A century year is a year that is divisible by 100 but not divisible by 400 (like the year 1900). For such years, the last day (31st December) cannot fall on certain weekdays due to the leap year cycle. Specifically, the last day of a century can never fall on a Tuesday.
This is due to the leap year correction cycle where the day of the week shifts based on the year's divisibility by 4, 100, and 400. After applying this rule, we find that Tuesday cannot be the last day of a century year.
Thus, the correct answer is (2) Tuesday.