Hi
Although such operations of coaching classes in residential areas is illegal as it creates chaos in the residential area, yet it has been operative in many cities.
There have been cases in Jaipur and Delhi where Court has ordered such coaching institutes to evacuate and move elsewhere in commercial areas.
On a lighter note, I would suggest that it won't be much a cause of concern if the institute is small and other residents of the building have no issue. Also, the building society rules must not prohibit such commercial use.