Science

Yes, you can apply for B.Sc Mathematics in the asked college. The admission are based on merit (12th marks).

No, in order to pursue BCA or B.Sc in CS you should complete your 12th with PCM as subjects, then only you will be eligible to apply for those courses.

It is not possible for you to get admission in any of the colleges until you complete your 12th. Therefore, if you clear 12th maths' compartment then you can take admission in any degree in any college.

It's better to go for CSE in NIT Hamirpur as CSE is the best branch and Hamirpur is really good and offering high package jobs.

There will be university entrance exam for all courses.

Yes, he can get into a government college, but that student must have more percentage in 12th. Then only he will be able to get admission.

Dear Yash,
B.Sc. Microbiology degree candidates needs to fulfil the below-mentioned eligibility criteria:
Completion of Higher Secondary (10+2) level of education.
Physics, chemistry and biology as main subjects at HSC level.
Minimum aggregate score of 60% at the level.
Instead of biology, one may even have had zoology or botany as one of the main subjects of study.

Dear Mohd,
Please refer the below link to see the colleges in Mumbai for B.Sc studies.
https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/science/colleges/b-sc-colleges-mumbai-all&ved=2ahUKEwiU-aqQlcriAhVPfH0KHcHUAdEQFjABegQIAxAB&usg=AOvVaw1rx9fW0Vuqc8YHTLbl-JnW.