How many chords can be drawn through $21$ points on a circle?

$T_m$ denotes the number of triangles that can be formed with the vertices of a regular polygon of $m$ sides. If $T_{m+1}-T_m=15$,then $m$ is equal to

In the given figure,$6$ '$A$'s should be written in such a manner that every row contains at least one '$A$'. The number of ways this is possible is

There are $10$ points in a plane,out of which $6$ are collinear. If $N$ is the number of triangles formed by joining these points,then . . . .

If a polygon of $n$ sides has $275$ diagonals,then $n$ is

There were two women participating in a chess tournament. Every participant played two games with every other participant. The number of games that the men played between themselves exceeded the number of games that the men played with the women by $66$. The total number of participants is