Explanation

(c)
Given, $T_{m} = n,\ T_{n} = m$ in HP, therefore the corresponding AP of $m$th term and $n$th term is of AP are $\frac{1}{n}\ and\frac{1}{\ m}$ respectively.
Let $a\ and\ d$ be the first and common difference of an AP, then
$a + (m - 1)d = \frac{1}{n}$ …(i)
$a + (n - 1)d = \frac{1}{m}$ …(ii)
On solving Eqs. (i) and (ii), we get
$a = \frac{1}{mn},\ d = \frac{1}{mn}$
Now, $r$th term of AP$= a + (r - 1)d$
$= \frac{1}{mn} + (r - 1)\frac{1}{mn}$
$= \ \frac{1 + r - 1}{mn} = \frac{r}{mn}$
$\therefore r$th term of HP is $\frac{mn}{r}.$