Dear Aspirant ,

You have only mentioned you belong to economically backward castes but you have not mentioned your category but let me tell you in detail :-

1. If you belong to General - EWS  or OBC - NCL then you don't have chance in any NIT . You may have chance in NIT Srinagar , Manipur , Mizoram or Sikkim only in spot round with lower branch options but still the propability is low .
2. If you belong to SC or ST you have fair chances to get NITs like  NIT Patna , Jamshedpur , Una and chances in top NITs like NIT Tirichy , Rourkela , Warangal with lower branch in spot round.
3. PWD category has chance in all NIT with this percentile .