CBSE 12th

Olympiad exams are competitive examination conducted at school level. It is totally based on the school curriculum and is conducted by various independent organisations. These competitive exams aim to provide exposure to students and make them ready to face any challenge in future.
Moreover, these exams have become a status symbol with many parents and also a big business of making money for the schools and also the organisation.
But these exams are not meant to enhance your career anyways.

English (core) i.e. compulsory in any CBSE school.
Accountancy
Business Studies
Economics
Mathematics
One Language paper i.e. Hindi or English (selective)
Physical Education (not compulsory)

You must also clear an engineering entrance examination as applicable to your college with a good score.

Yes, you can repeat.
All the best.

Yes, after 12th PCM, you can pursue B.Sc in maths. The admission will depend on the cut-off released by the university. If you meet the criteria, you will get admission in DU.

Hi Sagar Nikitha,
Please elaborate your stream and subjects as without which it is impossible to suggest.

Hi Sourav,
You haven't specified the subjects so it's difficult to suggest if medicine or engineering or agriculture would be apt. Other courses can include bio technology, geology, forensic science, pharma, etc. Use this career page to get guidance:
https://www.shiksha.com/careers

Hi Sandeep,
You can opt for B.Com or pursue a Bachelor's degree in economics, actuarial sciences, mathematics or statistics. BBA and other business related programmes can also be taken up. Go through programme structures and check what all interests you. You have to know his areas of strengths and weaknesses. Let him analyse.

Hi Rakshit,
A PCM student can study business related courses. You can consider bachelor of business administration. Other options include bachelor of marketing and communication, bachelors programme in business,
bachelor of business communication, etc.

Hi Heera Lal,
You should mention your stream and subjects irrespective of the location. Please share details.