On the sides $AB, BC, CA$ of a $\Delta ABC$,$3, 4, 5$ distinct points (excluding vertices $A, B, C$) are respectively chosen. The number of triangles that can be constructed using these chosen points as vertices is:

Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball,the second row consists of two balls and so on. If $99$ more identical balls are added to the total number of balls used in forming the equilateral triangle,then all these balls can be arranged in a square whose each side contains exactly $2$ balls less than the number of balls each side of the triangle contains. Then the number of balls used to form the equilateral triangle is

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

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

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:

How many numbers divisible by $5$ and lying between $3000$ and $4000$ can be formed from the digits $1, 2, 3, 4, 5, 6$ (repetition is not allowed)?