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:

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

Among $10$ points in a plane,no three points are collinear and $4$ points are concyclic. How many distinct circles can be drawn using at least $3$ of these points?

There are $10$ points in a plane of which no three points are collinear except $4$ points. The number of distinct triangles that can be formed by joining these points such that at least one of the vertices of every triangle formed is from the given $4$ collinear points is:

There are $10$ points in a plane,out of which $4$ are collinear. How many straight lines can be formed by joining any two of these points?

Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between themselves exceeds the number of games that the men played with the women by $66$,then the number of men who participated in the tournament lies in the interval