The value of $\frac{(p - q)^3 + (q - r)^3 + (r - p)^3}{12(p - q) ( q - r) ( r - p)}$, where p ≠ q ≠ r, is equal to :

$\frac{1}{9}$ $\frac{1}{3}$ $\frac{1}{4}$ $\frac{1}{2}$

$\frac{1}{4}$

$\frac{(p - q)^3 + (q - r)^3 + (r - p)^3}{12(p - q) ( q - r) ( r - p)}$ Put p = 2 q = 1 r = 0 $\frac{(2 - 1)^3 + (1 - 0)^3 + (0 - 2)^3}{12(2 - 1) ( 1 - 0) ( 0 - 2)}$ = \(\frac{-6}{-24}\) =  \(\frac{1}{4}\)