If

$f(x)= \begin{vmatrix}1 & x & x+1\\2x& x(x-1) & (x+1)x\\ 3x(x-1) & (x-1)(x-2) & (x+1) x(x-1)\end{vmatrix}$

then f(100) is equal to

0

The correct answer is option (1) : 0

We have,

$f(x) = \begin{vmatrix}1 & x & x+1\\2x& x(x-1) & (x+1)x\\ 3x(x-1) & (x-1)(x-2) & (x+1) x(x-1)\end{vmatrix}$

Applying $C_3→C_3-C_2, $ we get

$f(x) = \begin{vmatrix}1 & x & 1\\2x& x(x-1) & 2x\\ 3x(x-1) & x(x-1)(x-2) & 3x(x-1)\end{vmatrix}=0$

$∴f(100)= 0.$