Question 1

Find the angle between minute hand and hour hand at 1 : 40 AM

Accepted Answer

At 1 : 40 from the formula here P = 1 and Q = 40 so required angle is 11 x 40/2 - 30 x 1 = 220 - 30 = 190 the required angle is 190°

Question 2

Find the angle between minute hand and hour hand at 10 : 10 AM

Accepted Answer

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°

Question 3

At what time between 3 PM to 4 PM minute hand and hour hand will coincide?

Accepted Answer

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

Question 4

At what time between 3 PM to 4 PM minute hand and hour hand will be opposite to each other?

Accepted Answer

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

Question 5

At what time between 4 PM to 5 PM minute hand and hour will be at right angle to each other?

Accepted Answer

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

Question 6

At what time between 9 PM to 10 PM minute hand and hour hand will be opposite to each other?

Accepted Answer

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

Question 7

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

Accepted Answer

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 hand will travel 11/2° more than the hour hand. Then will be perpendicular to each other when the minute hand will travel 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 perpendicular to each other at 9 : 49 minute : 0.09 second

Question 8

If 14th October 2005 is Friday then which day is 14th October 2006?

Accepted Answer

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.

Question 9

If today is Monday then which day of the week is after 59 days.

Accepted Answer

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.

Question 10

If 14th October 2005 is Friday then which day is 14th October 2009?

Accepted Answer

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.

Question 11

If 2nd June 2012 is Saturday then which day is 7th July 2012?

Accepted Answer

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.

Question 12

If 1st Jan 2001 is Monday then which day was on 1st Jan 2013.

Accepted Answer

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.

Question 13

Which of the following is not a leap year?

Accepted Answer

The century divisible by 400 is a leap year. 2100 is not divisible by 400 hence is not a leap year.

Question 14

Which of the following is a leap year?

Accepted Answer

The century divisible by 400 is a leap year. 2100 is not divisible by 400 hence is not a leap year so 2100 is not a leap year, out of remaining 1128 is divisible by 4, so 1128 is a leap year.

Question 15

If Jan 1, 2006 was Sunday. What was the day of the week Jan 1, 2010

Accepted Answer

On 31st December, 2005 it was Saturday. Number of odd days from the year 2006 to the year 2009 = (1 + 1 +2 + 1) = 5 days. ∴ On 31st December, 2009, it was Thursday. Thus, on 1st Jan, 2010 it is Friday.

Question 16

Tuesday is Sunday. After 69 days, it will be

Accepted Answer

When 69 is divided by 7 we will get remainder 6 so the day will be 6 days more than Sunday i.e Saturday.

Question 17

If 6th March, 2005 is Sunday, what was the day of the week on 6 th March, 2002?

Accepted Answer

Number of odd days between 6th march 2002 to 6th march 2003 is 1 Number of odd days between 6th march 2003 to 6th march 2004 is 2 Number of odd days between 6th march 2004 to 6th march 2005 is 1 Hence total Number of odd days between 6th march 2002 to 6th march 2005 is 1 + 2 + 1 = 4 odd days so 6th march 2002 is 4 days before Sunday i.e. Wednesday.

Question 18

Find the angle between minute hand hour hand at 11 : 50 AM

Accepted Answer

At 11 : 50 A.M. from the formula here P = 11 and Q = 50 so required angle is 11 x 50/2 - 30 x 11 = 275 - 330 = -55 or ignoring the negative sign the required angle is 55°

Question 19

At what time between 2 PM and 3 PM the angle between minute hand and hour hand is 100°.

Accepted Answer

Same as previous question Option A is correct.

Question 20

Find the angle between minute hand and hour hand at 2 : 18 AM

Accepted Answer

39°

Calendar Questions