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A man travels by a motor boat down a river to his office and back. With the speed of the river unchanged, if he doubles the speed of his motor boat, then his total travel time gets reduced by 75%. The ratio of the original speed of the motor boat to the speed of the river is

Q. There are two vessels - A, and B. A contains water and milk in the ratio 3: 2 and vessel B contains milk and honey in the ratio 5: 4. If one takes equal quantities of solutions from vessels A and B, and pours it into vessel C, what will be the concentration of milk in the new solution?

Q. A और B दो पात्र है। पात्र A में पानी और दूध 3:2 के अनुपात में और पात्र B में दूध और शहद 5:4 के अनुपात में उपस्थित है। यदि एक व्यक्ति पात्र A और B से समान मात्रा में विलयन निकलता है और इसे पात्र C में डाल देता है, तो नए विलयन में दूध की सांद्रता क्या होगी?

A function f(x) is defined as:
f(x) = x${}^{15}$- 2013x${}^{14}$ + 2013x${}^{13}$- 2013x${}^{12}$ + .... - 2013x${}^2$ + 2013x. Find the value of f(2012).

The remainder obtained when ${2681}^{2681}$ is divided by 3 is

How many 5-digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once ?

How many male employees left in 2004? ___

The number of registered foreigners from Bangladesh increases by 10% every 2 years and that of unregistered foreigners from Bangladesh decreases by 10% every 2 years. If the total population of Afghanistan remain the same for all years and the number of foreigners from Bangladesh are 2% of the total population in 2012, then how many unregistered Bangladeshi were present in 2006. [In 2006, there were no foreigners in Afghanistan from any country except Bangladesh]

Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are5:3and1:2, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio4:3. What is the ratio of the composition of the two basic elements in alloy X?

Study the following table carefully to answer the questions that follow:

Number (N) of candidates (in lakhs) appearing for an entrance examination from six different states and the percentage (P) of candidates clearing the same over the years
$\begin{array}{ccccccc}State\to & A& B& C& D& E& F\\ Year\downarrow & & & & & & \\ & N\mid P& N\mid P& N\mid P& N\mid P& N\mid P& N\mid P\\ 2004& 1.23\mid 42& 1.04\mid 51& 1.11\mid 32& 1.32\mid 24& 1.23\mid 36& 1.33\mid 31\\ 2005& 1.05\mid 43& 1.12\mid 62& 1.07\mid 47& 1.15\mid 49& 1.18\mid 55& 1.24\mid 24\\ 2006& 2.04\mid 38& 1.48\mid 32& 1.08\mid 28& 1.96\mid 35& 1.42\mid 49& 1.58\mid 26\\ 2007& 1.98\mid 41& 2.07\mid 43& 1.19\mid 30& 1.88\mid 46& 1.36\mid 47& 1.79\mid 29\\ 2008& 1.66\mid 53& 1.81\mid 50& 1.56\mid 42& 1.82\mid 60& 1.73\mid 57& 1.86\mid 34\\ 2009& 1.57\mid 39& 1.73\mid 36& 1.64\mid 52& 2.01\mid 56& 1.69\mid 55& 1.95\mid 37\end{array}$
What is the number of candidates not clearing the entrance exam from State A in the year 2007?

What percent of the total number of girls in the college do not know Hindi? Round off your answer to the nearest integer.

Q63. In a school there are 2000 students out of whom 36 per cent are girls. Each boy's monthly fee is Rs 480 and each girl's monthly fee is 25 per cent less than a boy. What is the total of the monthly fees of girls and boys together?

A few tickets of a show are sold at Rs.10 per ticket and the other tickets are sold at Rs.12 per ticket. In all, 100 tickets are sold on a specific day. If the amount collected on that day was Rs.1056, find the number of tickets sold at Rs.12.

Mr. Gopal invested Rs. 8,000 in 7% Rs. 100 shares at Rs. 80. After a year he sold these shares at Rs. 75 each and invested the proceeds (including dividend) in 18% Rs. 25 shares at Rs. 41. Find

In Little Flowers School, for a school drill, the students are divided into two groups of Lilies and Daisies. The ratio of Lilies:Daisies = 8:3. The ratio of boys:girls = 7:4. 60% of the Daisy group is boys.

What is the ratio of the number of girls in the Lily group and the number of boys in the Daisy group?

Measure of two quantities along with the precisionof respective measuring instrument is :-
$A=2.5m/s\pm 0.5m/s$
$B=0.10s\pm 0.01m/s$
The value of AB will be :-

Statements: W ≤ X < Y = Z >A; W<B

Conclusion:
I. B > Z
II. W < A

What is the total number of students who opted for a job in Calcutta over the three years 1995, 1997 and 1999?

If $x=\frac{\sqrt{3}+1}{\sqrt{3}-1}andy=\frac{\sqrt{3}-1}{\sqrt{3}+1},thenthevalueof\left(x^2+y^2\right)is:$

Tickets numbered from 1 to 18 are mixed up together and then a ticket is drawn at random. Find the probability that the ticket has a number, which is a multiple of 2 or 3.

What will be the third step for the following input?

Input: 113 23 48 225 515 175 349

If $3^{x-y}$ = 27and $3^{x+y}$ = 243, then x is equal to:

The root(s) of the equation (2x - 3) = $\sqrt{2x^2-2x+21}$are:

A group of 100 people plays carrom, snooker and chess. 90 people play chess, 80 people play snooker and 80 people play carom. Find the maximum number of people who play all 3 games, if each person plays at least one game.

If $f\left(x\right)$ = $\frac{9^x}{9^x+3}$,find the value of $f\left(\frac{1}{50}\right)$ + $f\left(\frac{2}{50}\right)$ + ...... + $f\left(\frac{48}{50}\right)$ + $f\left(\frac{49}{50}\right)$

Three balls of equal radius are placed such that they are touching each other. A fourth smaller ball is kept such that it touches the other three. Find the ratio of the radii of smaller to larger ball.

If two opposite sides of a square lie on the lines 3x + 4y = 7 and 3x + 4y + 3 = 0. What is the area of the square in (sq.unit)?

A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is:

Find the number of non-negative integers below 10000 which when divided by 7 and 89 leaves a remainder 1?

A round balloon of radius 'r' subtends an angle $\alpha$ at the eye of the observer, while the angle of elevation of its centre is $\beta$. Find the height of the centre of balloon.

Consider the map given below: The dotted (broken) line in the map is the:

A can finish a work in 6 days whereas B can finish the work in 9 days. If both of them work together what is the probability that work will be finished on third day?

Who among them scored highest in Maths?

If 12 men and 16 boys can do a piece of work in 5 days; 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is:

Statements: W $\delta$ U, U G, G $\$$ M

Conclusions:

I. M * U

II. G * W

Two circles centered at points A and B, respectively, intersect at points E and F as shown. These circles intersect segment AB at points C and D. If AC=1 and CD = DB = 2, determine EF.

If $f\left(x\right)=\frac{x}{x+1},$ determine the value of g(2) if, $g\left(x\right)=f\left[\frac{1}{x+1}\right]-\frac{1}{f(x+1)}.$

Write the negation of the following statement

'All students study Mathematics at the elementary level'.

Pick the odd pair out.

Two people started simultaneously from points A and B towards each other. At the moment the person who started from A had covered two-thirds of the way, the other person had covered 2 km less than half the total distance. If it is known that when the person who started from B had covered $\frac{1}{4}$ of the way, the other person was 3 km short of the midpoint. Find the distance between A and B. The speeds of the two people were constant.

The number of non - negative integral solutions of $x_1+x_2+x_3+x_4\le n$ (where n is a positive integer) is: