First day of the month is Tuesday and Last day of the same month is Monday. Then which one will be that month ?

We know that the day repeats after every seven days. 

Given that first day of the month is Tuesday

i.e    1st - Tuesday

1+7 = 8 - Tuesday

8+7 =15- Tuesday

15+7=22-Tuesday

22+7=29-Tuesday

But given that last day of the same month is Monday

It is possible only in he month of Febuary with 28 days.