At what time between 9 PM to 10 PM minute hand and hour hand will coincide?

Correct Answer: 9 : 124/11

Explanation:

Consider exactly at 9 : 00, minute hand is at position '12' and hour hand is at '9' hence angle between these two hands at 9 : 00 is 270°
Since relative speed between them is 11/2° per minute or every minute the minute hand will travel 11/2° more than the hour hand.
Then will be together when the minute hand will travel (270 - 180) = 90° more than the hour hand. And time taken for this is (90)/(11/2) = 180/11 or 16 4/11 minute
Hence they will be opposite to each other at 9 : 49 minute : 21.81 second

Correct Answer: None of these

Explanation:

Consider exactly at 4 : 00, minute hand is at position '12' and hour hand is at '4' hence angle between these two hands at 4 : 00 is 120°
Since relative speed between them is 11/2° per minute or every minute the minute hand will travel 11/2° more than the hour hand.
Then will be perpendicular to each other when the minute hand will travel (120 - 90) = 30° more than the hour hand. And time taken for this is (30)/(11/2) = 60/11 or 5 5/11 minute
Hence they will be perpendicular to each other at 4 : 11 minute : 45.45 second

Correct Answer: 3 : 491/11

Explanation:

Consider exactly at 3 : 00, minute hand is at position '12' and hour hand is at '3' hence angle between these two hands at 3 : 00 is 90°
Since relative speed between them is 11/2° per minute or every minute hand will travel 11/2° more than the hour hand.
Then will be opposite to each other when the minute hand will travel (90 + 180) = 270° more than the hour hand. And time taken for this is (270)/(11/2) = 540/11 or 49 1/11 minute
Hence they will be opposite to each other at 3 : 49 minute : 0.09 second

Correct Answer: 3 : 164/11

Explanation:

Consider exactly at 3 : 00, minute hand is at position '12' and hour hand is at '3' hence angle between these two hands at 3 : 00 is 90°.
Since relative speed between them is 11/2° per minute or every minute the minute hand will travel 11/2° more than the hour hand.
They will be together when the minute hand will travel 90° more than the hour hand. And time taken for this is (90)/(11/2) = 180/11 or 16 4/11 minute.
Hence they will coincide at 3 : 16 minute : 21.81 second

Correct Answer: 245°

Explanation:

At 10 : 10 from the formula here P = 10 and Q = 10 so required angle is 11 x 10/2 - 30 x 10 = 55 - 300 = - 245 the required angle is 245°

Correct Answer: Saturday

Explanation:

Since in 1 year we have one odd day while in one leap year we have two odd days.
Number of odd days are 1 (for 2006)
1 days more than Friday means Saturday.

Correct Answer: Thursday

Explanation:

Since a day of the week repeat after every 7 days, divide 59 by 7, remainder is 3 so number of odd days is 3, and 3 days after Monday is Thursday.

Correct Answer: Wednesday

Explanation:

Since in 1 year we have one odd day while in one leap year we have two odd days .
Number of odd days are: 1(for 2006) + 1(for 2007) + 2 (For leap year 2008) + 1 (for year 2009) so total number of odd days are 1 + 1 + 2 + 1 = 5 days. 5 days more than Friday means Wednesday.

Correct Answer: Saturday

Explanation:

Number of days in June is 30 -2 = 28, and number of days in July is 7, total number of days is 28 + 7 = 35, when we divide 35 by 7 remainder is 0, or number of odd days is 0 hence 7th July must be the same day as that of 2nd June i.e. Saturday in this case.

Correct Answer: Tuesday

Explanation:

Number of years between 2001 to 2013 is 12 years (2013 - 2001 = 12 years)
Number of leap years between 2001 to 2013 is 3, since a year has 1 odd days and a leap year has 2 odd days , so total number of odd days is 12 + 3 = 15 odd days.
When we divide 15 by 7 remainder is 1 or in total we have 1 odd day so 1st jan 2013 is Tuesday.