Q. If $H$ is the harmonic mean between $P$ and $\mathcal{Q}$, then the value of $\frac{H}{P} + \frac{H}{\mathcal{Q}}$ is
A) 2
B) $\frac{P\mathcal{Q}}{P + \mathcal{Q}}$
C) $\frac{1}{2}$
D) $\frac{P + \mathcal{Q}}{P\mathcal{Q}}$
Explanation
(a)
Since, $H = \frac{2P\mathcal{Q}}{P + \mathcal{Q}}$
$\Rightarrow \frac{H}{P} = \frac{2\mathcal{Q}}{P + \mathcal{Q}}$
and $\frac{H}{\mathcal{Q}} = \frac{2P}{P + \mathcal{Q}}$
$\therefore\ \frac{H}{P} + \frac{H}{\mathcal{Q}} = \frac{2\mathcal{Q}}{P + \mathcal{Q}} + \frac{2P}{P + \mathcal{Q}} = 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.