For which of the following, any number of the form ${10}^n-1$ is divisible by 11.

A fruit seller sells 45% of apples and still has 275 apples. How many apples he originally had?

What is the total number of students in the school who don’t like at least one of the five subjects?

To win a completion, Raghu needs to find out three prime numbers. To determine them, he has the following clues: 

a. The product of first two numbers is 1891 

b. The product of last two numbers is 7991 

Find the sum of first two numbers? 

Out of total number of student in the college, 15% are interested in sports, $\frac{3}{5}$ of total student are interested in dancing,10% of total numbers of student are interested in singing and remaining 45 students are not interested in any of the activities. What is total number of students in the college? 

In an election between two candidates, 10% of the people did not vote. Winning candidate won the election by 1080 votes and it was found that he had been supported by 60% of the total number of voters . Which of the following can be the number of votes receded for each candidate? 

Simplify the following expression.

$\left(\frac{{(9768+2345)}^2-{\left(9768-2345\right)}^2}{9768\times 2345}\right)$

Price of a movie ticket has increased by 6%, as a result, there was a reduction of 4% in the audience for the show. As an overall effect, revenue of the movie hall has increased by Rs. 94. Find the initial revenue of the movie hall.

Find the remainder when

$\frac{49\times 65}{9}$
 

The difference of the squares of two consecutive odd integers is divisible by which of the following integer?

Which of following will not leave any remainder when dividing 23n –1 for all the natural numbers ‘n’? 

If n is positive integer, then $3^{4n}-4^{3n}$ is always divisible by which of the following?

A two digit number is subtracted from the number formed by reversing the digits. The resulting number will be a multiple of which of the following?

If the numerator of a fraction be increased by 14.28% and its denominator be diminished by 11.11%, the values of the fraction is $\frac{54}{35}$. Find the original fraction.

The cost of ploughing a rectangular field whose length is 15 meters and breadth is 20 meters is Rs 20 per $m^2$.If the length of a rectangle is increased by 20% and breadth is decreased by 25% Find the cost of ploughing the new field .