Yes, you can trade in both Index and Stock Options Expiry Contract on the expiry day. We also, convert all the Expiry Day Stock Options and Stock Futures  Contract to MIS mode on the date of expiry to have them auto squared off wherever possible.

This is to avoid risk of contracts becoming ITM in the last moment but not been able to cover positions due to lack of buyer or seller on the expiry day, thus forcing to fall under physical delivery.

However, if you want to take position on the expiry day with a willingness to go for physical delivery, then the following are required

1) An email consent to one day prior to expiry day to hold or take fresh position on the expiry date contract at your own risk

2) To have a POA enabled demat account with  us

3) In case of holding short positions which involves delivery of shares, the required number of shares should be available in the demat account 

4) 100% of the Contract Value should be available in the Ledger to meet obligations 

All expenses, penalties, charges, loss etc., occurring due to the physical settlement process, should be borne by the client and hence, it is suggested to understand the physical settlement process thoroughly before opting for it.

Also read

Why am I blocked to trade in certain Options?