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

Suppose $BC$ is a given line segment in the plane and $T$ is a scalene triangle. The number of points $A$ in the plane such that the triangle with vertices $A, B, C$ (in that order) is similar to triangle $T$ is

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 $N=$

If the sides $AB, BC$ and $CA$ of a triangle $ABC$ have $3, 5$ and $6$ interior points respectively,then the total number of triangles that can be constructed using these points as vertices is equal to ....... .

Suppose that $20$ pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars,then the total number of beams is

$l_1, l_2, l_3$ are three parallel lines in the same plane. If there are $m$ points on $l_1$,$n$ points on $l_2$,and $k$ points on $l_3$,what is the maximum number of triangles that can be formed with vertices at these points?