as you are BSC student and wants to apply for various post in psu. yes you are eligible for various exams held by psu s.
for this you have to have 60% throughout carrier but it is not mandatory , the overall marks varies from organisation to organisation
you can apply for various psu like
BARK ,
SAIL ,
NTPC ,
NHPC


Eligibility criteria :


the eligibility criterion for different Public Sector unit is different and also depends on the post.

Education qualification :

but the general criterion is you should have minimum of 60% marks throughout

Age :

your age must be in between 21 to 27 for general category candidates. but it varies widely from organization to organization.