Which of the following belongs to the homologous series of ${\mathrm{C}}_5{\mathrm{H}}_8{\mathrm{O}}_2\mathrm{ }\mathrm{N}$ ?

Homologous series means any two consecutive hydrocarbons which are differing by a ${\mathrm{CH}}_2$ group.

${\mathrm{C}}_6{\mathrm{H}}_{10}{\mathrm{O}}_3 \mathrm{N}+{\mathrm{CH}}_2\to {\mathrm{C}}_6{\mathrm{H}}_{10}{\mathrm{O}}_2 \mathrm{N}$

Thus out of all options only ${\mathrm{C}}_6{\mathrm{H}}_{10}{\mathrm{O}}_2\mathrm{ }\mathrm{N}$ satisfies the condition for being a member of the homologous series of ${\mathrm{C}}_6{\mathrm{H}}_{10}{\mathrm{O}}_3\mathrm{ }\mathrm{N}$.

Hence, option (D) is correct.