Please can some one explain me how to use Fire-bug add-on to check about whether Ajax request successfully send from our application ???
When you turn on Firebug, there's tab called 'Network' - there are shown all requests, especially ajax. The network tab allows you to filter requests and check request/response headers, status code, and message.
So, if you turn on Firebug and open Network tab (it's possible you'll have to enable tracking first, in that case it will show appropriate message), you will see if there was a request, where you expected it should be.
To see only ajax requests, check XHR on top bar, just under general tabs.
It will display in 'console' tab in firebug. i show you ajax call and request. it show ajax request like if ajax is successful then is gives 200 request and display the data or if the ajax request if fails is gives you a 301 request or some other request.