1. Concept of basicity in amines

   Basicity depends on the availability of the lone pair on nitrogen for donation to a proton.

   • Greater availability of the lone pair $\Rightarrow$ stronger base.
   • If the lone pair is delocalized by resonance, basicity decreases.
   • Electron-withdrawing groups also decrease basicity.

2. Examine each option

   (A) Benzylamine, $\mathrm{C_6H_5CH_2NH_2}$

   • The amino group is attached to a $\mathrm{CH_2}$ group, not directly to the benzene ring.
   • Therefore, the lone pair on nitrogen is not conjugated with the aromatic ring.
   • It behaves like an aliphatic amine, so it is fairly basic.

   (B) Aniline, $\mathrm{C_6H_5NH_2}$

   • Here, $\mathrm{-NH_2}$ is directly attached to the benzene ring.
   • The lone pair on nitrogen is delocalized into the benzene ring by resonance.
   • Hence, the lone pair is less available for protonation.
   • So aniline is less basic than benzylamine.

   (C) Acetanilide, $\mathrm{C_6H_5NHCOCH_3}$

   • This is an amide derivative.
   • The nitrogen lone pair is strongly delocalized toward the carbonyl group: $\mathrm{-NHCOCH_3 \leftrightarrow -N^+=C(O^-)CH_3}$
   • Due to this strong resonance, the lone pair is much less available.
   • Therefore, acetanilide is very weakly basic.

   (D) $p$-Nitroaniline

   • Like aniline, the nitrogen lone pair is delocalized into the benzene ring.
   • Additionally, the $\mathrm{-NO_2}$ group is a strong electron-withdrawing group by both $-I$ and $-M$ effects.
   • This further decreases electron density on nitrogen.
   • Hence, $p$-nitroaniline is less basic than aniline.

3. Order of basicity

   From the above analysis: $\mathrm{benzylamine > aniline > p\text{-}nitroaniline}$ and acetanilide is the least/basicity is very low due to amide resonance.

   So the most basic compound is: $\boxed{\text{benzylamine}}$

4. Option check

   • A: benzylamine — correct
   • B: aniline — less basic due to resonance
   • C: acetanilide — very weak base due to amide resonance
   • D: $p$-nitroaniline — even less basic due to $\mathrm{-NO_2}$ group

Therefore, the correct answer is A.