hi,

see barc is not a academic institutions to pursue bachelors course, it is a research organizations which mostly focused on nuclear and atomic reseach and future scope in India. you may apply for barc oces or dgfs program after completing the masters course of science or bachelors course in engineering in relevant discipline, also final year bachelors or masters students are also eligible to apply,. see nuclear engineering is a interdisciplinary course, and most indian tier 1 colleges offers mtech course in nuclear engineering.

you may follow the below link to know about b.tech in nuclear engineering colleges in india,

https://engineering.careers360.com/colleges/list-of-be-btech-in-nuclear-engineering-colleges-in-india