The value of $\begin{vmatrix}1 & 1+p & 1+p+q\\2 & 3 + 2p & 1+3p + 2q\\3 & 6+3p & 1+6p + 3q\end{vmatrix} $ is :

1

The correct answer is Option (2) → 1

$Δ=\begin{vmatrix}1 & 1+p & 1+p+q\\2 & 3 + 2p & 1+3p + 2q\\3 & 6+3p & 1+6p + 3q\end{vmatrix}$

$R_2→R_2-2R_1$

$\begin{vmatrix}1 & 1+p & 1+p+q\\0 & 1 & -1+p\\3 & 6+3p & 1+6p + 3q\end{vmatrix}$

$R_3→R_3-3R_1$

$\begin{vmatrix}1 & 1+p & 1+p+q\\0 & 1 & -1+p\\0 & 3 & -2+3p\end{vmatrix}$

$=-2+3p+3-3p=1$