I am currently developing a windows store application, I need to connect my app with sql server 2008 R2 Db, some sql classes are not working in the WinRT API, please any one suggest me on this and tell me which RDBMS I can use to connect with.
You can't. The reason being that you can't put that kind of restriction on a store app, you should have no dependancy on an external database being available.
You can use sqlite however, and here is a guide: http://timheuer.com/blog/archive/2012/08/07/updated-how-to-using-sqlite-from-windows-store-apps.aspx
If you are wanting to connect to a database to pull data from it (as an enterprise app for example) then you can use web services as a wrapper around the database.