Which day is celebrated as the UN day?

The correct option is 24th October.

United Nations (UN) Day is celebrated annually on October 24th to mark the anniversary of the official entry into force of the UN Charter in 1945.
With the ratification of this founding document by the majority of its signatories, including the five permanent members of the Security Council, the United Nations officially came into being.
In 1947, the United Nations General Assembly declared 24th October as a day dedicated to making the aims and achievements of the organization known to the peoples of the world and to gaining their support for its work.