can I give barc exam after my graduation and become scientist at barc if I have repeated my class 12?
Yeah! Obviously you can appear for BARC examination provided you must have a First Class in Bachelors (for Engineering Graduates) & First Class in Masters (for Science Graduates).
You can visit the link provided below to know more about BARC through GATE :
https://engineering.careers360.com/articles/barc-recruitment-through-gate
I hope this answer helps. All the very best for your future endeavors!