CBSE 12th

Call from IIM will depend on your score that has to be above 99% at least. Your class 10th and class 12th percentage are fine.

Pure Science? Is it Physics, Chemistry and Biology? Then you should check out this link for possible choices. https://www.shiksha.com/courses-after-12th/science.

Here is a thing. Everybody has a different opinion. So here I am going to say what I think. And what I think is taking a drop is not an option. Go for the physiotherapy seat if you want to become a physiotherapist. In the end, it is your decision!

When your results relfect on the screen, the top 5 subjects are counted officially by CBSE for their merit list preparation. CBSE prefers a Core subject like CS IP, Hindi over a vocational subject like Physical Education, Music.

Yes, of course, you are eligible for taking admissions in B.Sc (Hons) in Mathematics if you are a commerce with maths student.

You can do BCA where you'll learn some coding languages but you can't do B.Tech in CS.

Dear Suman,
You should opt for B.com or BBA for Maharaja"s college. This college is about a decade old.
Kindly follow the link below to read reviews and important information about the college.
https://www.shiksha.com/accounting-commerce/course/b-com-maharaja-s-college-university-of-mysore-272681

Long distance B.Tech courses don't turn out to be very well because you are deprived of the hands-off practical experience that regular fill time engineering courses offer. However, if you are determined to pursue this, there a plethora of colleges and universities you can opt for. Choose a course that interests you and not just on the basis of usefulness and scope of the course.
All the best!