Class 12-science

If you belong to general or OBC category, you can get admission in a good government college. If you belong to SC or ST category, you can get admission in any of the NITs.

Opt for the engineering branch that you love the most and are most passionate about. Analyze the future work conditions, scope and growth prospects before taking admission in the same.
You can also opt for psychometric test comprising of aptitude, personality and career interest to clear confusion.
Check the link below for college prediction :
https://www.shiksha.com/kcet-college-predictor

Yes, you can and there are many colleges for the same. I am listing few of the best colleges there:
Sir JJ School of Art
Rachna Sansad School of Design
Pearl Academy
Raffles Design International
Aditya College Of Design Studios and many more.

You can appear for JEE Mains exam next year or if you want to go in defense services, then NDA is a good choice for you.

Hi Shankar,
No course can guarantee you a job or will not help you getting a job if you are not clear with what you want. So, weigh your likes and dislikes, figure out your career plans and decide. Here are some of the courses which can be pursued after PCM which are always in demand, see what interests you.
Engineering (Petroleum Engineering, Chemical Engineering, Core Engineering Branches such as Mechanical, Electrical and Civil Engineering, Instrumentation and Control Engineering etc can fetch high paying jobs)
Teaching
Architecture
Biotechnology
Scientist (Research in an area of your interest)
Aviation
Government jobs
I hope it helped.

Hi Arshaak,
The best thing for you to do is to stick to your syllabus like NCERT and CBSE. Nothing comes out of the syllabus and referring to too many external reference books won't help. Practice a lot from previous years sample papers. Improve your weak areas. With dedication and hard work, you will do well.

Hi, it's clear that you should go for engineering as you are much interested in Maths but you are also having another option that is B.Sc in Maths. It has also a good scope after doing B.Sc in Maths. You may go become a Professor of college or any university.
Good luck.

May I know your interest to guide you better?

It depends on your interest. Can I know your interest?

After class 12th, you can't earn lots of money. So, you should go for Bachelor degree.