Neeraj,
This issue doesn't have to do anything with
JSP. It's just a reference problem. When you say
list1.add(0,"test");
At this point the object reference in list1 is same as the object reference of the List in request.
If you don't want the changes to list1 to get reflect in the list hold by request object, then create new list1 object passing values of list in request as shown below.
List list1=new ArrayList((List)request.getAttribute("months"));
Instead of ArrayList, use the appropriate concrete class you are using
-Manoj