Recent questions and answers in Quantitative Aptitude

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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

admin asked in Quantitative Aptitude Dec 15, 2022

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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

admin asked in Quantitative Aptitude Dec 1, 2022

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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

admin asked in Quantitative Aptitude Dec 1, 2022

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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

admin asked in Quantitative Aptitude Nov 30, 2022

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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: $2$ $4$ $1$ $5$ $3$

admin asked in Quantitative Aptitude Nov 30, 2022

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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? $4$ $1$ $2$ $\pi$ $0$

admin asked in Quantitative Aptitude Nov 30, 2022

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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 $n \geq 1$

admin asked in Quantitative Aptitude Nov 29, 2022

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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: $2$ $17$ $13$ $3$

admin asked in Quantitative Aptitude Sep 15, 2022

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9

GATE ECE 2010 | Question: 62
If $137+276=435$ how much is $731+672?$ $534$ $1403$ $1623$ $1513$

admin asked in Quantitative Aptitude Sep 15, 2022

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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 asked in Quantitative Aptitude Sep 15, 2022

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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? $50$ $51$ $52$ $54$

admin asked in Quantitative Aptitude Sep 15, 2022

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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? $100$ $110$ $90$ $95$

admin asked in Quantitative Aptitude Sep 3, 2022

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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 $\mathrm{P}$ $\mathrm{Q}$ $\mathrm{R}$ $\mathrm{S}$

admin asked in Quantitative Aptitude Sep 3, 2022

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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? $38$ $31$ $48$ $41$

admin asked in Quantitative Aptitude Sep 3, 2022

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15

GATE ECE 2011 | Question: 65
The sum of $n$ terms of the series $4+44+444+\ldots .$ is $(4 / 81)\left[10^{n+1}-9 n-1\right]$ $(4 / 81)\left[10^{n-1}-9 n-1\right]$ $(4 / 81)\left[10^{n+1}-9 n-10\right]$ $(4 / 81)\left[10^{n}-9 n-10\right]$

admin asked in Quantitative Aptitude Sep 3, 2022

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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 answered in Quantitative Aptitude Mar 18, 2022

by two-ticks

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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 answered in Quantitative Aptitude Feb 21, 2022

by Lakshman Patel RJIT

11.2k points

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18

GATE ECE 2022 | GA Question: 8
Four points $\text{P(0, 1), Q(0, – 3), R( – 2, – 1),}$ and $\text{S(2, – 1)}$ 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 answered in Quantitative Aptitude Feb 21, 2022

by Lakshman Patel RJIT

11.2k points

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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 ₹ $ 1000$ more than $\text{S},$ what is the share of $\text{Q (in ₹)}?$ $500$ $1000$ $1500$ $2000$

Lakshman Patel RJIT answered in Quantitative Aptitude Feb 21, 2022

by Lakshman Patel RJIT

11.2k points

223 views

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20

GATE ECE 2022 | GA Question: 7
Consider the following inequalities. $2x – 1 > 7$ $2x – 9 < 1$ Which one of the following expressions below satisfies the above two inequalities? $x \leq – 4$ $ – 4 < x \leq 4$ $4 < x < 5$ $x \geq 5$

Lakshman Patel RJIT answered in Quantitative Aptitude Feb 19, 2022

by Lakshman Patel RJIT

11.2k points

183 views

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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 answered in Quantitative Aptitude Apr 10, 2021

by Lakshman Patel RJIT

11.2k points

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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 answered in Quantitative Aptitude Mar 31, 2021

by Lakshman Patel RJIT

11.2k points

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23

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 $2:3$ $3:4$ $4:5$ $5:6$

Lakshman Patel RJIT answered in Quantitative Aptitude Mar 22, 2021

by Lakshman Patel RJIT

11.2k points

412 views

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 answered in Quantitative Aptitude Mar 22, 2021

by Lakshman Patel RJIT

11.2k points

479 views

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 answered in Quantitative Aptitude Mar 22, 2021

by Lakshman Patel RJIT

11.2k points

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2 votes

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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 answered in Quantitative Aptitude Mar 22, 2021

by Lakshman Patel RJIT

11.2k points

307 views

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 answered in Quantitative Aptitude Mar 22, 2021

by Lakshman Patel RJIT

11.2k points

331 views

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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 answered in Quantitative Aptitude Aug 12, 2020

by haralk10

960 points

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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 $\beta =b/a$ $\beta^{2} =ac$ $\beta^{3} =bc/\left ( 2a^{2} \right )$ $\beta^{2} \neq 4ac$

haralk10 answered in Quantitative Aptitude Aug 11, 2020

by haralk10

960 points

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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 _______. $\pi a^{2}-a^{2}$ $\pi a^{2}-\sqrt{2}a^{2}$ $\pi a^{2}-2a^{2}$ $\pi a^{2}-3a^{2}$

haralk10 answered in Quantitative Aptitude Aug 11, 2020

by haralk10

960 points

2.1k views

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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 answered in Quantitative Aptitude May 10, 2020

by Madhav

1.4k points

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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 answered in Quantitative Aptitude Oct 12, 2019

by suraj20041995

190 points

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2 answers

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 ______. $2$ $6$ $12$ $120$

maha_m answered in Quantitative Aptitude Oct 12, 2019

by maha_m

140 points

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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. $2/3$ $3/4$ $4/3$ $7/3$

Shinei Nouzen answered in Quantitative Aptitude Jul 23, 2019

by Shinei Nouzen

180 points

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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 answered in Quantitative Aptitude Jul 23, 2019

by Shinei Nouzen

180 points

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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 ______. $30.43$ $33.43$ $34.43$ $35.43$

Arjun asked in Quantitative Aptitude Feb 12, 2019

by Arjun

6.0k points

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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)? $0$ $3$ $4$ $5$

Milicevic3306 asked in Quantitative Aptitude Mar 28, 2018

by Milicevic3306

15.8k points

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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. $14.95$ $15.25$ $15.70$ $20.35$

Milicevic3306 asked in Quantitative Aptitude Mar 28, 2018

by Milicevic3306

15.8k points

67 views

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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? $-0.030$ $-0.014$ $0.014$ $0.030$

Milicevic3306 asked in Quantitative Aptitude Mar 28, 2018

by Milicevic3306

15.8k points

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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? $1:1$ $1:2$ $1:4$ $2:1$

Milicevic3306 asked in Quantitative Aptitude Mar 28, 2018

by Milicevic3306

15.8k points

43 views