No, you cannot file an RTI to private institutions directly.
The RTI Act applies only to public authorities.A public authority is any government department, body, or institution funded or controlled by the government.Private institutions are not considered public authorities unless they get substantial government funding.
If a private body performs public functions, it might come under RTI indirectly.You can still get information about private institutions from the government body regulating them.
So, RTI is mainly for government-related information.

No, you cannot file an RTI directly to private institutions unless they are substantially financed or controlled by the government.
A 'public authority' under the RTI Act, 2005 is defined as:
Any authority, body, or institution of self-government established or constituted by the Constitution, law made by Parliament or State Legislature, or government notification.
It also includes bodies owned, controlled, or substantially financed by the government, including NGOs receiving substantial government funds.
In short, if a body is not governmental or publicly funded/controlled, it doesn't qualify as a public authority under RTI.