I read at dp using adsense on a web which is hosted at wordpress.org is not allowed? I want to know the reason if we can use adsense for free webhosting then why wordpress.org (freehosting ) is not allowed?
They don't allow it because they chose not to allow it, it doesn't have anything to do with it being a free service. If you want to have ads on your blog get yourself a domain and use Worpress.
In WORDPRESS.COM, you can't use any javascripts, hence you can't use Google Adsense. And not WORDPRESS.ORG my dear friend!
wordpress.com is where you host your blog and wordpress.org is where you download the software to install in a self hosted domain.
The best way to go is to get paid hosting plus your own domain, install Wordpress and use Adsense Ready Wordpress themes (-these are my themes, feel free to use them if you like them).
The best bet is to purchase a domain. This way you really own the site. I've heard of some cases where prople have found their blog has vanished from wordpress.