Who among the following was the shortest-serving Prime Minister of India?

The correct answer is Gulzarilal Nanda.

To determine the shortest-serving Prime Minister of India, let us examine the tenure details of each of the given options:
1. Atal Bihari Vajpayee: While his first term in 1996 lasted for only 16 days, he went on to serve subsequent terms (from 1998 to 2004), making his total cumulative tenure much longer.
2. Gulzarilal Nanda: He served as the interim Prime Minister of India twice. His first term was from May 27, 1964, to June 9, 1964 (13 days), following the death of Jawaharlal Nehru. His second term was from January 11, 1966, to January 24, 1966 (13 days), following the death of Lal Bahadur Shastri. His individual stints are the shortest of any Prime Minister in Indian history.
3. Chandra Shekhar: He served as Prime Minister from November 10, 1990, to June 21, 1991, which is approximately 7 months.
4. Charan Singh: He served as Prime Minister from July 28, 1979, to January 14, 1980, which is approximately 5 and a half months.

Comparing the tenures, Gulzarilal Nanda's service of 13 days in a single term makes him the shortest-serving Prime Minister of India.