At what time between 6 to 7 Oclock minute and hour hand will be at right angle or makes 90 angle?

More mathematically, it can be done as :

The minute hand moves 360 degrees in 60 minutes. This means that the angle of the minute hand is given by 6t, where t is number of minutes past midnight.

The hour hand moves 30 degrees in 60 minutes. This means that the angle of the hours hand is given by 0.5t.

The hands start together at midnight. The first time they make a 90 degree angle is when the minute hand has moved 90 degrees further than the hour hand, so this is given by the equation:

6t = 0.5t + 90

5.5t = 90

t = 16 4/11 (16 minutes and 4/11 seconds)

In other words about 16 minutes past midnight.

The next time is when the minutes hand has gained another 180 degrees on the hour hand, and is 90 degrees behind it:

6t = 0.5t + 270

5.5t = 270

t = 49 1/11 (49 minutes and 1/11 seconds)

At about 11 minutes to 1 o'clock.

For every 180 degrees that the minute hand gains on the hour hand there will be one 90 degree angle, so every 49 1/11 - 16 4/11 = 32 8/11 minutes

24 hours is 1440 minutes. 1440/(32 8/11 ) = 44

So every 24 hours there are 44 right angles between minute hand and second hand.

Hope it helps :)

Exercise :: Clock - General Questions

• Clock - Important Formulas
• Clock - General Questions

6.	At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together?
A. 5 min. past 7 B. C. D. Answer: Option D Explanation: When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart. At 7 o'clock, they are 25 min. spaces apart. Minute hand will have to gain only 5 min. spaces. 55 min. spaces are gained in 60 min. 5 min. spaces are gained in 60 x 5 min = 5 5 min. 55 11 Required time = 5 5 min. past 7. 11

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7.	At what time between 5.30 and 6 will the hands of a clock be at right angles?
A. B. C. 40 min. past 5 D. 45 min. past 5 Answer: Option B Explanation: At 5 o'clock, the hands are 25 min. spaces apart. To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces. 55 min. spaces are gained in 60 min. 40 min. spaces are gained in 60 x 40 min = 43 7 min. 55 11 Required time = 43 7 min. past 5. 11

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Exercise :: Clock - General Questions

• Clock - Important Formulas
• Clock - General Questions

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12.	The angle between the minute hand and the hour hand of a clock when the time is 8.30, is:
A. 80° B. 75° C. 60° D. 105° Answer: Option B Explanation: Angle traced by hour hand in 17 hrs = 360 x 17 ° = 255°. 2 12 2 Angle traced by min. hand in 30 min. = 360 x 30 ° = 180°. 60 Required angle = (255 - 180)° = 75°.

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Exercise :: Clock - General Questions

• Clock - Important Formulas
• Clock - General Questions

16.	At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other?
A. B. C. D. Answer: Option D Explanation: At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand. To be coincident, it must gain 15 min. spaces. 55 min. are gained in 60 min. 15 min. are gained in 60 x 15 min = 16 4 min. 55 11 The hands are coincident at 16 4 min. past 3. 11

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17.	How many times do the hands of a clock coincide in a day?
Answer: Option C Explanation: The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock). AM 12:00 1:05 2:11 3:16 4:22 5:27 6:33 7:38 8:44 9:49 10:55 PM 12:00 1:05 2:11 3:16 4:22 5:27 6:33 7:38 8:44 9:49 10:55 The hands overlap about every 65 minutes, not every 60 minutes. The hands coincide 22 times in a day.

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