Q. If $ f(x)=\left| \begin{matrix} x-3 & 2{{x}^{2}}-18 & 3{{x}^{3}}-81 \\ x-5 & 2{{x}^{2}}-50 & 4{{x}^{3}}-500 \\ 1 & 2 & 3 \\ \end{matrix} \right|, $ then $ f(1).f(3)+f(3).f(5)+f(5).f(1) $ is equal to:
KEAMKEAM 2005
Solution: