Aspire Faculty ID #3625 · Topic: NIMCET 2012 · Just now
NIMCET 2012

If $H$ is the harmonic mean between $P$ and $Q$, then $\dfrac{H}{P} + \dfrac{H}{Q}$ is

Solution

Harmonic mean of $P$ and $Q$ is $H = \dfrac{2PQ}{P+Q}$
 
 Now, 
$\dfrac{H}{P} + \dfrac{H}{Q} = H\left(\dfrac{1}{P} + \dfrac{1}{Q}\right) = H \cdot \dfrac{P+Q}{PQ}$ 

Substitute 

$H = \dfrac{2PQ}{P+Q}$: 

$\dfrac{H}{P} + \dfrac{H}{Q} = \dfrac{2PQ}{P+Q} \cdot \dfrac{P+Q}{PQ} = 2$
 
So the correct Answer is $2$.
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