ among the following shapes, which one has the largest area? Square A regular pentagon A regular hexagon A regular septagon A regular octagon
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Quantitative Aptitude
Nov 30, 2022
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43.6k
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tifrece2021
quantitative-aptitude
geometry
area
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5
TIFR ECE 2021 | Question: 8
The maximum area of a parallelogram inscribed in the ellipse (i.e. all the vertices of the parallelogram are on the ellipse) $x^{2}+4 y^{2}=1$ is: $2$ $4$ $1$ $5$ $3$
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Quantitative Aptitude
Nov 30, 2022
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43.6k
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13
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tifrece2021
quantitative-aptitude
geometry
area
1
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6
TIFR ECE 2021 | Question: 12
An ant does a random walk in a two dimensional plane starting at the origin at time $0.$ At every integer time greater than $0,$ it moves one centimeter away from its earlier position in a random direction independent of its past. After $4$ steps, what is the expected square of the distance (measured in centimeters) from its starting point? $4$ $1$ $2$ $\pi$ $0$
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Nov 30, 2022
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43.6k
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12
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tifrece2021
quantitative-aptitude
geometry
1
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7
TIFR ECE 2017 | Question: 5
Consider the inequality \[ n-\frac{1}{n} \geq \sqrt{n^{2}-1}, \] where $n$ is an integer $\geq 1$. Which of the following statements is $\text{TRUE?}$ This inequality holds for all integers $n \geq 1$ ... not hold for any integer $n \geq 1$ $n-\frac{1}{n}=\sqrt{n^{2}-1}$ for infinitely many integers $n \geq 1$
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Nov 29, 2022
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43.6k
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13
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tifrece2017
quantitative-aptitude
inequality
1
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0
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8
GATE ECE 2010 | Question: 60
$25$ persons are in a room. $15$ of them play hockey, $17$ of them play football and $10$ of them play both hockey and football. Then the number of persons playing neither hockey nor football is: $2$ $17$ $13$ $3$
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Sep 15, 2022
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43.6k
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7
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gate2010-ec
quantitative-aptitude
venn-diagrams
1
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0
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9
GATE ECE 2010 | Question: 62
If $137+276=435$ how much is $731+672?$ $534$ $1403$ $1623$ $1513$
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Sep 15, 2022
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43.6k
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10
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gate2010-ec
quantitative-aptitude
number-system
1
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0
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10
GATE ECE 2010 | Question: 63
$5$ skilled workers can build a wall in $20$ days: $8$ semi-skilled workers can build a wall in $25$ days: $10$ unskilled workers can build a wall in $30$ days. If a team has $2$ skilled, $6$ semi-skilled and $5$ unskilled workers, how long will it take to build the wall? $20$ days $18$ days $16$ days $15$ days
admin
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Quantitative Aptitude
Sep 15, 2022
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admin
43.6k
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11
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gate2010-ec
quantitative-aptitude
work-time
1
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0
answers
11
GATE ECE 2010 | Question: 64
Given digits $2,2,3,3,3,4,4,4,4$ how many distinct $4$ digit numbers greater than $3000$ can be formed? $50$ $51$ $52$ $54$
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Quantitative Aptitude
Sep 15, 2022
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admin
43.6k
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9
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gate2010-ec
quantitative-aptitude
counting
1
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0
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12
GATE ECE 2011 | Question: 57
There are two candidates $\mathrm{P}$ and $\mathrm{Q}$ in an election. During the campaign, $40 \%$ of the voters promised to vote for $\mathrm{P}$, and rest for $\text{Q}$. However, on the day of election $15 \%$ of the voters went back on their promise ... $\mathrm{P}$ lost by $2$ votes, then what was the total number of voters? $100$ $110$ $90$ $95$
