The correct answer is (b).
A common way to solve this problem is to use the following formula:
Day on January 20, 1990 = (Day on January 15, 1989 + 365 days) mod 7
In this case, January 15, 1989 is a Monday. Adding 365 days to this gives us February 28, 1990. This is a leap year, so we need to add 1 day to get March 1, 1990. March 1, 1990 is a Tuesday. Modulo 7, this gives us 2, which is Monday.
Another way to solve this problem is to use a calendar. If you look at a calendar for 1989, you will see that January 15 is a Monday. If you then look at a calendar for 1990, you will see that January 20 is also a Monday.
The other options are incorrect because they do not follow the formula or the calendar.