Question: why we create private classes in c#? As we know that private class couldn't be make base class and we couldn't derived the classes from them.And what is the use and purpose of private class?

Answer: 
Private classes (or private anything, really) are important because control of scope is important, due to the notion of [encapsulation](https://en.wikipedia.org/wiki/Encapsulation_(computer_programming)).

If you are building a library with "private" (`internal`) classes, your library can use those classes while anyone using your library will not be able to even see them. This can hide implementation-specific details that you wish to conceal.

If you are building a class that has private nested classes, the containing class can use those private classes without anyone else being able to see them. Again, you can use this to hide implementation-specific details that you wish to conceal.

If you don't hide implementation-specific details (e.g. by making a private or internal class public) then it becomes more difficult to change the implementation, since you can't be sure that users of your library haven't created dependencies on those classes. But if they are non-public, you can change them, replace them, or remove them, all without any worry of disrupting external dependencies.
Private classes can only be created inside nested classes and are used to retrict access and to only be used inside this nested class.