There are $16$ points in a plane out of which $6$ are collinear. How many lines can be drawn by joining these points?

Let $P_{1}, P_{2}, \ldots, P_{15}$ be $15$ points on a circle. The number of distinct triangles formed by points $P_{i}, P_{j}, P_{k}$ such that $i+j+k \neq 15$ is:

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

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?

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 $............$.

Let $T_n$ denote the number of triangles which can be formed using the vertices of a regular polygon of $n$ sides. If $T_{n+1} - T_n = 21$,then $n$ equals