What will India do if Pakistan suddenly fires a nuclear missile towards Delhi?

Most likely Delhi will not be the first target of the Pakistani nuclear missiles as Delhi host embassy of more than 150 plus Countries.

But in case Indian radars detect the Pakistani nuclear missiles coming towards Delhi, then they would have very little time (a couple of minutes) to react. S-400 or indigenous missile defense system would try to intercept it. But I think Pakistan would fire a volley of missiles knowing Indian air defense capabilities. There are high chances that at least one missile would hit Delhi. I don't think that Pakistan would only Target Delhi but most likely it would Target 3–4 cities. Once Pakistan attacks then it would be Indian turn and Pakistan may not survive Indian retaliation so they will try to attack more cities in 1st wave.

After the attack, India would respond in kind. India will probably attack Pakistan from nuclear missiles fired from land, submarine and fighter aircraft. At least 200 IAF fighters would go airborne and 20–30 would be carrying nuclear war heads. Tens of missiles would be also fired. India would overwhelm Pakistan with its response so that Pakistan doesn't have capability to attack India back.

Millions of lives would be lost and the people would suffer most. It will bring unimaginable damage to people of the sub-continent. No one wins a nuclear war.