Does an Ex-President of India qualify to become Prime Minister of the country?

Yes. An ex-president is qualified to become Prime Minister of the country if his party got a majority in the parliament and his party members elect him as their chief. Technically all this is possible, and even the constitution says it is possible.

But on the ground reality, nothing of that sort has happened in India till now. Presidents after serving their term remain as mere citizens with a nominal security and lead a normal life of their choice. We always have presidents who are above 60 - 70 years of age and who are not actively involved in politics.