If $2x,\;x + 8,\;3x + 1$ are in $A.P.$, then the value of $x$ will be
If $a,\;b,\;c$ are in $A.P.$, then $\frac{{{{(a - c)}^2}}}{{({b^2} - ac)}} = $
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 arithmetic progression is
Given that $n$ A.M.'s are inserted between two sets of numbers $a,\;2b$and $2a,\;b$, where $a,\;b \in R$. Suppose further that ${m^{th}}$ mean between these sets of numbers is same, then the ratio $a:b$ equals