Solution:

By the definition of an Union Territory, should NOT have an Legislative Assembly. It should be governed by the Central Government with a lieutenant-governor or an Administrator.But, the Parliament of India can pass a law to amend the Constitution and provide a Legislature with elected Members and a Chief Minister for a Union Territory, as it has done for Delhi and Puducherry.
The President appoints the Chief Minister and Ministers for Union Territories, who will hold office during the President’s reign, although, they are sworn in by the Lt. Governor.