Yes, you can appear for WBJEE entrance exam for Self-Financing Institutions offering Engineering/ Technology/ Pharmacy /Architecture courses and State-Aided Universities offering Engineering/ Technology/ Pharmacy /Architecture courses.

To check in detail about the eligibility criteria you can refer below link

WBJEE Eligibility Criteria

Good Luck!!

You can appear WBJEE exam. But to get admission in Gov. colleges you should have the domicile of West Bengal.  In Self Finance colleges you can apply without  having the domicile of it. For further information about the eligibility you can go through with given below link.

WBJEE Eligibility

Good Luck!