NOTE : Aromatic amines are less basic than aliphatic amines. Among aliphatic amines the order of basicity is $${2^ \circ } > {1^ \circ } > {3^ \circ }.$$ The electron density is decreased in $${3^ \circ }$$ amine due to crowing of alkyl group over $$N$$ atom which makes the approach and bonding by a proton relatively difficult. Therefore the basicity decreases. Further Phenyl group show $$ - {\rm I}$$ effect, thus decreases the electron density on nitrogen atom and hence the basicity.

$$\therefore$$ dimethylamine ($${2^ \circ }$$ aliphatic amine) is strongest base among gtiven choices.

$$\therefore$$ The correct order of basic strength is Dimethyl amine $$>$$ Methyl amine $$>$$ Trimethyl-amine $$>$$ Aniline.