Hello Aspirant,

Yes one can repeat class 12th from RBSE board even if he/she is private and instead of wasting your year what you can do is you can appear for improvement examination which is conducted in the month of June/July, or what you can do is either you can appear for NIOS or any other recognized open board and they provide the facility for On Demand Examinations and for the same you can appear either in the subject in which you have less score or for some other subjects in which you want improvement, from this you can save your year but make sure to check the applicable dates on the respective board's official website.

I hope this information helps you.

Good Luck!!