If a top level executive ( GM onwards) has a facility of Mobile phone provided by the Comapy , then is it mandatory to open that mobile phone for 24 hours or only for office timing??

There is NO law governing this activity at all.
This would be down to the particular company and the contractual terms of employment.

As a side, if my company mandated when I was to use my company phone, then I would refuse to have one.

At my company the expectation is that if they provide the mobile phone then they expect the employee to be available and reachable at any time, including evenings, weekends, and holidays.

Usually, general managers and top level officers are not required to observe normal office hours. So in exchange for the privilege, we may presume that they should at least be reachable at all times.