I am confused that whether we should take only inductive or hyperconjugation effect also into consideration while finding the order. As the answer in the book is only according to inductive effect . Will hyperconjugation effect come into play or not ? If we take hyperconjugation effect then order must be 2>4>3>1.
The question is: how will these molecules react to the presence of a nucleophile (which would add to the more electrophilic center, i.e. the carbonyl carbon atom)?
The more the carbon atom of the carbonyl group has a partial positive charge, the more it is susceptible to be attacked by a nucleophile, so the problem is to compare the relative positive charge on the carbonyl carbon atom between those molecules.
Remember that an alkyl group has an electron-donating effect AND that a longer alkyl group has more electron-donating effect.
With all that, you should be able to answer your problem.