At what time are the hands of clocks together between 6 and 7?

According to question , we know that
Starting with 2000, count for number of odd days in successive years till the sum is divisible by 7.
2000 + 2001 + 2002 + 2003 + 2004 = 2 + 1 + 1 +1 + 2 = 7 odd days
? Number of odd days up to 2004 = 0 odd day
Hence , Calendar for 2000 will serve for 2005 also.

We can say that ,
During the interval we have two leap years as 1992 and 1996 and it contains February of both these years.
? The interval has ( 5 + 2 ) = 7 days = 0 odd day.
Hence, January 7, 1997 was also Tuesday.

As per the given above question , we know that
August 15, 1947 = ( 1600 + 300 + 46 ) years + January 1 to August 15th, of 1947
August 15, 1947 = ( 1600 + 300 + 46 ) years + ( 365 - August 16 to December 31 1947 )
1600 + 300 + 46 ) years
August 15, 1947 = ( 1600 + 300 + 46 ) years + ( 365 - 138 ) days
Now , 1600 years give 0 odd day
300 years give 1 odd day
46 years give 1 odd day
Number of odd days = 0 + 1 + 1 (from 11 leap years and 35 ordinary years) + 3 = 5 odd days
Hence , The day was Friday.

Since minute hand gains 5 minutes in every 60 minutes
⇒ second hand gains 5 seconds in every 60 seconds
∴ In every 60 seconds true time, it moves 65 seconds
⇒ 65 × 6° = 390°.
Hence , required answer will be 390° .

As we can say that ,
There are 3 intervals when the clock strikes 4 Time taken in 3 intervals = 9 seconds
? Time taken for 1 interval = 3 seconds
In order to strike 12, there are 11 intervals, for which the time taken is 11 × 3 seconds = 33 seconds.
Therefore , Required time taken is 33 seconds .