What is Nature of Business and the Business code for the Google Adsense Income?

I'm no expert, but I have to agree with Mr Ready that the nature of the primary income generating activity is the determining factor.

Not necessarily the TDS, because you don't decide whether or not to deduct TDS and what section / rate to apply for this TDS deduction. The same activity may have different meanings for the provider and recipient.

That said, there is definitely a lot of room for interpretation because of the lack of clarity on the meaning of "business" when it comes to income tax. And the only way you will know if you can use (or get away with) 44ADA is to is to try it by returning your income under this option. At worst it will not be accepted and you will be asked to re-file and pay the applicable shortfall / interest etc. You should be prepared to accept that, if it comes down to it.