Science

This link should give an idea:
https://www.shiksha.com/resources/college-comparison-51912-51570.

The starting date of college is provided by college itself to the students at the time of admission or later on. You can inquire in the college and get the details. Hope this will help you.
Good luck.

It depends on college if you choose government college than fee structure is 7 to 8 thousand and for private college it is more than 30 thousand per year.

You won't recieve your Passing Certificate unless you clear your backlogs. So, you can't pursue anything else until you clear your backlog.

Hello there,
But, you cannot take admission in 3rd year directly until and unless your previous college gives you an NOC regarding any matter such as transfer of locations or any other reason. So, study little hard and clear the exam.
Regards.

Hello there,
Both are carrying good scope in their respective field. Its up to you what you like more engineering or B.Sc Maths. Engineering is creative application of Science maths, innovations design, construction operation of machines, etc. And B.Sc. Maths is a undergraduate programme related to maths and its applications. After B.Sc, you can go for software, insurance, market research banking sector etc., and for government sector, you can opt out Tax assistant, statistical investigator, IES, teacher, etc.
Regards.

You are eligible for the course. Name the university to get more information.

Yes, it is possible. http://www.gujaratuniversity.ac.in/web/custom/pdfs/admissions-pg-nursing-physiotherapy-optometry-2018.