The DFA would like this.
Try making the DFA for $(a+(b+aa)^*b)^*$, we can easily see $q_3$ will be the final state.
@Shobhit Joshi, Thank you.
Is there any alternative approach to solve this question quickly?
Something making DFA consumes a lot of time if given RE is complicated.
@Soumya29 I don't know if there is some method, I do it this way only.
Ok.. Thanks @Shobhit
@Soumya29 I first made the NFA for the smallest string that the given regular expression was accepting and then completed it as to accept the other strings also.. So I guess for the minimum no of states of a particular NFA we should see the minimum no of states required to accept the string of minimum length and then proceed with the necessary modifications.