If the roots of the equation $x^3 - 12x^2 + 39x - 28 = 0$ are in $A.P.$,then their common difference will be

The sum of $n$ arithmetic means between $a$ and $b$ is:

If the sum of the first four terms of an $A.P.$ is $6$ and the sum of its first six terms is $4$,then the sum of its first twelve terms is

Three numbers are in $A.P.$ such that their sum is $18$ and the sum of their squares is $158$. The greatest number among them is

The number of $5$-tuples $(a, b, c, d, e)$ of positive integers such that:
$I.$ $a, b, c, d, e$ are the measures of angles of a convex pentagon in degrees.
$II.$ $a \leq b \leq c \leq d \leq e$.
$III.$ $a, b, c, d, e$ are in an arithmetic progression.

If $a_r > 0, r \in N$ and $a_1, a_2, a_3, ..., a_{2n}$ are in an arithmetic progression,then $\frac{a_1 + a_{2n}}{\sqrt{a_1} + \sqrt{a_2}} + \frac{a_2 + a_{2n-1}}{\sqrt{a_2} + \sqrt{a_3}} + \frac{a_3 + a_{2n-2}}{\sqrt{a_3} + \sqrt{a_4}} + ... + \frac{a_n + a_{n+1}}{\sqrt{a_n} + \sqrt{a_{n+1}}} = ?$