Explanation

(c)
Given, $f(x) = \left| \begin{matrix}
1 & 2(x - 1) & 3(x - 1)(x - 2) \\
x - 1 & (x - 1)(x - 2) & (x - 1)(x - 2)(x - 3) \\
x & x(x - 1) & x(x - 1)(x - 2)
\end{matrix} \right|$
$= (x - 1)(x - 1)(x - 2)\left| \begin{matrix}
1 & 2 & 3 \\
x - 1 & x - 2 & x - 3 \\
x & x & x
\end{matrix} \right|$
Applying $C_{1} \rightarrow C_{1} - C_{2},\ C_{2} \rightarrow C_{2} - C_{3}$
$= (x - 1)^{2}(x - 2)\left| \begin{matrix}
- 1 & - 1 & 3 \\
1 & 1 & x - 3 \\
0 & 0 & x
\end{matrix} \right|$
$= (x - 1)^{2}(x - 2)x( - 1 + 1) =$0
$\Rightarrow f(x) = 0$
$\therefore f(49) = 0$