What exactly is C# version of Java RMI?
I want to invoke the methods of client from the server, ping the client from server etc.
How the server and client communication is done with c#?
As svick said in his comment Windows Communication Foundation would be the technology in question.
Introduced in .NET 3.0, its goal was to pull together all manner of client-server communications, replacing various disparate methods (webservices, remoting, message queueing, etc.) with a single unified framework.