Explanation

(c)
Since, $\overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}} = 0$ …(i)
Also, $\left( \overrightarrow{\mathbf{a}} + 3\overrightarrow{\mathbf{b}} \right) \bullet \left( 2\overrightarrow{\mathbf{a}} - \overrightarrow{\mathbf{b}} \right) = - 10$
$\Longrightarrow 2\left| \overrightarrow{\mathbf{a}} \right|^{2} - \overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}} + 6\overrightarrow{\mathbf{b}} \bullet \overrightarrow{\mathbf{a}} - 3|{\overrightarrow{\mathbf{b}}|}^{2} = - 10$
$\Longrightarrow 2 - 3|{\overrightarrow{\mathbf{b}}|}^{2} = - 10 \Longrightarrow \left| \overrightarrow{\mathbf{b}} \right| = 2$ [from Eq. (i)]