I am using C#. I have created a class which can be included in any c#.net project (desktop or web based), but I want that only 10 objects will be created in that application
I believe that you want some form of the multiton pattern.
The multiton pattern is a variation on the singleton pattern, but that allows for n instances of an object. Much like how the singleton class has a static variable to hold the single instance, the multiton is often implemented with a static array or map of instances, depending on how you want to access the instances - arrays only allow for numerical access, but by using a map, you could provide String keys to your instances, making them named.