Which from following amines has lowest $\mathrm{pK}_{\mathrm{b}}$ value?

Identifying the amine with the lowest $\mathrm{pK}_{\mathrm{b}}$ reveals the strongest base among the given options.

Ethylamine ($\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{NH}_{2}$) is a primary aliphatic amine where the ethyl group donates electrons via the +I effect, enhancing nitrogen's electron density and basicity; $\mathrm{pK}_{\mathrm{b}} \approx 3.25$.

Trimethylamine ($(\mathrm{CH}_{3})_{3}\mathrm{N}$) is a tertiary aliphatic amine with significant +I effects, but steric hindrance reduces solvation of its conjugate acid, lowering basicity; $\mathrm{pK}_{\mathrm{b}} \approx 4.20$.

Aniline ($\mathrm{C}_{6}\mathrm{H}_{5}\mathrm{NH}_{2}$) is an aromatic amine with resonance delocalization of the nitrogen lone pair into the benzene ring, drastically reducing basicity; $\mathrm{pK}_{\mathrm{b}} \approx 9.38$.

Benzylamine ($\mathrm{C}_{6}\mathrm{H}_{5}\mathrm{CH}_{2}\mathrm{NH}_{2}$) is a primary amine where the phenyl group exerts a weak -I effect through the methylene spacer, with no resonance delocalization; it is less basic than ethylamine but stronger than aniline; $\mathrm{pK}_{\mathrm{b}} \approx 4.67$.

Comparing $\mathrm{pK}_{\mathrm{b}}$ values, ethylamine has the lowest at approximately $3.25$, confirming it as the strongest base.