# Recent questions and answers in Numerical Ability

1
The ratio of boys to girls in a class is $7$ to $3$. Among the options below, an acceptable value for the total number of students in the class is $21$ $37$ $50$ $73$
2
We have $2$ rectangular sheets of paper, $M$ and $N$, of dimensions $6$ cm $\times$ $1$ cm each. Sheet $M$ is rolled to form an open cylinder by bringing the short edges of the sheet together. Sheet $N$ is cut into equal square patches and assembled to form the largest possible closed cube. ... to that of the cube is _____________ $\frac{\pi}{2}\\$ $\frac{3}{\pi} \\$ $\frac{9}{\pi} \\$ $3 \pi$
3
$\begin{array}{|c|c|c|c|} \hline \textbf{Items} & \textbf{Cost} & \textbf{Profit} \% & \textbf{Marked Price} \\ & (₹) && (₹) \\ \hline P & 5,400 & \dots & 5,860 \\ \hline Q & \dots & 25 & 10,000 \\ \hline \end{array}$ ... $Q$, as a percentage of its marked price, is ___________ $25$ $12.5$ $10$ $5$
4
There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag. The probability that at least two chocolates are identical is _________ $0.3024$ $0.4235$ $0.6976$ $0.8125$
5
The difference between the sum of the first $2n$ natural numbers and the sum of the first $n$ odd natural numbers is ______ $n^2-n$ $n^2+n$ $2n^2-n$ $2n^2+n$
6
The distance between Delhi and Agra is $233$ km. A car $P$ started travelling from Delhi to Agra and another car $Q$ started from Agra to Delhi along the same road $1$ hour after the car $P$ started. The two cars crossed each other $75$ minutes after the car $Q$ started. Both ... car $Q$. How many kilometers the car $Q$ had travelled when the cars crossed each other? $66.6$ $75.2$ $88.2$ $116.5$
7
For a matrix $M=[m_{ij}]; \: i,j=1,2,3,4$, the diagonal elements are all zero and $m_{ij}=-m_{ji}$. The minimum number of elements required to fully specify the matrix is ________ $0$ $6$ $12$ $16$
8
The profit shares of two companies $P$ and $Q$ are shown in the figure. If the two companies have invested a fixed and equal amount every year, then the ratio of the total revenue of company $P$ to the revenue of company $Q$, during $2013-2018$ is ________. $15 : 17$ $16 : 17$ $17 : 15$ $17 : 16$
9
The radius as well as the height of a circular cone increases by $10\%.$ The percentage increase in its volume is ________. $17.1$ $21.0$ $33.1$ $72.8$
10
In a country of $1400$ million population, $70\%$ own mobile phones. Among the mobile phone owners, only $294$ million access the Internet. Among these Internet users, only half buy goods from e-commerce portals. What is the percentage of these buyers in the country? $10.50$ $14.70$ $15.00$ $50.00$
11
Two trains started at $7$AM from the same point. The first train travelled north at a speed of $80$km/h and the second train travelled south at a speed of $100$ km/h. The time at which they were $540$ km apart is ________ AM. $9$ $10$ $11$ $11.30$
12
A window is made up of a square portion and an equilateral triangle portion above it. The base of the triangular portion coincides with the upper side of the square. If the perimeter of the window is $6$ m, the area of the Window in $m^2$ is $1.43$ $2.06$ $2.68$ $2.88$
13
Students taking an exam are divided into two groups: $P$ and $Q$ such that each group has the same number of students. The performance of each of the students in a test was evaluated out of $200$ marks. It was observed that the mean of group $P$ was $105$, while that of ... of group $Q$ scored marks in a narrower range than students in group $P$. The median of the marks of group $P$ is $100$.
14
The binary operation $\square$ is defined as $a \square b = ab+(a+b)$, where $a$ and $b$ are any two real numbers. The value of the identity element of this operation, defined as the number $x$ such that $a \square x = a$, for any $a$, is $0$ $1$ $2$ $10$
15
Which of the following curves represents the function $y = \ln (\mid e^{ [ \mid \sin ( \mid x \mid ) \mid ]} \mid )$ for $\mid x \mid < 2 \pi$?. Here, $x$ represents the abscissa and $y$ represents the ordinate.
