You can apply for Karnataka colleges, COMED K is the state level Entrance Exam for the admission to engineering programme in the state of Karnataka private colleges.

You can apply for JEE Main Entrance Exam, Generally all the state private colleges accept JEE Main score. If you belong to Bihar then you will be eligible to get into private colleges of other states.

If you mention the particular state, You wish to take the admission then I can help you better about.

Good Luck!