This depends on any such arrangements or agreement between the parties and banks.

There's no legal infirmity in it.

it up to the bank to decide whether they would accept another FD of other bank as security deposit 

It should accompany an affidavit or other supporting document in favour of bank to do the same 

It's depends on bank, whether they would accept other bank Fd's as security deposit. 

1. Fixed deposit of another bank can be made a security for another bank if there is an agreement in that regard.

2. in other words specific lien can be created to make this a security for a different bank.

3. Another option is to make a bank guarantee.

Sir it completely depend on the policy and agreement of the bank. 

1) If the customer has taken any loan from second bank for security purpose may accept deposit of another bank and can send mandate in that particular bank.

yes that is permissible

the original FD receipt can be submitted as a security 

Yes, it can be accepted as security deposit if offered by the said agency and if the daid FD is without any encumbrances.