A person was born on the fifth Monday of February in a particular year. Which one of the following statements is correct based on the above information?

The correct option is "The 2nd February of that year is a Tuesday ".

Let us analyze the problem step-by-step to understand why this statement is correct.
The question states that a person was born on the fifth Monday of February in a particular year.

First, let us determine the number of days in February for this year:
Normally, February has 28 days in a non-leap year and 29 days in a leap year.
A standard week has 7 days. If a month has 28 days, it has exactly 4 full weeks (since $28÷7=4$). This means every day of the week (Monday through Sunday) occurs exactly 4 times.
For any day of the week to occur 5 times in February, the month must have 29 days. Therefore, the year in question must be a leap year, and February has exactly 29 days.

Next, let us find the date of the fifth Monday:
In a 29-day February, there are 4 full weeks plus 1 extra day (the 29th).
The only day of the week that can occur 5 times in a 29-day month is the day of the week that falls on the 1st of that month, which also falls on the 29th of that month.
Since we are given that there is a fifth Monday, the 1st of February must be a Monday, and consequently, the 29th of February is also a Monday.

Let us write down the dates of all the Mondays in February for this year:
1. First Monday: 1st February
2. Second Monday: 8th February (1 + 7)
3. Third Monday: 15th February (8 + 7)
4. Fourth Monday: 22nd February (15 + 7)
5. Fifth Monday: 29th February (22 + 7)

Now, let us evaluate the given options based on this schedule:
Since the 1st of February is a Monday, the next day, 2nd February, must be a Tuesday. This directly matches the correct option: "The 2nd February of that year is a Tuesday ".

For completeness, let us see why the other options are incorrect:
- "There will be five Sundays in the month of February in that year": Incorrect, because only Monday occurs 5 times (the 1st and 29th are Mondays). Sunday occurs only 4 times (on the 7th, 14th, 21st, and 28th).
- "The 1st February of that year is a Sunday ": Incorrect, as we established the 1st February must be a Monday.
- "All Mondays of February in that year have even dates ": Incorrect, as the Mondays fall on the 1st, 15th, and 29th, which are odd dates.