List of top Quantitative Aptitude Questions on Divisibility and Remainder

$10^{68}$ is divided by 13, the remainder is  is

When 3³³³ is divided by 11, the remainder is

If $1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}....\frac{1}{29} =\frac{N}{29!}$ Find the remainder when N is divided by 19.

A school has less than 5000 students and if the students are divided equally into teams of either 9 or 10 or 12 or 25 each, exactly 4 are always left out. However, if they are divided into teams of 11 each, no one is left out. The maximum number of teams of 12 each that can be formed out of the students in the school is