b
During acetylation, one \(H\) atom with atomic mass \(1\,amu\) of \(- NH_2\) group is replaced by  an acetyl group \(\mathrm{CH}_{3} \mathrm{CO}[\text { molecular mass }=434 \,\mu ]\). Thus

\(-\mathrm{NH}_{2}+\mathrm{CH}_{3} \mathrm{COCl} \longrightarrow-\mathrm{NHCOCH}_{3}+\mathrm{HCl}\)

The above equation suggests that, the acylation of each \(-\mathrm{NH}_{2}\) group increases the mass by \(42 \,\mu\) \([43-1] .\) If the molecular mass of the organic compound is \(180 \,\mu\) while that of the acylated product is \(390 \,\mu\), then the increase in the mass due to acylation is given by

\(390-180=210 \,\mu\)

Hence, the number of \(-\mathrm{NH}_{2}\) groups \(=\frac{210\, \mu}{42\, \mu}=5\)