Hi anu, 

Yes you can apply for management seat in tamil nadu self financial college only through all India quota counselling. In which you would have to choose the private colleges in the counselling form of all India quota counselling. 

There you have the chance to get a seat out of 15 % quota.  But it would be expensive. It will be better to get a state quota seat. And  bihar self financing seat will also be expensive but not that much as you get in other state. 

Go for the counselling and do the choice filling for the colleges on the above you want to have most. 

For any other query you can ask us.