The intakes on NIT and IITs are entirely on the entrance exams - JEE MAINS and JEE ADVANCED respectively. So, the board of school doesn't matter. 

Prepare hard for the exams and get into your coveted institute.

They intake the students according to rank of the corresponding entrance exam. So there is no problem if are you jharkhand school open school, as it is recognised to MHRD, Govt of India. So work hard to score a decent rank.
Best of luck