NIMCET 2012 — Mathematics PYQ

1. Definition of Harmonic Mean ($H$):

The harmonic mean $H$ between two numbers $P$ and $Q$ is given by the formula:

2. Rearranging the formula:

We can rewrite the above equation as:

3. Evaluating the required expression:

The expression we need to find is $\frac{H}{P}+\frac{H}{Q}$. Let's factor out $H$:

4. Simplify the terms inside the bracket:

Find a common denominator for $\frac{1}{P}+\frac{1}{Q}$:

5. Substitute the value of $H$:

Now, substitute $H=\frac{2PQ}{P+Q}$ into the expression:

6. Final Cancellation:

The terms $(P+Q)$ and $(PQ)$ cancel each other out:

Correct Option:

(a) 2