Find the total number of rectangles on a normal chessboard.

There are $m$ men and $2$ women participating in a chess tournament. Each participant plays $2$ games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by $84$,then the value of $m$ is

Let $t_n$ denote the number of integral-sided triangles with distinct sides chosen from $\{1, 2, 3, \ldots, n\}$. Then,$t_{20} - t_{19}$ equals

The number of diagonals in a polygon of $m$ sides is

If a polygon has $44$ diagonals,then the number of its sides is:

The greatest possible number of points of intersection of $8$ distinct straight lines and $4$ distinct circles is