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Sep 3, 2022
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43.6k
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10
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gate2011-ec
quantitative-aptitude
percentage
1
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0
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13
GATE ECE 2011 | Question: 62
The fuel consumed by a motorcycle during a journey while traveling at various speeds is indicated in the graph below. The distances covered during four laps of the journey are listed in the table below ... the fuel consumed per kilometre was least during the lap $\mathrm{P}$ $\mathrm{Q}$ $\mathrm{R}$ $\mathrm{S}$
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Sep 3, 2022
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admin
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32
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gate2011-ec
quantitative-aptitude
speed-time-distance
1
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0
answers
14
GATE ECE 2011 | Question: 63
Three friends, $\mathrm{R}, \mathrm{S}$ and $\mathrm{T}$ shared toffee from a bowl. $\mathrm{R}$ took $1 / 3^{\text {rd }}$ of the toffees, but returned four to the bowl. $\text{S}$ took $1 / 4^{\text {th }}$ of what was left but ... two back into the bowl. If the bowl had $17$ toffees left, how many toffees were originally there in the bowl? $38$ $31$ $48$ $41$
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Quantitative Aptitude
Sep 3, 2022
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admin
43.6k
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25
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gate2011-ec
quantitative-aptitude
number-system
1
vote
0
answers
15
GATE ECE 2011 | Question: 65
The sum of $n$ terms of the series $4+44+444+\ldots .$ is $(4 / 81)\left[10^{n+1}-9 n-1\right]$ $(4 / 81)\left[10^{n-1}-9 n-1\right]$ $(4 / 81)\left[10^{n+1}-9 n-10\right]$ $(4 / 81)\left[10^{n}-9 n-10\right]$
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Quantitative Aptitude
Sep 3, 2022
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65
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gate2011-ec
quantitative-aptitude
sequence-series
0
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1
answer
16
GATE ECE 2016 Set 3 | GA Question: 5
It takes $10$s and $15$s, respectively, for two trains traveling at a different constant speeds to completely pass a telegraph post. The length of the first train is $120$ m and that of the second train is $150$ m. The magnitude of the difference in the speeds of the two trains (in m/s) is _________ $2.0$ $10.0$ $12.0$ $22.0$
two-ticks
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Quantitative Aptitude
Mar 18, 2022
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two-ticks
670
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gate2016-ec-3
numerical-ability
speed-time-distance
1
vote
1
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17
GATE ECE 2022 | GA Question: 3
A trapezium has vertices marked as $\text{P, Q, R}$ and $\text{S}$ (in that order anticlockwise). The side $\text{PQ}$ is parallel to side $\text{SR}.$ Further, it is given that, $\text{PQ = 11 cm, QR = 4 cm, RS = 6 cm}$ and $\text{SP = 3 cm.}$ What is the shortest distance between $\text{PQ}$ and $\text{SR (in cm)}?$ $1.80$ $2.40$ $4.20$ $5.76$
Lakshman Patel RJIT
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Quantitative Aptitude
Feb 21, 2022
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Lakshman Patel RJIT
11.2k
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gateece-2022
quantitative-aptitude
geometry
1
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1
answer
18
GATE ECE 2022 | GA Question: 8
Four points $\text{P(0, 1), Q(0, â€“ 3), R( â€“ 2, â€“ 1),}$ and $\text{S(2, â€“ 1)}$ represent the vertices of a quadrilateral. What is the area enclosed by the quadrilateral? $4$ $4 \sqrt{2}$ $8$ $8 \sqrt{2}$
Lakshman Patel RJIT
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in
Quantitative Aptitude
Feb 21, 2022
by
Lakshman Patel RJIT
11.2k
points
211
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gateece-2022
quantitative-aptitude
cartesian-coordinates
area
1
vote
1
answer
19
GATE ECE 2022 | GA Question: 2
A sum of money is to be distributed among $\text{P, Q, R,}$ and $\text{S}$ in the proportion $5:2:4:3,$ respectively. If $\text{R}$ gets â‚¹ $ 1000$ more than $\text{S},$ what is the share of $\text{Q (in â‚¹)}?$ $500$ $1000$ $1500$ $2000$
Lakshman Patel RJIT
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in
Quantitative Aptitude
Feb 21, 2022
by
Lakshman Patel RJIT
11.2k
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223
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gateece-2022
quantitative-aptitude
ratio-proportions
1
vote
1
answer
20
GATE ECE 2022 | GA Question: 7
