If the number of diagonals in a polygon with $n$ sides is $275$,then $n = .....$

$15$ persons are sitting around a circular table. The number of ways of selecting three persons at a time from them,such that the selected three do not sit together at one place is

If the number of rectangles formed on a chessboard is $1296$,then the total number of squares formed on the chessboard is:

There are $10$ points in a plane,of which no three points are collinear except $4$. Then,the number of distinct triangles that can be formed by joining any three points of these ten points,such that at least one of the vertices of every triangle formed is from the given $4$ collinear points is

Suppose $t_n$ is the number of triangles formed using the vertices of a regular polygon of $n$ sides. If $t_{n+1} = t_n + 28$,then $n =$

$A$ parallelogram is cut by two sets of $m$ lines parallel to its sides. The number of parallelograms thus formed is