16
In the summer, water consumption is known to decrease overall by $25\%$. A Water Board official states that in the summer household consumption decreases by $20\%$. While other consumption increases by $70\%$. Which of the following statements is correct? The ratio of ... other consumption is $1/17$ The ratio of household to other consumption is $17/8$ There are errors in the official s statement
17
$40\%$ of deaths on city roads may be attributed to drunken driving. The number of degrees needed to represent this as a slice of a pie chart is $120$ $144$ $160$ $212$
18
Trunks ($10$ m long) and cars ($5$ m long) go on a single lane bridge. There must be a gap of at least $20$ m after each trunk and a gap of at least $15$ m after each car. Trunks and cars travel at a speed of $36$ km/h. If cars and trunks go alternately, what is the maximum number of vehicles that can use the bridge on one hour? $1440$ $1200$ $720$ $600$
19
There are $3$ Indians and $3$ Chinese in a group of $6$ people. How many subgroups of this group can we choose so that every subgroup has at least one Indian? $56$ $52$ $48$ $44$
20
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 $25$ n 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
21
Operators $\square$, $\lozenge$ and $\rightarrow$ are defined by: $a \: \square \: b = \dfrac{a-b}{a+b}$; $a \: \lozenge \: b = \dfrac{a+b}{a-b}$; $a \rightarrow b = ab$. Find the value of $(66 \: \square \: 6) \rightarrow (66 \: \lozenge \: 6)$. $-2$ $-1$ $1$ $2$
22
If $\log_x (5/7) = -1/3$, then the value of $x$ is $343/125$ $125/343$ $-25/49$ $-49/25$
23
A cube of side $3$ units is formed using a set of smaller cubes of side $1$ unit. Find the proportion of the number of faces of the smaller cubes visible to those which are NOT visible. $1:4$ $1:3$ $1:2$ $2:3$
24
In any given year, the probability of an earthquake greater than Magnitude $6$ occurring in the Garhwal Himalayas is $0.04$. The average time between successive occurrences of such earthquakes is_____ years.
25
The population of a new city is $5$ million and is growing at $20\%$ annually. How many years would it take to double at this growth rate? $3-4$ years $4-5$ years $5-6$ years $6-7$ years
26
Q8The total exports and revenues from the exports of a country are given in the two pie charts below.The pie chart for exports shows the quantity of each item as a percentage of the total quantity ofexports. The pie chart for the revenues shows the percentage of the total ... of Item 1per kilogram to the revenue generated through export of Item 4 per kilogram?Exports Revenues 1:2 2:1 1:4 4:1
27
$10\%$ of the population in a town is HIV+. A new diagnostic kit for HIV detection is available; this kit correctly identifies HIV+ individuals 95% of the time, and HIV individuals $89\%$ of the time. A particular patient is tested using this kit and is found to be positive. The probability that the individual is actually positive is_______
28
If $\text{|-2X + 9| = 3}$ then the possible value of $|-X|-X^2$ would be: $30$ $-30$ $-42$ $42$
29
Following table gives data on tourists from different countries visiting India in the year $2011$ ... the one third of the total number of tourists ho visited India in $2011$? USA and Japan USA and Australia England and France Japan and Australia
30
In a factory, two machines $M1$ and $M2$ manufacture $60\%$ and $40\%$ of the autocomponents respectively. Out of the total production $2\%$ of $M1$ and $3\%$ of $M2$ are found to be defective. If a randomly drawn autocomponent from the combined lot is found defective, what is the probability that it was manufactured by $M2$? $0.35$ $0.45$ $0.5$ $0.4$
31
d 8 S Y S 11 then which of the following options is TRUE?
32
Velocity of an object fired directly in upward direction is given by $V = 80-32 t$, where $t$ (time)is in seconds. When will the velocity be between $32 m/sec$ and $64 m/sec$. $(1,3/2)$ $(½,1)$ $(½, 3/2)$ $(1, 3)$
33
A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation $y = 2x -0.1x^2$ where $y$ is the height of the arch in meters. The maximum possible height of the arch is 8 meters 10 meters 12 meters 14 meters
34
An automobile plant contracted to buy shock absorbers from two suppliers $X$ and $Y$. $X$ supplies $60\%$ and $Y$ supplies $40 \%$ of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable. Of $X's$ ... a randomly chosen shock absorber, which is found to be reliable, is made by $Y$ is $0.288$ $0.334$ $0.667$ $0.720$
35
Which of the following assertions are CORRECT? P: Adding 7 to each entry in a list adds 7 to the mean of the list Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list R: Doubling each entry in a list doubles the mean of the list S: Doubling each entry in a list leaves the standard deviation of the list unchanged P, Q Q, R P, R R, S
36
The cost function for a product in a firm is given by $5q^2$, where q is the amount of production. The firm can sell the product at a market price of ₹ 50 per unit. The number of units to be produced by the firm such that the profit is maximized is $5$ $10$ $15$ $25$
37
In a detailed study of annual crow births in India, it was found that there was relatively no growth during the period $2002$ to $2004$ and a sudden spike from $2004$ to $2005$. In another unrelated study, it was found that the revenue from cracker sales ... birth rate. If cracker sale declines, crow birth will decline. Increased birth rate of crows will cause an increase in the sale of crackers.
If $x^2 + x – 1 = 0$ what is the value of $x^4 + \dfrac{1}{x^4}$? $1$ $5$ $7$ $9$
To pass a test, a candidate needs to answer at least $2$ out of $3$ questions correctly. A total of $6,30,000$ candidates appeared for the test. Question A was correctly answered by $3,30,000$ candidates. Question B was answered correctly by $2,50,000$ candidates. Question C ... as the number answering none, how many candidates failed to clear the test? $30,000$ $2,70,000$ $3,90,000$ $4,20,000$
A set of $4$ parallel lines intersect with another set of $5$ parallel lines. How many parallelograms are formed? $2$0486072\$