Hi Saqib, it's advisable to reappear for the subjects that couldn't be cleared in the first attempt. As a matter of fact, since failing in 3 subjects means a compartment, you can also appear for the same subjects again in a compartment exam, as scheduled by CBSE.

Coming to the private exam, if you would feel like giving a private exam while devoting time to some other important work such as a family's business or like that- It's always good to appear for a private exam.

Hope that answers your query.

Best wishes !!