b
The given charge assembly can be represented using the three co-ordinate axes \(\mathrm{x}, \mathrm{y}\) and \(\mathrm{z}\) as shown in figure.

The charge \(-2 q\) is placed at the origin \(\mathrm{O}\). One \(+q\) charge is place at \((a, 0,0)\) and the other \(+q\) charge is placed at \((0, a, 0) .\) Thus the system has two dipoles along \(x-\)axis and \(y-\)axis respectively.

As the electric dipole moment is directed from the negative to the positive charge hence the resultant dipole moment will be hong \(\overline{\mathrm{OA}}\) where co-ordinates of point \(\mathrm{A}\) are \((a, a, 0) .\) The magnitude of each dipolemoment,

\(p=q a\)

So, the magnitude of resultant dipole moment is

\(\mathrm{P}_{\mathrm{R}}=\sqrt{\mathrm{p}^{2}+\mathrm{p}^{2}}=\sqrt{(\mathrm{qa})^{2}+(\mathrm{qa})^{2}}\)

\(=\sqrt{2}\, \mathrm{qa}\)