At what time between 5 and 6 O'clock are the hands of a clock 3 minutes apart?

On 31 st December, 2005 it was Saturday, Number of odd days from the year 2006 to the year 2009
= 1 odd day of 2006 + 1 odd day of 2007 + 2 odd days of 2008 (leap year) + 1 odd day of 2009
= 1 + 1 + 2 + 1 = 5
? On 31st December 2009, it was Thursday
Thus, on 2nd January 2010, it was Saturday .

6th March 2005 = Monday.
Then, 6th March 2004 = Monday - 1 days = Sunday.
(2004 is a leap year but it does not cross 29th February of 2004, so only 1 is taken as odd day).
6th March 2004 = Sunday
7th March 2004 = Monday.

5th March, 1999 is Friday.
Then, 5 March 2000 = Friday + 2 = Sunday
(2000 is leap year and it crosses 29th feb 2000, so 2 is taken as odd day}

? 5th March 2000 = Sunday
Then, 9th March 2000 = Thursday.

The year 2008 is a leap year, so it has 2 odd days, 3rd day of the year 2008 was Friday.
? 3rd day of the year 2009 will be 2 days beyond the Friday.
Hence, the required answer is Sunday.

As per the given above question , we can say that
At 11 O'clock, the hour hand is 4 spaces apart from the minute hand. Since there are 60 spaces in one hour, so (60 - 4) times, i.e., 56 times the hands of the clock are an integral number of minutes apart.
Hence , required answer is 56 times .

We know that, any relative position of the hands of a clock is repeated 11 times in every 12 hours.
? In every 12 hours, hands coincide 11 times and are opposite to each other 11 times.
? In every 12 hours, hands are in a straight line 11 + 11 = 22 times.
? In every 24 hours hands are in a straight line 44 times.

On the basis of above given question , we know that
400 consecutive years contain 97 leap years.
? In 400 consecutive years February has 29 days 97 times and the remaining 11 months have 29th day
400 × 11 = 4400 times
? 29th day of the month occurs ( 4400 + 97 ) = 4497 times.

As per the above given question , we can say that
Number of days from January 25, 1994 to March 2, 1994 is
January + February + March = 6 + 28 + 2 = 36 days = 5 weeks + 1 odd day
? Number of odd days = 1
? Day on January 25, 1994 is one day before the day on March 2, 1994.
But March 2, 1994 was on Wednesday.
Therefore , January 1994 25 was on Tuesday