The number of diagonals in a polygon is $20$. The number of sides of the polygon 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

On an $n \times n$ chessboard,the total number of rectangles which are not squares is $350$. Then,the number of white squares on the chessboard is .......

The sum of all absolute values of the differences of the numbers $1, 2, 3, \ldots, n$,taken two at a time,i.e.,$\sum \limits_{1 \leq j < i \leq n} |i-j|$ equals:

If $3$ squares are chosen at random from the $64$ squares of a chess board,then the probability that all of them lie along the same diagonal line is

$15$ lines are concurrent at a point $P$. $A$ line $L$ not passing through $P$ intersects all the $15$ lines and forms triangles with them. Then the number of triangles having $L$ as one of its sides is