Science

Chemical engineering is somewhat better than biotechnology in India. If you want to join chemical engineering then try to crack some good GATE rank so that you can get jobs in ONGC, HPL and also in government based chemical sectors. Otherwise, try to go for any booming stream in engineering like civ

You have many choices after class 12th:
MBBS,
BDS
Veterinary
BAMS
BHMS
B.Sc AG-ICAR
B.Pharm,
Pharm.D,
BE in Environmental Engineering,
BPT (Bachelor of Sciences or Forensic Sciences)
B.Sc in Zoology, Microbiology, Nursing, Paramedical courses B.Sc in geology, biochemistry, pathology, radiology and speech

Yes, you can apply for B.Sc in Patna University with that score.

Yes, entrance exam is meant to check your knowledge of what you studied so far and for your case, it is 11th and 12th class.

Check out the colleges in the UK that accepts students to do BBA course without Maths. There would be some colleges that would take your admission only if you meet their eligibility criteria.

Firstly, you need to tell which college you are aspiring to do M.Sc. Because every college has different requirements.

Yes, you can write NEST exam. The National Entrance Screening Test or NEST is a compulsory online/ computer based test for admission to the five year Integrated M.Sc. Programme in basic sciences, Biology, Chemistry, Mathematics and Physics, at National Institute of Science Education and Research (NI

Interested candidates can apply online with the required information. Admission is based on the marks obtained in 10+2. Any how, you need to write entrance exam to take admission.