Government Bans Mobile Gaming During School Hours

Imagine the Central Government introduces a notification in The Gazette of India making it an offense to operate a mobile phone or engage in mobile gaming during school hours. Students caught doing so would face penalties, including detention, suspension, and even a fine imposed by their school authorities. If a student, let's say, Rohan, is caught playing mobile games during school hours and is thus denied permission to appear in the board exams due to continuous suspensions, would it be justified if the CBSE decides to bar him from taking the exams?

In this scenario, under Administrative Law, would the CBSE's actions be arbitrary or would the government's notification be considered a valid exercise of its legislative powers? Can the government dictate to private educational institutions what their policies should be during school hours?