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

On an $n \times n$ chessboard,the total number of rectangles which are not squares is $350$. Then,the number of white squares on the chessboard is .......

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

Let $n \geq 2$ be an integer. Take $n$ distinct points on a circle and join each pair of points by a line segment. Colour the line segment joining every pair of adjacent points blue and the rest red. If the number of red and blue line segments are equal,then the value of $n$ is

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:

There are two women participating with some men in a chess tournament. Each participant played two games with every other participant. The number of games that the men played between themselves is $66$ more than the number of games that the men played with the women. Find the total number of participants in the tournament.