In a regular $15$-sided polygon with all its diagonals drawn,a diagonal is chosen at random. The probability that it is neither a shortest diagonal nor a longest diagonal is

There are $20$ straight lines in a plane such that no two of them are parallel and no three of them are concurrent. If their points of intersection are joined,then the number of new line segments formed is

The number of non-congruent integer-sided triangles whose sides belong to the set $\{10, 11, 12, \ldots, 22\}$ 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

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 .......

Out of $20$ points,no three points are collinear except for $4$ points which are collinear. How many lines can be drawn by joining these points?