If the number of diagonals in a polygon with $n$ sides is $275$,then $n = .....$

In how many ways can $21$ white balls and $19$ black balls be arranged in a row such that no two black balls are together?

There are $6$ points on a circle. Two triangles are drawn such that they have no common vertices. What is the probability that none of the sides of the triangles intersect?

Six '$X$'s have to be placed in the squares of the figure such that each row contains at least one '$X$'. In how many different ways can this be done?

The number of straight lines that can be formed by joining $20$ points,no three of which are in the same straight line,except $4$ of them which are in the same line,is:

If $5$ parallel lines are intersected by $4$ parallel lines,then what is the number of parallelograms formed?