Please explain basicity order of the following molecules.

Basicity depends on  electron giving tendency of the substance.In the given questions we have amines in which N atom has a lone pair and is basic in nature.

All alky groups are electron releasing in nature and hence helps in increasing the basicity.However presence of many alkyl group can cause Steric hindrance and reduces the basicity of N lone pairs as they are hindered by bulky R groups.
Nitro group is electron withdrawing  group and reduces electron density on the N atom and hence the basicity.
Now try to figure out answer based on above explanation.

Acidity and basicity trends: It means 's' should be most basic with electron releasing groups on the ring also. Q should be least basic with electron with drawing group on the ring. Order is . S>R>P>Q.

Correct Rohit