5p
$latex \because \frac{p}{1} = \frac{q}{2} = \frac{r}{4} = k (let)&s=1$
$latex => p = k, q = 2k, r = 4k$
$latex \therefore \sqrt{5p^{2}+q^{2}+r^{2}} = \sqrt{5k^{2}+4k^{2}+16k^{2}}$
$latex => \sqrt{25k^{2}}$
$latex => 5k = 5p$
Hence option [B] is the right answer.