The correct option is C (c) < (a) < (b)
(c) < (a) < (b)
In compound (c), the lone pair on nitrogen is involved in resonance with carbonyl group and forms two resonating structures which will make the lone on nitrogen less available for donation. This is not the case in other compounds .
Hence (c) will be the least basic.
Comparing (a) and (b):
Nitrogen in (b) is 2∘ whereas it is 1∘ in case of (a) .
More the alkyl groups attached , more is the +I effect shown, and hence greater is the electron density on nitrogen.
So, basic strength of (b) will be higher than that of (a)
Hence the order of increasing order of basic strength is :
(c) < (a) < (b)