Opening a corporate office different from registered office

sir you can inform the ROC about the change of address of corporate office.

Which RoC?

The one in UP or Bihar or both?

Will any backup documentation be required? and can the RoC be approached by a company representative in person?

sir ,

1. you need to follow a procedure of change of registered office from one state to another state so please contact practicing  company secretary or any other professional because 
2. and yes u need to maintain u r books of account @ u r new office.

There is no need to inform abour the address of your corporate office.
ROC is concerned only with your registered office address .

Board Meetings can be held anywhere,

Statutory Books of accounts are required to be kept only at Registered Office