The sum of all two-digit positive numbers which,when divided by $7$,yield $2$ or $5$ as a remainder is:

If $\frac{1}{b - c}, \frac{1}{c - a}, \frac{1}{a - b}$ are consecutive terms of an $A.P.$,then $(b - c)^2, (c - a)^2, (a - b)^2$ will be in

Find the maximum sum of the series $20 + 19\frac{1}{3} + 18\frac{2}{3} + 18 + .....$

If $a, b,$ and $c$ are positive real numbers,then the minimum value of $(a + b + c)(1/a + 1/b + 1/c)$ is .......

Given that $n$ arithmetic means are inserted between two sets of numbers $(a, 2b)$ and $(2a, b)$,where $a, b \in \mathbb{R}$. Suppose the $m^{th}$ means between these sets are equal,then the ratio $a : b$ is equal to:

For three positive integers $p, q, r$,$x^{pq p^2} = y^{qr} = z^{p^2 r}$ and $r = pq + 1$ such that $3, 3 \log_y x, 3 \log_z y, 7 \log_x z$ are in $A$.$P$. with common difference $\frac{1}{2}$. Then $r - p - q$ is equal to