Principle of the test with $\mathrm{AgNO_3}$

Haloalkanes give a precipitate with $\mathrm{AgNO_3}$ when the halide ion is released as $\mathrm{X^-}$, which then forms insoluble silver halide: $\mathrm{Ag^+ + X^- \rightarrow AgX \downarrow}$

This generally happens readily for alkyl halides that undergo ionization/substitution.

When does precipitate not form?

A compound will not give precipitate if the halogen is not easily released as halide ion.

This is especially true for:

• Aryl halides (like chlorobenzene, bromobenzene)
• Vinyl halides

In aryl halides, the $\mathrm{C-X}$ bond has partial double bond character due to resonance, so it is difficult to break. Hence they do not react with $\mathrm{AgNO_3}$ under ordinary conditions.

Identify the expected correct type of compound

Since the options are not visible in the prompt, the only chemically correct conclusion is that the compound which will not produce a precipitate must be the aryl halide / haloarene among the given options.

Comparison with stored answer

The stored correct answer is B. This is consistent if option B is the haloarene/aryl halide among the options.

Since the actual structures/options are missing from the prompt, I cannot verify from the drawings directly, but based on standard chemistry and the stored key, option B is most likely the aryl halide that does not give precipitate with $\mathrm{AgNO_3}$.

Final answer

$\boxed{B}$

because the compound in option $B$ is expected to be the one whose halogen is not ionized easily, so no $\mathrm{AgX}$ precipitate is formed.