battery problem

do mean you are using it and browsing for 10 hours straight ? Then that sounds about right. if you mean just on standby with the screen off for 10 hours then that would be a problem.

Most battery problems can be traced back to as follows;

dodgy battery – buy a second battery with external charger from ebay (for a reasonable price you should get a genuine one) and see if it is improved. this also gives you a spare charged battery to keep with you for long trips too. I’ve heard even some of the genuine ones have problems and have been replaced by samsung
battery bedding in – it might take a while for a genuine battery to get a proper charge. Give it a few weeks and see if it improves.
Version – Even early versions of ICS (even up to 4.0.4) were very crummy. I’m running PDA:LQR and its very much improved. 5-10% drain overnight in standby mode. It still chews the battery when in use.
Apps running in the background not allowing sleep – Check the blog post on this site on how to install some apps to troubleshoot which app is stopping your phone going into sleep. usually only a problem if you are getting charge loss when the phone should be sleeping

This does talk about ICS but the same could be true for GB.  you need to find which app is stopping your phone going into deep sleep mode. Once done get rid of that app or update it;

https://www.allaboutgalaxynote.com/how-to-solve-battery-issues-after-ics-update-in-your-galaxy-note/

Are you running rooted firmware or sideloaded apps ? This could be caused by a malicious app. You could also try a clean factory install and install your apps one by one until you find which was causing the problem but using the linked process above is better.