If p = 101, then the value of 3 p ( p^2 - 3p + 3 ) - 1 is?

Answer: Option A

$$\begin{array}{rl}& p=101\\ & \text{root}3\text{of}p\left(p^2-3p+3\right)-1\\ & =\text{root}3\text{of}{p}^3-3p^2+3p-1\\ & \therefore \left[{\left(p-1\right)}^3=p^3-{\left(1\right)}^3-3p\left(p-1\right)\right]\\ & =\text{root}3\text{of}{\left(p-1\right)}^3\\ & =p-1\\ & =101-1\\ & =100\end{array}$$