The hard facts is no you can not use any free domains with Adsense they will not allow it. But if you can not spend 6 – 10 US dollar on a domain name, maybe should not start with Google Adsense.
Most people know this “to make money you need to spend money” and that is true in this case. Google is looking for quality pages now and mass pages with same content will be punished and maybe banned from Google Adsense. Go for quality and some domain register like go daddy give away a free 50 dollar Adword coupon that you can use to drive your first traffic to your new domain. When you ready with your name you can apply for Adword here and use your cupon

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