If in a regular polygon the number of diagonals is $54$,then the number of sides of this polygon is

There are $16$ points in a plane,no three of which are in a straight line except $8$ which are all in a straight line. The number of triangles that can be formed by joining them is equal to:

In a plane,there are $10$ points,out of which $4$ are collinear. The number of triangles that can be formed by joining these points is:

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 ....... .

Statement-$1$: If a polygon has $45$ diagonals,then the number of sides is $10$. Statement-$2$: Out of $n$ non-collinear points,$2$ points can be selected in $^nC_2$ ways.

There are $n$ straight lines in a plane,no two of which are parallel and no three pass through the same point. Their points of intersection are joined. Then the number of fresh lines thus obtained is