1
Three Englishmen and three Frenchmen work for the same company. Each of them knows a secret not known to others. They need to exchange these secrets over person-to- person phone calls so that eventually each person knows all six secrets. None of the Frenchmen knows English, and only one Englishman knows French. what is the minimum number of phone calls needed for the above purpose? 5 10 9 15
2
Anil alone can do a job in $20$ days while Sunil alone can do it in $40$ days. Anil starts the job, and after $3$ days, Sunil joins him. Again, after a few more days, Bimal joins them and they together finish the job. If Bimal has done $10$% of the job, then in how many days was the job done? $14$ $13$ $15$ $12$
3
Read the following information carefully and answer the question based on that. Two families are planning to go on a canoe trip together. The families consist of the following people: Robert and Mary Henderson and their three sons Tommy, Don and William, Jerome and Ellen Penick ... Penick parents do not ride together. The Henderson parents do not ride together. Only I Only II I and II I and III
1 vote
4
Let $x$ and $y$ be positive real numbers such that $\log _{5}(x+y)+\log _{5}(x-y)=3$, and $\log _{2}y-\log _{2}x=1-log_{2}3$. Then xy equals $250$ $25$ $100$ $150$
1 vote
5
If the population of a town is $p$ in the beginning of any year then it becomes $3+2p$ in the beginning of the next year. If the population in the beginning of $2019$ is $1000$, then the population in the beginning of $2034$ will be $(997)2^{14}+3$ $(1003)^{15}+6$ $(1003)2^{15}-3$ $(997)^{15}-3$
6
The line AB is $6$ metres in length and is tangent to the inner one of the two concentric circles at point C. It is known that the radii of the two circles are integers. The radius of the outer circle is $5$ metres $4$ metres $6$ metres $3$ metres
1 vote
7
Corners are cut off from an equilateral triangle T to produce a regular hexagon H. Then, the ratio of the area of H to the area of T is $5:6$ $4:5$ $3:4$ $2:3$
1 vote
8
If $a_{1}+a_{2}+a_{3}+\dots+a_{n}=3(2^{n+1}-2)$, for every $n\geq 1$, then $a_{11}$ equals ____
1 vote
9
The product of two positive numbers is $616$. If the ratio of the difference of their cubes to the cube of their difference is $157:3$, then the sum of the two numbers is $58$ $50$ $95$ $85$
10
The number of solutions to the equation $|x|(6x^{2}+1)=5x^{2}$ is _____.
11
Consider a function $f$ satisfying $f(x+y)=f(x)f(y)$ where $x,y$ are positive integers, and $f(1)=2$. If $f(a+1)+f(a+2)+\ldots +f(a+n)=16(2^{n}-1)$ then $a$ is equal to ______
12
A chemist mixes two liquids $1$ and $2$. One litre of liquid $1$ weighs $1$ kg and one litre of liquid $2$ weighs $800$ gm. If half litre of the mixture weighs $480$ gm, then the percentage of liquid $1$ in the mixture, in terms of volume, is $85$ $70$ $75$ $80$
1 vote
13
In a circle of radius $11$ cm, CD is a diameter and AB is a chord of length $20.5$ cm. If AB and CD intersect at a point E inside the circle and CE has length $7$ cm, then the difference of the lengths of BE and AE, in cm, is $2.5$ $3.5$ $0.5$ $1.5$
14
Meena scores $40$% in an examination and after review, even though her score is increased by $50$%, she fails by $35$ marks. If her post-review score is increased by $20$%, she will have $7$ marks more than the passing score. The percentage score needed for passing the examination is $70$ $60$ $75$ $80$
15
The wheel of bicycles $A$ and $B$ have radii $30$ cm and $40$ cm, respectively. While traveling a certain distance, each wheel of $A$ required $5000$ more revolutions than each wheel of $B$. If bicycle $B$ traveled this distance in $45$ minutes, then its speed, in km per hour, was $18\pi$ $12\pi$ $16\pi$ $14\pi$
16
In a race of three horses, the first beat the second by $11$ metres and the third by $90$ metres. If the second beat the third by $80$ metres, what was the length, in metres,of the racecourse? ____
17
For any positive integer $n$, let $f(n)=n(n+1)$ if n is even, and $f(n)=n+3$ if n is odd. if $m$ is a positive integer such that $8f(m+1)-f(m)=2$, then $m$ equals____
18
The age of a son, who is more than two years old, is equal to the units digit of the age of his father. After ten years, the age of the father will be thrice the age of the son. What is the sum of the present ages of the son and the father? $30$ years $36$ years $40$ years Cannot be determined
1 vote
19
If $a_{1},a_{2}\dots$ are in A.P., then, $\frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\dots+\frac{1}{\sqrt{a_{n}}+\sqrt{a_{n+1}}}$ is equal to $\frac{n-1}{\sqrt{a_{1}}+\sqrt{a_{n-1}}}$ $\frac{n}{\sqrt{a_{1}}+\sqrt{a_{n+1}}}$ $\frac{n-1}{\sqrt{a_{1}}+\sqrt{a_{n}}}$ $\frac{n}{\sqrt{a_{1}}-\sqrt{a_{n+1}}}$
