The last day of century cannot be either Tuesday, Thursday or Saturday.
At 6 : 30 A.M. from the formula here P = 6 and Q = 30 so required angle is 11 x 30/2 - 30 x 6 = 165 - 180 = - 15 or ignoring the negative sign the required angle is 15°
Number of days in K weeks is 7K hence total number of days is 7K + K = 8k
Similarly number of days in 2Kth day of the 2Kth week is 2k x 7 + 2k = 16k
Required number of days is 16K - 8K = 8K or number of days must be a multiple of 8.
Number of days in K weeks is 7K hence total number of days is 7K + K = 8k or number of days must be a multiple of 8.
The year 2008 is a leap year. It has 2 odd days. The day on 14th feb, 2008 is 2 days before the day on 14th Feb 2009. Hence this day is Thursday.
January and August or October depends on leap year or non leap year. But if we find the number of odd days between March and November we will get number of odd days is 0 hence they will have same calendar.
Total number of odd days
30 September, 1997-98 = 1
30 September, 1998-99 = 1
30 September, 1999-2000 = 2
30 September, 2000-02 = 1
30 September, 2001-02 = 1
30 September, 2002-03 = 1/7
? Tuesday + 7 = Tuesday
So, the next Tuesday will come on the Mrs Susheela's wedding anniversary in 30th September, 2003
26 January, 1996 to 15 August, 2000 days were = 1663
1663 having odd day = 4
? In the year 2000, Independence day will on Tuesday.
18th February, 1997 is Tuesday. So, 17th February, 1998 will also be Tuesday.
Again 16th February, 1999 will also be Tuesday.
Hence, 18th February, 1999 will be Thursday.
Mohan was born on 31st July, August 15 falls on Monday.
At 3 O'clock, then minute hand is 15 min away from the hour hand. To coincide, it must gain 15 min as 55 min are gained in 60 min.
15 min are gained in (60/55) x 15 min = 164/11 min
Hence, the hands are coincide at 164/11 min past 3.
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