Which of the following Prime Minister has served a term of 13 days?

The correct answer is Option 1 - Atal Bihari Vajpayee

The Prime Minister who served a term of 13 days is Atal Bihari Vajpayee.

Atal Bihari Vajpayee was the 10th Prime Minister of India. He interestingly held the office for three non-consecutive terms:

First term: 13 days in 1996 (his government fell short of a majority)
Second term: 13 months from 1998 to 1999 (again, his government lost a vote of confidence)
Third term: A full five-year term from 1999 to 2004