20
A person invested a total amount of Rs $15$ lakh. A part of it was invested in a fixed deposit earning $6$% annual interest, and the remaining amount was invested in two other deposits in the ratio $2:1$, earning annual interest at the rates of $4$% and $3$%, respectively. If the total annual interest income is Rs $76000$ then the amount (in Rs lakh) invested in the fixed deposit was___
21
$AB$ is a diameter of a circle of radius $5$ cm. Let $P$ and $Q$ be two points on the circle so that the length of $PB$ is $6$ cm, and the length of $AP$ is twice that of $AQ$. Then the length, in cm, of $QB$ is nearest to $7.8$ $8.5$ $9.1$ $9.3$
1 vote
22
Two cars travel the same distance starting at $10:00$ am and $11:00$ am, respectively, on the same day. They reach their common destination at the same point of time. If the first car traveled for at least $6$ hours, then the highest possible value of the percentage by which the speed of the second car could exceed that of the first car is $30$ $25$ $10$ $20$
23
If $m$ and $n$ are integers such that $(\sqrt{2})^{19}3^{4}4^{2}9^{m}8^{n}=3^{n}16^{m}(\sqrt[4]{64})$ then $m$ is $-20$ $-12$ $-24$ $-16$
1 vote
24
If $x= \frac{\sqrt{p^{2}+q^{2}}+\sqrt{p^{2}-q^{2}}}{{\sqrt{p^{2}+q^{2}}-\sqrt{p^{2}-q^{2}}}}$ then $q^{2}x^{2}-2p^{2}x+q^{2}$ equals to : $3$ $-1$ $-2$ $0$
25
If $\left (-4, 0 \right), \left(1, -1 \right)$ are two vertices of a triangle whose area is $4$ Sq units then its third vertex lies on : $y=x$ $5x+y+12=0$ $x+5y-4=0$ $x-5y+4=0$
26
The roots of the equation $x^{2/3}+x^{1/3}-2=0$ are : $1, -8$ $-1, -2$ $\frac{2}{3}, \frac{1}{3}$ $-2, -7$
27
Advanced LIGO recently observed the Black Hole activity Gravitational waves UFO Sun Temperature
1 vote
28
Ramesh and Gautam are among $22$ students who write an examination. Ramesh scores $82.5$. The average score of the $21$ students other than Gautam is $62$. The average score of all the $22$ students is one more than the average score of the $21$ students other than Ramesh. The score of Gautam is $49$ $48$ $51$ $53$
1 vote
29
A club has $256$ members of whom $144$ can play football, $123$ can play tennis, and $132$ can play cricket. Moreover, $58$ members can play both football and tennis, $25$ can play both cricket and tennis, while $63$ can play both football and cricket. If every member can play at least one game, then the number of members who can play only tennis is $45$ $38$ $32$ $43$
30
If $(5.55)^{x}=(0.555)^{y}=1000$, then the value of $\frac{1}{x}-\frac{1}{y}$ is $3$ $1$ $\frac{1}{3}$ $\frac{2}{3}$
1 vote
31
On selling a pen at $5$% loss and a book at $15$% gain, Karim gains Rs. $7$. If he sells the pen at $5$% gain and the book at $10$% gain, he gains Rs. $13$. What is the cost price of the book in Rupees? $80$ $85$ $95$ $100$
32
At their usual efficiency levels, A and B together finish a task in $12$ days. If A had worked half as efficiency as she usually does, and B had worked thrice as efficiency as he usually does, the task would have been completed in $9$ days. How many days would A take to finish the task if she works alone at her usual efficiency? $24$ $18$ $12$ $36$
33
Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job. If two machines can finish the job in $13$ days, then how many men can finish the job in $13$ days?______
1 vote
34
The income of Amala is $20$% more than that of Bimala and $20$% less than that of Kamala. If kamala’s income goes down by $4$% and Bimala’s goes up by $10$%, then the percentage by which kamala’s income would exceed Bimala’s is nearest to $31$ $28$ $32$ $29$
35
In a class, $60$% of the students are girls and the rest are boys. There are $30$ more girls than boys. If $68$% of the students, including $30$ boys, pass an examination, the percentage of the girls who do not pass is____
1 vote
36
Amala, Bina, and Gouri invest money in the ratio $3:4:5$ in fixed deposits having respective annual interest rates in the ratio $6:5:4$. what is their total interest income (in Rs) after a year, if Bina’s interest income exceeds Amala’s by Rs $250$? $6350$ $7250$ $7000$ $6000$
1 vote
37
There are 8 houses in a line and in each house only one boy lives with the conditions as given below: Jack is not the neighbour of Siman. Harry is just next to the left of Larry. There is at least one to the left of Larry. Paul lives in one of the two houses in ... at the left end. Robert is in between Simon and Taud. Taud is in between Paul and Jack. There are three persons to the right of Paul.
A box contains $6$ red balls, $7$ green balls and $5$ blue balls. Each ball is of a different size. The probability that the red ball selected is the smallest red ball, is $1/18$ $1/3$ $1/6$ $2/3$