CBSE 12th

Of-course. HSC in any stream is the eligibility criteria for BBA admission. As a commerce student, it will be more suitable for you. Mathematics is actually not commerce combination. But now a days commerce with Maths/ Computer Application - Science are available. This will help commerce students to turn their career into Science subjects such as BCA/B.Sc-CS/IT, B Arch (Maths) etc.
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MBA is a best potion for getting jobs in Australia after graduation. IELTS minimum 7 is mandatory for Masters programs

SOL should be your first preference.

You can try for Jaypee, Amity, Galgotia, KR Manglam, etc.

Not really
You can justify yourself in the interview that why you have low scores. You should carry a genuine and acceptable reason for that.

Nursing is most suitable option for you to get job and citizenship in Australia and Other countries. Nursing profession in UK,US, Australia etc. are highly paid and reputed. So please join for Professional Graduation (B.Sc- Nursing) in Nursing. It will take 4 years to complete the course. There may be 1 year clinical internship in some universities. But it will considered as One year experience which is compulsory for getting job in foreign countries. You need to clear IELTS also.
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You can seek admission in BBA even if you are from Biology stream. BBA is a generalist degree open for all stream students. You will not face any challenges except you may be required to put extra effort in Maths & Commerce subjects.

Please tell us your area of interest, so that we can guide you better.

You can go for IIIT Lucknow, NIT Bhopal and IIEST Shibpur.