Simplify the following expression.

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

A school has 945 girls and 2475 boys. The principal wants to divide them into minimum number of groups for the annual day such that in each group there should be either boys or girls and there should be equal number of students in each groups. Find the minimum number of group that can be formed?

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? 

Find the greatest number which when divided to 169,289 and 369 gives the same remainder.

The sum and difference of HCF and LCM of two numbers is 592 and 518. Find the numbers if the sum of two number is 296.

A number, when divided by 4, leaves 3 as remainder. Find the remainder when twice the number is divided by 4?

Find the remainder when

$\frac{49\times 65}{9}$
 

Find the remainder when$\frac{1!+2!+3!+4!+5!\mathrm{.......100}!}{8}$.

Find the last two digits in the following expression
$32599\times 196\times 97$

Rajul brought some mangoes and divided them into groups of 2,3 and 5. In each of the time one mango is left out. Find the minimum number of mangoes Rajul had?

In a race, the racer who completes the maximum number of loops wins the race. If the racers take 9 min, 12 min, 15 min and 18 min to complete a loop. How many times will they be together in 7 hours (including the time they started) if all the racers started at the same time?

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

Find the remainder in the following expression.
$\frac{2^{110}}{9}$

Find the value of x if ${32}^{x-2}=\frac{64}{8^x}$