In how many ways can $5$ boys and $5$ girls stand in a row so that no two girls may be together?

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

Out of $10$ points in a plane,$6$ are in a straight line. The number of triangles formed by joining these points is:

$A$ regular polygon of $n$ sides has $170$ diagonals,then $n$ is equal to

If $a, b, c, d$ are four distinct numbers chosen from the set $\{1, 2, 3, \ldots, 9\}$,then the minimum value of $\frac{a}{b} + \frac{c}{d}$ is

The number of diagonals in an octagon is