When all the students in a school are made to stand in rows of $54,$ $30$ such rows are formed. If the students are made to stand in rows of $45,$ how many such rows will be formed?

The number of rectangles that can be obtained by joining four of $12$ vertices of a $12$-sided regular polygon is:

$A$ test consists of $6$ multiple choice questions,each having $4$ alternative answers of which only one is correct. The number of ways in which a candidate answers all six questions such that exactly four of the answers are correct is:

$m$ men and $n$ women are to be seated in a row so that no two women sit together. If $m > n$,then the number of ways in which they can be seated is

The number of ways in which ten candidates $A_1, A_2, ....... A_{10}$ can be ranked such that $A_1$ is always above $A_{10}$ is

The number of positive integral solutions of the equation $xyz = 90$ is equal to: