BACKCalendara) Odd Days : The number of days more than the complete number of weeks in a given period is number of odd days during that period. b) Leap year : Every year which is divisible by 4 is called a leap year. Thus each one of he year 1992,1996,2004,2008,2012,,etc, is a eap year. Every 4th century is a leap year but no other century is a leap year thus each one of 400,800,1200,1600,2000,etc is a leap year. None of the 1900,2010,2020,2100,etc is a leap year. An year which is not a leap year is called Ordinary year. c)An ordinary year has 365 days. d) A leap year has 366 days. e)Counting of odd days : i)1 ordinary year = 365 days =52 weeks+1 day,Therefore An ordinary year has 1 Odd day. ii)One leap year = 366 days =52 weeks+2 days, Therefore a leap year has 2 Odd days. iii) 100 years = 76 ordinary years+ 24 leap years = [(76*52) weeks+76 days]+[(24*52)weeks+48 days] = 5200 weeks+124days=[5217 weeks+5 days] therefore 100 years contain 5 odd days iv)200 years contain 10(1week+3days), i.e 3 odd days v)300 years contain 15(2 weeks+1 day), i.e 1 odd day vi)400 years contain (20+1), i.e 3 weeks,so 0 Odd days similarly each one of 800,1200,1600,2000,etc contains o odd days. Note: (7n+m) odd days , where m less than or equal to 7 is equivalent to m odd days ,thus ,8 odd days = 1 odd day etc. a) Week Sunday - 1 Monday - 2 Tuesday - 3 Wednesday - 4 Thursday - 5 Friday - 6 Saturday - 0 b) Month jan - 1 july - 0 feb - 4 Aug - 3 Mar - 4 Sep - 6 Apr - 0 Oct - 1 May - 2 Nov - 4 june - 5 Dec - 6 BACK |