Multiple-Choice Questions — Question 13

Since, p, q, and r are in continued proportion.

$\therefore \dfrac{p}{q} = \dfrac{q}{r} \\[1em] \Rightarrow q^2 = pr \text{ ........(1)}$

Solving,

p : r = p² : q²

$\Rightarrow \dfrac{p}{r} = \dfrac{p^2}{q^2} \\[1em] \Rightarrow q^2 = \dfrac{p^2 \times r}{p} \\[1em] \Rightarrow q^2 = pr \text{ .........(2)}$

Since, equation (1) and (2) are equal.

Hence, Option 4 is the correct option.