MAT Exam 2021 Paper

Concept:The weekday pattern in the Gregorian calendar repeats after every $400$ years.So only the century-ending weekdays found in one $400$-year cycle are possible.Explanation:In $400$ years there are $97$ leap years.Total days $= 400 \times 365 + 97 = 146097$, which has $0$ odd days.Hence the same weekdays repeat after $400$ years.Taking $1$ January of year $1$ as Monday, the $400$-year cycle gives these last days of centuries:Year $100$ ends on Friday.Year $200$ ends on Wednesday.Year $300$ ends on Monday.Year $400$ ends on Sunday.This cycle then repeats.Therefore, a century can end only on Friday, Wednesday, Monday or Sunday.It cannot end on Tuesday, Thursday or Saturday.Answer:Correct option: C. I, II and III.