I read on axis website somewhere that they do check your soft enquiries before approval. It was suggested to not pull your report unnecessarily. I can't find it now. Also, I don't know what the allowed frequency is.
It's already been few days since the offer has started. I mean you can apply for it, if you have other bank's credit card.they seem to have made this card lifetime free with zero registration fees now. got an alert from flipkart. not applying though.