Ch.19:- Calendar : Exercise 1


1. What was the day on 1StJan 1901 ?
(a) Monday
(b) Wednesday
(c) Sunday
(d) Tuesday

View Answer
Ans.(d)
1st Jan 1901 means (1900 years and 1 day)

Now,
1600 years have 0 odd day
300 years have 1 odd day
1 day has 1 odd day

Total no. of odd days
= 0 + 1 + 1= 2 days

Hence, the day on 1st Jan 1901 was Tuesday

2. What was the day on 31 st Oct 1984 ?
(a) Friday
(b) Sunday
(c) Wednesday
(d) Monday

View Answer
Ans.(c)
31st Oct 1984 means (1983 years and 10 months)

Now,
1600 years have 0 odd day
300 years have 1 odd day

83 years have 20 leap years and 63 ordinary years.
= (40 + 63) odd days
= (103) odd days i.e., 5 odd days

10 months of the year 1984 have 305 days.
(Feb is of 29 days, being the month of leap year).
305 days have (43 weeks and 4 days) or 4 odd days

Total no. of odd days
= (1 + 5 + 4)
= 10 odd days or 3 odd days

Hence, it was Wednesday on 31st Oct 1984.

3.hat was the day on 14th Mar 1993 ?
(a) Friday
(b) Thursday
(c) Sunday
(d) Saturday

View Answer
Ans.(c)
14th Mar 1993 means (1992 years, 2 months and 14 days)

Now,
1900 years have 1 odd day
92 years have 23 leap years and 69 ordinary years
= (46 + 69)
= 115 days = 3 odd days

2 months + 14 days
= 31 + 28 + 14 = 73 = 3 odd days

Total no. of odd days
= (1 + 3 + 3) = 7 odd days

Hence, it was Sunday on 14th Mar 1993.

4. Prove that Calendars for 1992 and for 1997 are identical.

View Answer
Ans.
To prove the calendar for 1992 and 1997 to be identical we have to show that number of odd days between 31st Dec 1991 and 1st Jan 1997 is O.

Year          : 1992   1993   1994   1995   1996
Days         : 366      365     365     365      366
Odd days : 2          1          1         1          2

= 7 = 0 odd day

Since, the total no. of odd days between 31st Dee 1991 and 1st Jan 1997 comes to zero, hence it is proved that the calendars for 1992 and 1997 are identical.

5. On what dates of Aug 1980 did Monday fall ?
(a) 4th, 11th, 18th and 25th
(b) 3rd, 10th, 17th and 24th
(c) 6th, 13th, 20th and 27th
(d) 9th, 16th, 23rd and 30th

View Answer
Ans.(a)
We have to find, 1st of all the day on 1st Aug 1980 1st Aug 1980 means (1979 years, 7 months and 1 day)

Now,
1900 years have 1 odd day
79 years have 19 leap years and 60 ordinary years.
Which have 98 odd days = 0 odd day

7 months and 1 day.

Jan  Feb  Mar  Apr  May  June  July  Aug
31    29    31     30     31      30      31     1

= 214 days = 4 odd day

Total number of odd days
= (1 + 4) = 5

so,it was Friday on 1st Aug 1980, and 1st Monday of the month was on 4th and subsequently Mondays, of the month were on 4th, 11th, 18th and 25th.

6. On what dates of Dee 1984 did Sunday fall ?
(a) 6th, 13th, 20th & 27th
(b) 7th, 14th, 2ISt, & 28th
(c) 2nd, 9th, 16th, 23rd & 30th
(d) 1St ,8th, 15th & 22nd

View Answer
Ans.(c)
We have to find, pt of all the day on pt Dee, 1984. 1st Dee 1984 means (1983 years 11 months and 1 day)

Now,
1900 years have 1 odd day
83 years have (20 leap years and 63 ordinary years)
= (40 + 63) odd days
= 103 odd days
= 5 odd days

11 months and 1 day

Jan  Feb  Mar  Apr  May  June  July  Aug  Sep  Oct  Nov  Dee
31    29    31     30     31     30      31      31    30     31    30    1
= 336 days => 0 odd day

Total no. of odd days
= (1 + 5 + 0) = 6

Hence, it was Saturday on 1stDee 1984 and 1st Sunday was on 2nd Dee 1984. Subsequently, Sunday’s of the month were on 2nd, 9th, 16th, 23rd and 30th.

7. Today is Wednesday, what will be the day after 94 days?
(a) Monday
(b) Tuesday
(c) Wednesday
(d) Sunday

View Answer
Ans.(c)
Every day of the weeks is repeated after 7 days. Hence,if will be Wednesday after 94 days

8. Today is Thursday. The day after 59 days will be
(a) Sunday
(b) Monday
(c) Tuesday
(d)Wednesday

View Answer
Ans.(a)
Every day of the week is repeated after 7 days. Hence,after 56 days it would be Thursday again and after 59 days it would be Sunday.

9. Today is Friday. The day after 63 days will be
(a) Friday
(b) Thursday
(c) Saturday
(d) Monday

View Answer
Ans.(c)
Explanations as above.

10. What was the day of the week on 2nd July 1984 ?
(a) Wednesday
(b) Tuesday
(c) Monday
(d) Thursday

View Answer
Ans.(c)
2nd July 1984 means (1983 years 6 months and 2 days)
1900 years have 1 odd day

83 years have 20 leap years and 63 ordinary years.
= (40 + 63) odd days
= 103
= 5 odd days

6 months and 2 days.

Jan  Feb  Mar  Apr  May  June  July
31    29    31     30     31     30       2
= 184 days = 2 odd days

Total no. of odd days
= (1 + 5 + 2 )
= 8 odd days
= 1 odd day

Hence, it was Monday on 2nd July, 1984

11. The year next to 1990 will have the same calendar as that of the year 1990
(a) 1995
(b) 1997
(c) 1996
(d) 1992

View Answer
Ans.(c)
The year 1990 has 365 days i.e., 1 odd day, year 1991 has 365 days i.e., 1 odd day, year 1992 has 366 days i.e., 2 odd days. Likewise year 1993,1994,1995, have 1 odd day each. The sum of odd days so calculated from years 1990 to 1995

(1 + 1 + 2 + 1 + 1 + 1 )
= 7 odd days
= 0 odd day.

Hence, the year 1996 will have the same calendar as that of the year 1990.

12. The year next to 1996 will have the same calendar as that of the year 1996
(a) 2001
(b) 1996
(c) 1997
(d) 1999

View Answer
Ans.(a)
Calculation is the same as given to Q.NO.11.