​What was the day of the week on 28^th May, 2006?​

We have, 28^thMay, 2006

2005 years + (1 January 2006 to 28 may 2006)

For every 400 years, there are 0 odd days

400 years × 5 = 2000 years in 0 odd days

Now, 2001 to 2005 years

Ordinary years have 1 odd days

Leap years have 2 odd days.

2001 to 2003 is ordinary years + 2004 leap year  + 2005 is ordinary year

3 + 2 + 1 = 6 odd days

Odd days in 2006 (up to 28th May):
January → 31 days → 31 mod​ 7 = 3 odd days
February (2006 is not a leap year) → 28 days → 28 mod 7 = 0 odd days
March → 31 days → 31 mod 7 = 3 odd days
April → 30 days → 30 mod 7 = 2 odd days
May → 28 days (up to 28th) → 28 mod 7 = 0 odd days

3 + 0 + 3 + 2 + 0 = 8 mod 7 = 1 odd day.

Total odd days = 0 + 6 + 1 = 7 mod 7 = 0 odd days

0 odd days correspond to Sunday

Thus, the correct answer is (a)