Hello Dear,

Yes, you can appear for two state board Join Entrance Examination (JEE). But if you comes under reservation category then the state which domicile you have you will get benefit in that state only for the other state you will be consider a general category. For more details about these two entrance examination you can follow the link:

https://engineering.careers360.com/articles/wbjee-eligibility-criteria

https://engineering.careers360.com/articles/jeece

Good Luck