The number of diagonals in a regular polygon of $100$ sides is

Let $T_n$ be the number of all possible triangles formed by joining vertices of an $n$-sided regular polygon. If $T_{n+1}-T_n=10$,then the value of $n$ is

$A$ polygon has $54$ diagonals. The number of sides of this polygon is

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

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

If all the six-digit numbers $x_1 x_2 x_3 x_4 x_5 x_6$ with $0 < x_1 < x_2 < x_3 < x_4 < x_5 < x_6$ are arranged in increasing order,then the sum of the digits in the $72^{\text{th}}$ number is $............$.