Let $f(x) = x + 1/2$. Then, the number of real values of $x$ for which the three unequal terms $f(x), f(2x), f(4x)$ are in $HP$ is

The harmonic mean of $4, 8, 16$ is

If $\frac{1}{b + c}, \frac{1}{c + a}, \frac{1}{a + b}$ are in Arithmetic Progression $(AP)$,then $a^2, b^2, c^2$ are in which progression?

If $H$ is the harmonic mean between $a$ and $b$,then what is the value of $\frac{1}{H - a} + \frac{1}{H - b}$?

If the $m^{th}$ term of a $H.P.$ is $n$ and the $n^{th}$ term is $m$,then the $r^{th}$ term will be

If the $p^{th}$,$q^{th}$,and $r^{th}$ terms of a harmonic progression are $u$,$v$,and $w$ respectively,then the value of $(q - r)vw + (r - p)wu + (p - q)uv$ is equal to: