The total number of possible ways in which a person can go from $A(0,0)$ to $B(3,3)$ if he can travel only to the right or upward along the grid lines is:

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

Let $p_n$ denote the total number of triangles formed by joining the vertices of an $n$-sided regular polygon. If $p_{n+1} - p_n = 66$, then the sum of all distinct prime divisors of $n$ is:

Out of $n$ points in a plane,$p$ points are collinear. (No three of the remaining points are collinear). The number of lines that can be drawn passing through these points is:

There are $n$ points in a plane,of which $p$ points are collinear. How many lines can be formed from these points?

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