Mr Ambati i have gone through the code of two servlets and find that you placed HttpSession session = request.getSession(); this code. But what you have to do is get session through reqest.getSession(false) in the SecondServlet, and one thing you have to do in Second servlet is dont set any attributes in the second servlet.
Then you see the difference by first executing FirstServlet and SecondServlet what you get is the result what you are getting now.

Now close the browser and open a new window browser and execute the SecondServlet then you can find the difference what i am going to say.
Thats all i can say. If you still dont understand no one can help you.