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

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

The sides $AB, BC, CA$ of a triangle $ABC$ have respectively $3, 4$ and $5$ points lying on them. The number of triangles that can be constructed using these points as vertices is

If $T_n$ denotes the number of triangles which can be formed using the vertices of a regular polygon of $n$ sides and $T_{n+1}-T_{n}=21$,then $n=$

In how many ways can $5$ boys and $3$ girls sit in a row so that no two girls are together?

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