Which from following is a correct increasing order of basic strength of compounds?

The basic strength of amines in aqueous solution depends on three competing factors: inductive effects, solvation effects, and steric hindrance.

Alkyl groups exert an electron-donating inductive effect (+I), increasing electron density on the nitrogen atom and enhancing basicity. Solvation stabilizes the conjugate acid through hydrogen bonding: $\mathrm{NH}_4^+$ forms 4 H-bonds, $\mathrm{CH}_3\mathrm{NH}_3^+$ forms 3, $(\mathrm{CH}_3)_2\mathrm{NH}_2^+$ forms 2, and $(\mathrm{CH}_3)_3\mathrm{NH}^+$ forms only 1. Greater solvation yields stronger basicity. Steric hindrance from bulky groups impedes protonation, reducing basicity.

$(\mathrm{CH}_3)_2\mathrm{NH}$ achieves optimal balance with strong inductive effects and adequate solvation, making it the strongest base. $\mathrm{CH}_3\mathrm{NH}_2$ follows with moderate inductive and solvation effects. $(\mathrm{CH}_3)_3\mathrm{N}$ has maximal inductive effect but suffers from poor solvation and steric hindrance. $\mathrm{NH}_3$, lacking inductive donation, is weakest despite excellent solvation.

The experimentally observed order is $(\mathrm{CH}_3)_2\mathrm{NH} > \mathrm{CH}_3\mathrm{NH}_2 > (\mathrm{CH}_3)_3\mathrm{N} > \mathrm{NH}_3$, corresponding to increasing order $\mathrm{NH}_3 < (\mathrm{CH}_3)_3\mathrm{N} < \mathrm{CH}_3\mathrm{NH}_2 < (\mathrm{CH}_3)_2\mathrm{NH}$.

This matches option $\boxed{\text{D}}$.