Hello candidate,

Of course you can appear for JEE Mains and Jee Advance if you are appearing for intermediate exams from State board, provided you satisfy the eligiblity criteria. 

You can find the eligibility criteria for JEE Mains by following the below link:

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

You can find out about the eligibility criteria for JEE Advanced by following the below mentioned llink:

Https://engineering.careers360.com/articles/jee-advanced-eligibility-criteria/amp

Hello.

Of course, students of various boards other than CBSE can attempt the Jee after completion of 12th.

Refer this link to check the complete eligibility criteria:

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

Good luck!