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

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

If the number of diagonals of a regular polygon is $35$,then the number of sides of the polygon is

In how many ways can a mixed doubles tennis game be arranged from $7$ married couples if no husband and wife are in the same game?

There are $16$ points in a plane out of which $6$ are collinear. How many lines can be drawn by joining these points?

Let $ABC$ be a triangle. Consider four points $p_1, p_2, p_3, p_4$ on the side $AB$, five points $p_5, p_6, p_7, p_8, p_9$ on the side $BC$, and four points $p_{10}, p_{11}, p_{12}, p_{13}$ on the side $AC$. None of these points is a vertex of the triangle $ABC$. The total number of pentagons that can be formed by taking all the vertices from the points $p_1, p_2, \ldots, p_{13}$ is . . . . . . .