Consider the following inequalities. $2x â€“ 1 > 7$ $2x â€“ 9 < 1$ Which one of the following expressions below satisfies the above two inequalities? $x \leq â€“ 4$ $ â€“ 4 < x \leq 4$ $4 < x < 5$ $x \geq 5$
Lakshman Patel RJIT
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in
Quantitative Aptitude
Feb 19, 2022
by
Lakshman Patel RJIT
11.2k
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183
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gateece-2022
quantitative-aptitude
inequality
1
vote
2
answers
21
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 $x > 1$? $e^{x}$ $\sqrt{x}$ $1/x$ $e^{-x}$
Lakshman Patel RJIT
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in
Quantitative Aptitude
Apr 10, 2021
by
Lakshman Patel RJIT
11.2k
points
979
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gate2020-ec
numerical-ability
functions
1
vote
2
answers
22
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 _______. $8 : 23$ $23 : 8$ $23 : 31$ $31 : 23$
Lakshman Patel RJIT
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Quantitative Aptitude
Mar 31, 2021
by
Lakshman Patel RJIT
11.2k
points
1.4k
views
gate2020-ec
numerical-ability
data-interpretation
bar-graph
1
vote
1
answer
23
GATE ECE 2021 | GA Question: 10
â€‹â€‹ 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 $2:3$ $3:4$ $4:5$ $5:6$
Lakshman Patel RJIT
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Quantitative Aptitude
Mar 22, 2021
by
Lakshman Patel RJIT
11.2k
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412
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gateec-2021
numerical-ability
geometry
triangles
area
1
vote
1
answer
24
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 $4$ $5$ $6$ $7$
Lakshman Patel RJIT
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Quantitative Aptitude
Mar 22, 2021
by
Lakshman Patel RJIT
11.2k
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479
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gateec-2021
numerical-ability
data-interpretation
bar-graph
2
votes
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 ____________ $\frac{\pi }{3}$ $\frac{2\pi }{3}$ $\frac{3\pi }{2}$ $3\pi$
Lakshman Patel RJIT
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Quantitative Aptitude
Mar 22, 2021
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Lakshman Patel RJIT
11.2k
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2.0k
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gateec-2021
numerical-ability
mensuration
cones
2
votes
1
answer
26
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? $9,92,500$ $9,95,006$ $10,00,000$ $12,51,506$
Lakshman Patel RJIT
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Quantitative Aptitude
Mar 22, 2021
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Lakshman Patel RJIT
11.2k
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307
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gateec-2021
numerical-ability
simple-compound-interest
1
vote
2
answers
27
GATE ECE 2021 | GA Question: 2
$p$ and $q$ are positive integers and $\dfrac{p}{q}+\dfrac{q}{p}=3,$ then, $\dfrac{p^{2}}{q^{2}}+\dfrac{q^{2}}{p^{2}}=$ $3$ $7$ $9$ $11$
Lakshman Patel RJIT
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Quantitative Aptitude
Mar 22, 2021
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Lakshman Patel RJIT
11.2k
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331
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gateec-2021
numerical-ability
algebra
0
votes
1
answer
28
GATE ECE 2019 | GA Question: 9
Two design consultants, $P$ and $Q,$ started working from $8$ AM for a client. The client budgeted a total of USD $3000$ for the consultants. $P$ stopped working when the hour hand moved by $210$ degrees on the clock. $Q$ stopped working when ... paying the consultants, the client shall have USD _______ remaining in the budget. $000.00$ $166.67$ $300.00$ $433.33$
haralk10
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Quantitative Aptitude
Aug 12, 2020
by
haralk10
960
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156
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gate2019-ec
numerical-ability
work-time
1
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1
answer
29
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 $\beta =b/a$ $\beta^{2} =ac$ $\beta^{3} =bc/\left ( 2a^{2} \right )$ $\beta^{2} \neq 4ac$
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Quantitative Aptitude
Aug 11, 2020
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haralk10
960
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492
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gate2020-ec
numerical-ability
quadratic-equations
1
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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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Quantitative Aptitude
Aug 11, 2020
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haralk10
960
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gate2020-ec
numerical-ability
geometry
circle
area
1
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1
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31
