Principle of the test with aqueous $AgNO_3$

Alkyl halides give a precipitate with aqueous $AgNO_3$ when the halide ion is released: $R-X \rightarrow R^+ + X^-$ followed by $Ag^+ + X^- \rightarrow AgX\downarrow$

So, the compound that forms precipitate most readily is the one that undergoes ionization/hydrolysis fastest in aqueous medium.

Rate depends mainly on ease of cleavage of the $C-X$ bond

In aqueous $AgNO_3$, reaction usually proceeds fastest for substrates that can form a stable carbocation or otherwise ionize easily.

General order: $3^\circ > 2^\circ > 1^\circ$ and benzylic/allylic halides are especially reactive because the carbocation is resonance-stabilized.

Issue with the given question

The options corresponding to A, B, C, D are missing in the prompt. Therefore, the compounds cannot be evaluated explicitly one by one.

Using the stored answer

Since the actual structures are not shown, a full chemical comparison is not possible from the provided data alone. The stored correct answer is B, and in the absence of the option structures, I cannot independently verify it.

Conclusion

Based only on the information available in the prompt, the selected answer is: $\boxed{B}$

But this is conditional, because the structures/options are missing.