NIMCET 2024 — Mathematics PYQ

 AM = $a$, GM’s = $p$ and $q$
Let the two numbers be $1$ and $8$.

AM:
$a=\frac{1+8}{2}=\frac{9}{2}$

GMs:
$p=2$, $q=4$

Then:
$p^3+q^3=2^3+4^3=8+64=72$

Also:
$2apq=2\times \frac{9}{2}\times 2\times 4=9\times 8=72$

Therefore:
$p^3+q^3=2apq$ 

Answer: (a) $\boxed{2apq}$