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 ________. $0^{\circ}$ $7.5^{\circ}$ $15^{\circ}$ $22.5^{\circ}$
Madhav
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Quantitative Aptitude
May 10, 2020
by
Madhav
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431
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gate2020-ec
numerical-ability
clock-time
0
votes
1
answer
32
GATE ECE 2017 Set 2 | GA Question: 9
The number of $3$-digit numbers such that the digit $1$ is never to the immediate right of $2$ is $781$ $791$ $881$ $891$
suraj20041995
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Quantitative Aptitude
Oct 12, 2019
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suraj20041995
190
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206
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gate2017-ec-2
numerical-ability
counting
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2
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33
GATE ECE 2019 | GA Question: 4
Five different books $(P, Q, R, S, T)$ are to be arranged on a shelf. The books $R$ and $S$ are to be arranged first and second, respectively from the right side of the shelf. The number of different orders in which $P, Q$ and $T$ may be arranged is ______. $2$ $6$ $12$ $120$
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Quantitative Aptitude
Oct 12, 2019
by
maha_m
140
points
163
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gate2019-ec
numerical-ability
permutations-and-combinations
0
votes
1
answer
34
GATE ECE 2019 | GA Question: 3
It would take one machine $4$ hours to complete a production order and another machine $2$ hours to complete the same order. If both machines work simultaneously at their respective constant rates, the time taken to complete the same order is ________ hours. $2/3$ $3/4$ $4/3$ $7/3$
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Quantitative Aptitude
Jul 23, 2019
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Shinei Nouzen
180
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133
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gate2019-ec
numerical-ability
work-time
0
votes
1
answer
35
GATE ECE 2017 Set 1 | GA Question: 10
A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at $25$ m intervals in this plot. The path from $P$ to $Q$ is best described by Up-Down-Up-Down Down-Up-Down-Up Down-Up-Down Up-Down-Up
Shinei Nouzen
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Quantitative Aptitude
Jul 23, 2019
by
Shinei Nouzen
180
points
140
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gate2017-ec-1
numerical-ability
data-interpretation
contour-plots
0
votes
0
answers
36
GATE ECE 2019 | GA Question: 7
The bar graph in panel (a) shows the proportion of male and female illiterates in $2001$ and $2011.$ The proportions of males and females in $2001$ and $2011$ are given in Panel (b) and (c), respectively. The total population did not change during this period. ... in the total number of literates from $2001$ to $2011$ is ______. $30.43$ $33.43$ $34.43$ $35.43$
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Quantitative Aptitude
Feb 12, 2019
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Arjun
6.0k
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219
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gate2019-ec
numerical-ability
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bar-graph
0
votes
0
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37
GATE ECE 2016 Set 3 | GA Question: 6
The velocity $V$ of a vehicle along a straight line is measured in m/s and plotted as shown with respect to time in seconds. At the end of the $7$ seconds, how much will the odometer reading increase by (in m)? $0$ $3$ $4$ $5$
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64
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gate2016-ec-3
numerical-ability
speed-time-distance
0
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0
answers
38
GATE ECE 2016 Set 3 | GA Question: 9
Find the area bounded by the lines $3x+2y=14$, $2x-3y=5$ in the first quadrant. $14.95$ $15.25$ $15.70$ $20.35$
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gate2016-ec-3
numerical-ability
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0
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39
GATE ECE 2016 Set 3 | GA Question: 10
A straight line is fit to a data set $(\text{ln }x,y).$ This line intercepts the abscissa at $\text{ln } x =0.1$ and has a slope of $-0.02$. What is the value of $y$ at $x=5$ from the fit? $-0.030$ $-0.014$ $0.014$ $0.030$
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gate2016-ec-3
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40
GATE ECE 2016 Set 2 | GA Question: 5
$S$, $M$, $E$ and $F$ are working in the shifts in a team to finish a project. $M$ works with twice the efficiency of others but for half as many days as $E$ worked. $S$ amd $M$ have $6$ hour shifts in a day, whereas $E$ and $F$ have $12$ hours shifts. What is the ratio of contribution of $M$ to contribute of $E$ in the project? $1:1$ $1:2$ $1:4$ $2:1$
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