If $a, b, c$ are in $A.P.$,then $\frac{1}{bc}, \frac{1}{ca}, \frac{1}{ab}$ will be in

Consider the real-valued function $h: \{0, 1, 2, \ldots, 100\} \rightarrow \mathbb{R}$ such that $h(0) = 5$, $h(100) = 20$, and satisfying $h(p) = \frac{1}{2}\{h(p+1) + h(p-1)\}$ for every $p = 1, 2, \ldots, 99$. Then the value of $h(1)$ is:

What is the sum of all two-digit numbers which give a remainder of $4$ when divided by $6$?

The sequence $\frac{5}{\sqrt{7}}, \frac{6}{\sqrt{7}}, \sqrt{7}, \dots$ is

If $a, b, c$ are in $A.P.$,then $3^a, 3^b, 3^c$ shall be in

If $S_1, S_2$ and $S_3$ are the sums of the first $n_1, n_2$ and $n_3$ terms of an arithmetic progression respectively,then $\frac{S_1}{n_1}(n_2 - n_3) + \frac{S_2}{n_2}(n_3 - n_1) + \frac{S_3}{n_3}(n_1 - n_2) = ....$