Hi Shivam, 

Yes, a B.Sc student can appear for the NEEt exam. Theres is a possibilty. The eligibility criteria provided by the NTA is 'quoted' below. 

Code 05 - The first year of the three years degree course of a recognised University with Physics, Chemistry and Biology/Bio-technology including practical tests in these subjects provided the examination is a University Examination and candidate has passed the earlier qualifying examination with Physics, Chemistry, Biology/Biotechnology with English at a level not less than a core course.

Code 06 - B.Sc. Examination of an Indian University provided that he/she has passed the B.Sc. Examination with not less than two of the subjects Physics, Chemistry, Biology (Botany, Zoology)/Bio-technology and further that he/ she has passed the earlier qualifying examination with Physics, Chemistry, Biology and English.

In your case, code 06 is applicable. You should have passed the graduate program, and should have had not less than two of the given subjects in the graduate program. 

All The Best.