Ion/Counter ion layers in the colloid precipitate of silver chloride
It isn't absolutely clear from the wording, but it seems you're adding $\ce{Cl^{-}}$ to a $\ce{Ag^{+}}$ solution.

As some of the $\ce{Cl^{-}}$ is added, $\ce{Ag^{+}}$ is still in excess in the solution so virtually all of the $\ce{Cl^{-}}$ precipitates. $\ce{Ag^{+}}$ will be the primary adsorbent on the precipitate, and the colloidal particles will have a positive charge.  

Since the colloidal particles have a positive charge, the ion in the counter-ion layer around the particle needs to be negatively charged. There isn't any  $\ce{Cl^{-}}$ in solution so it has to be $\ce{NO3^{-}}$ as the anion. 

Thus the correct answer is (D).