Explanation:

Correct option:4

Solution:

Given: 12 January 2019 was on Monday.
The number of odd days between 14 December 1917 to 12 January 2019
Note:- Generally in 100 years, there are 5 odd days but when the century year is a leap year then 1 extra odd day is added and hence, the total odd days is 6. 
Century years which are leap years:- 400, 800, 1200, 1600, 2000, 2024, and so on. 
The number of odd days between 14 December 1917 to 14 December 2017 = 100 years = 6 odd days (2000 is a leap century year)
The number of odd days between 14 December 2017 to 14 December 2018 = 1 odd days
The number of odd days between 14 December 2018 to 12 January 2019 = 17 + 12 = 29 days
So, The number of odd days between 14 December 1917 to 12 January 2019 = 6 + 1 + 29 = 35 days = 36/7 = 5 weeks and 1 odd days. So, 14 December 1917 will be = Monday - 1 = Sunday.
Hence, the correct answer is "Sunday".