Explanation

(c)
Since, three vectors $\left( \overrightarrow{\mathbf{a}} + 2\overrightarrow{\mathbf{b}} + 3\overrightarrow{\mathbf{c}} \right),\left( \lambda\ \overrightarrow{\mathbf{b}} + 4\overrightarrow{\mathbf{c}} \right)\ and\ (2\lambda - 1)\overrightarrow{\mathbf{c}}$ are non-coplanar
$\therefore\ \left| \begin{matrix}
1 & 2 & 3 \\
0 & \lambda & 4 \\
0 & 0 & 2\lambda - 1
\end{matrix} \right| \neq 0$
$\Longrightarrow (2\lambda - 1)(\lambda) \neq 0$
$\Longrightarrow \ \lambda \neq 0,\frac{1}{2}$
Hence, these three vectors are non-coplanar for all except two values of λ.