Search any question & find its solution
Question:
Answered & Verified by Expert
If $\mathrm{H}$ is the harmonic mean between $\mathrm{P}$ and $\mathrm{Q}$, then the value of $\frac{\mathrm{H}}{\mathrm{P}}+\frac{\mathrm{H}}{\mathrm{Q}}$ is
Options:
Solution:
1890 Upvotes
Verified Answer
The correct answer is:
2
Given : $\mathrm{H}$ is the harmonic mean between $\mathrm{P} \& \mathrm{Q}$
$\begin{array}{l}
\therefore \mathrm{H}=\frac{2 \mathrm{PQ}}{\mathrm{P}+\mathrm{Q}} \Rightarrow \frac{1}{\mathrm{H}}=\frac{\mathrm{P}+\mathrm{Q}}{2 \mathrm{PQ}} \\
\Rightarrow \frac{2}{\mathrm{H}}=\frac{1}{\mathrm{Q}}+\frac{1}{\mathrm{P}} \Rightarrow \frac{\mathrm{H}}{\mathrm{P}}+\frac{\mathrm{H}}{\mathrm{Q}}=2
\end{array}$
$\begin{array}{l}
\therefore \mathrm{H}=\frac{2 \mathrm{PQ}}{\mathrm{P}+\mathrm{Q}} \Rightarrow \frac{1}{\mathrm{H}}=\frac{\mathrm{P}+\mathrm{Q}}{2 \mathrm{PQ}} \\
\Rightarrow \frac{2}{\mathrm{H}}=\frac{1}{\mathrm{Q}}+\frac{1}{\mathrm{P}} \Rightarrow \frac{\mathrm{H}}{\mathrm{P}}+\frac{\mathrm{H}}{\mathrm{Q}}=2
\end{array}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.