Yes, a BIPC student (Biology, Physics, Chemistry) can write the JEE Mains exam. The eligibility criteria for JEE Mains doesn't discriminate based on your chosen stream in Class 12.

JEE Mains focuses on assessing your knowledge and problem-solving abilities in Physics, Chemistry, and Mathematics. As per the JEE Mains information brochure, candidates must have passed the Class 12 qualifying exam (or equivalent) with Physics, Chemistry, and any other subject (which can include Biology).

https://engineering.careers360.com/exams/jee-advanced

I hope it helps!