Is caste certificate of one state and domicile of another state valid for government exams?

This is not valid because the list of  Castes is State specific. As such a member of SC/ST/OBC is eligible for benefits in his state of origin only. A member of Backward Community, who migrates to other State is not entitled to get benefits, from the state of migration.

Moreover, there are cases where my caste may be considered as OBC/SC/ST in my home state, but in the migrated state it might not be considered as part of a backward community. So it is better to give caste certificate and domicile of the same state that is either your home state or migrated state.