The number of ordered pairs $(x, y)$ of integers such that their product $xy$ is a positive integer less than $100$ is:

If $a + b + c = 50$ and $a, b, c$ are non-negative even integers,then the greatest value of $ab^2c$ is:

In an examination,a student has to write exams in $8$ different subjects. He is declared fail if he fails in at least one subject. The number of ways in which he can fail is

$A$ building has a ground floor and $10$ more floors. Nine persons enter a lift at the ground floor. The lift goes up to the $10$th floor. The number of ways in which any $4$ persons exit at a floor and the remaining $5$ persons exit at a different floor, if the lift does not stop at the first and the second floors, is equal to:

The letters of the word $ASSASSIN$ are written down at random in a row. The probability that no two $S$ occur together is

There are $4$ men and $5$ women in Group $A$,and $5$ men and $4$ women in Group $B$. If $4$ persons are selected from each group,then the number of ways of selecting $4$ men and $4$ women is: