NATO is the most successful political and military alliance in human history precisely because it was built on a foundation of core shared values: democracy, free markets, the rule of law, civil liberties.
Any strategic partnership with Russia would be a matter of convenience, and those partnerships never last.
India has the world's 6th largest economy, Russia isn't even in the top ten. Outside of oil, arms, and vodka, Russia doesn't export much to the world markets.
As I understand it, India is a major player in IT and computer hardware on developing world markets, and India has given every indication of having a true entrepreneurial spirit in the way Russia does not. Probably because rule of law and a dynamic civil society does not exist in Russia