You are doing a great job mentioning where the questions come from Jothi
B is an inner class (non-static nested class) of A so it needs an instance of A to exist before an instance of B can exist. So that's what the new A() is for - to get the outer instance of A. Now we can use our instance of A to create an instance of B. The Java syntax for that is new A().new B(). So now we have our instance of B together with its containing instance of A. We can now call B's methods on this instance of B. So new A().new B().m1() calls method m1 on an instance of inner class B contained in an instance of A.
To be frank and honest, I know a good deal of information with respect to inner classes and nested classes. But when I was answering the question from Dan's website, I didn't notice that class B is inside class A. I failed to notice it and I was wondering how we can do new A().new B() on normal classes other than innser classes. In some of the mock exams that I took from whizlabs, I have comitted similiar mistakes where I forget to see the code throughly. So I leant that I should see the question with my both eyes wide open.