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I would suggest to you one university best in north India with NAAC A+ GRADE. If you want to do B.Com. Why not you go to this university. Chandigarh University has good academic excellent and find more.

Yes, you can. Bachelor of Business Administration BBA An undergraduate course is designed to enhance leadership skills, management skills, interpersonal and communication skills. If you are interested in Management related field so this is better option for u. I am sharing you the link below, you can find all the relevant details related to respective Course. Link:-
https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/bba-bachelor-of-business-administration-chp&ved=2ahUKEwia_Y3wnJXqAhUkwzgGHVzfBaMQtwIwIXoECAgQAQ&usg=AOvVaw0UFOtPoazkGzO7pQRBnD47
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AIIMS only provide M. Biotech in the stream of biotechnology which is a master's degree. The college which provides B.Tech Biotech like IITs, NITs, CFTIs and GFTIs etc. You have to gone through JEE-Mains then JEE Advanced. The 12th subjects combination for JEE Main for Biotechnology is given below. Subjects: Candidates must have to take minimum 5 subjects in 12th/equivalent examination. Candidates appearing for JEE Main must have passed class 12th with Physics & Mathematics as compulsory subjects along with anyone from the Chemistry/Biotechnology/Biology/ Technical Vocational subject.

The B.Tech fee details of asked colleges are given below.
1. BITS Mesra : Rs 268000 First year fee
2. SRMIST-Kattankulathur (KTR) : Rs 250000 First year fee
3. Manipal University : Rs 325000 First year fee.

You can apply for it in the online mode.

The following are the BCA colleges in Mumbai offering BCA without Maths at 12th level.
1. Amity University Mumbai
2. VVES Vikas College of Arts Science & Commerce, Mumbai
3. KPB Hinduja College of Commerce, Mumbai
4. Dr BMN College of Home Science, Mumbai
The following are the BCA colleges in Pune offering BCA without Maths at 12th level.
1. Tilak Maharashtra Vidyapeeth
2. Symbiosis Institute of Computer Studies and Research
3. Bharati Vidyapeeth Deemed University
4. SPPU.

No, there are no age criteria for BCA course but your minimum age should be above 17 years. Candidate should have completed 12th in any stream preferably Science stream with at least 50% marks with Mathematics as one of the subject of studies from a recognised Board are eligible for BCA course.