Dear Amarendra

Amarendra not an issue you can do the Class 12th board from any private school but it should be under State / Central / ICSE board or may be NIOS will only be acceptable during the time of counselling of both JEE mains and Advance. Below the link is given through which you can able to check the further details about that.

https://engineering.careers360.com/articles/jee-main-eligibility-criteria

All the best

Hello amrendra,
What do you mean wih private? You will complete you 10+2 from private school then also no problem. For IITs, your 10+2 % is 75.
Here is the eligibility criteria for JEE main
https://www.google.com/amp/s/engineering.careers360.com/articles/jee-main-eligibility-criteria/amp
Good luck.