how to pay maintenance

To start with, You can give crossed cheque in her name.  That is OK.  Thereafter, you can get her account number details and then directly transfer the amount from your bank to her account. That should also be ok.  So long as you will be able to establish that amount has been paid by you to her, that should be ok from your point.  If you take care of this, then pl do not insist on signature/acknowledgement etc. etc.  

Considering maintenance amount be 10000/-  per month.

First time you pay any way by account payee cheque or cash in front of judge.

From  second time onwards you can make account to account transfer, ask her account details for depositing maintenance.