If we / my child wants to, how can an open learning child give 10th/12th to join a college?

These are the current options available:
The child can give 10th/12th via the central government’s NIOS (National Institute of Open Schooling). Some state boards also allow private candidates.
Another interesting option is to join a school around 9th/10th grade so that that child can give 10th via CBSE or ICSE or state board.
If a child is considering going abroad then International General Certificate of Secondary Education (IGCSE) – what is known as Cambridge board, is also a good option.