I am a B.Sc zoology student. Can I apply for IIT JAM?

Hello, You can apply for it in your final year or after at the end of your degree! Better to prepare thoroughly for these pre- final years. All the best!

Yes. You can certainly apply for JAM in your final year and after passing B.Sc too.

Yes, you are eligible. You can apply for both papers IIT JAM biotechnology (BT) and biological sciences (BL). For more information you can read previous year prospectus and question papers, which is available on site of previous years organizing institutions IIT JAM2018 organized by IIT Bombay).