how can I know the remaining balance in my bsnl pre-paid data card on line without removing the sim then entering it into a mobile device and then call *112#,

Almost all DATA cards support USSD codes, see your card and you can dial *123*6# to know your data balance without removing SIM from data card.

it did not work. in USSD there is a provision to send message no calls. and while calling it did not work at all

Yes, USSD are not call, they are special kind of message. I also use BSNL 3G sometimes, I just use USSD to remaining data. I use *123*6#. In my case , it works only before making data connection, for next I need to reconnect USB modem.