Hello Amrit,
Yes, some universities in India permit you to do one regular and one distance mode. You can do 12th standard through regular mode and Diploma course through distance. But, the problem is that it is difficult to concentrate on both the 12th standard and Diploma course at the same time.
Some of the universities allow doing open learning if you are doing a regular course from some specific institution.
You have to check the list from their official website.
It is better to talk to your school authorities. They can help you with this issue.
Good luck!
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