According to my admission, my default centre is at Kollam ( Kerala state), which is a newly started local centre. But it is not in exam centre list.Can we appear in exams from this local centre ?

Generally nearest exam centre will be the default exam centre. You may contact your local centre to know your default exam centre. For phone number/address of local/state centres, click at http://www.amiestudycircle.com/centres.htm
A blind approach is to fill code number of exam centre of your choice in the exam form and enclose an application stating the reason of selecting a particular exam centre (such as you are staying in that city for few days, company project in that city etc.). You will definitely be given exam centre of your choice.