How many operations SQL Server support per connection I am making a multi threaded application in which I will use a single SQL Server connection and perform select, insert, update and delete.  

So once my application starts, it will open connection with SQL Server and then multiple threads will run each doing select, insert, update and delete (in no particular order) on multiple tables using the same connection.  

I want to ask how many operations can SQL Server handle for a single connection?
a multi threaded application in which I will use a single SQL Server connection


Bad idea. A database connection usually is not thread-safe, and as you suspect, at any one time one connection can only execute one statement. You should open a separate connection for each application thread instead, or at least use a connection pool shared between the threads.