Yes, you can take a GST registration at your residential premise, but there are certain conditions. For example, your flat number, colony, nearby landmark, state, village, etc., along with the PIN code, must be clearly mentioned, and you must mention this business address while applying for the GST registration.
After registration in GST, the GST department will send you a welcome kit. If you receive that kit, consider your premises verification completed, and the officers will not come to check your place. If the welcome kit is returned, it will be assumed that your residential address is incorrect, and your GST number can also be suspended.
