I recd huge internet bills, without my knowledge data is being transferred, what is the solution?

Go to the care center and ask them for the hours you used with ful datails they will give it to you within tn days,check the details if you find anything wrong the go to the nodal officer of the region and file a complain they will surely take care that. And from your part go to the folder that has been created during the installation of modem and check the log books for login and the hourly you used it. I think after all this you will surely get the answer

Always give clear questions ?
you are asking a question which has no feedback from your side eg what is your plan ? which ISP you are using and you may be making mistake yourself and you may be under wrong impression also whether you have checked with your ISP regarding this
Data can not be transferred if that is the case change the modem to wired type in place of wireless or just disable wireless on your router.
here are so many reasons without proper input from yourside it is really not befitting to reply or reply may not be very clear to you.

your 'unseen' downloads may include . .
1. Windows automatic updates may b on
to switch it off just go to properties of the my computer --- automatic updates tab --- and turn it off
its seriously of no use
2. Antivirus Updates its very essential update to keep ur system safe but its of very low memory space so shud not make much difference hence let it b ON
3. Uploads from file sharing and P2P software like Torrents, Limewire , Ares etc .
better just remove this softwares these are of no use
and instead gives nice virus infection to ur system
4. Some external Pc might b connecting to urs using ur IP address and using ur net without ur knowledge
to avoid this check out the remote assistance option in the properties of my computer and just switch this feature off
and even see for the properties of ur dialer to see if there is any option for other pc connecting u
as bsnl has that feature so close that also

if still it doesnt help u than contact me anytime ill tell u further soln but according to me normally this shud work

If you have a limited download connection . . . your 'unseen' downloads may include . .
1. Windows automatic updates(can be turned on)
2. Antivirus Updates (small in size and useful)
3. Uploads from file sharing and P2P software like Torrents, Limewire , Ares etc . .(can be removed from autorun and should be used only when downloading etc.)
4. Spyware can cause data transfers (Use an antispyware)

Hope This Helps !

I;m confused with your info?
Do you have broadband? Or dial-up?
It sounds as if,you have a Trojan phone dialer,which has hijacked your internet;but that's only possible with dial-up, I think.
Did you scan your system?
More info please.

Solutions at your side
From Henceforth,

Install Firewalls
Study Web Traffic Log Files
Lookout for unwanted application programs sending / receiving web traffic
Install Anti-Spyware
Keep PC updated with Antivirus

Hope ur PC is not being used as a Zombie
Install Proxy Server
It saves bandwidth by maintaining cache of images etc
Use Mozilla Firefox 2.0+ rather than Internet Explorer 6.0
It transfers text/html ASCII data as GZipped Compressed streams
==> Faster page loading + less data transfer
==> Less Bill

Now Do Mark this as Best Answer ???

Call them and explain the situation. Contest the payment with the credit card company. Make sure your wireless is secured by creating a key so that others cannot use your bandwidth.

It may be due to viruses and spywares...Install a good antivirus and antispyware program