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Fundamental Principle of Counting

A 12 dial clo...

Question

A 12 dial clock has its minute hand defective.Whenever it touches dial 12, it immediately falls down to 6 instead of running smoothly (the hour hand remains unaffected during that fall). It was set right at 12 '0' clock in the noon.
In a period of 12 hours how many times hours hand and minutes hand of a clock are in a straight line facing the opposite direction ?

A

22

times

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B

11

times

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C

12

times

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D

24

times

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Solution

The correct option is B $11$ times
When the time is below $6$ the hour hand and minute hand will be $2$ times in a straight line but opposite to each other.
As the clock turns $6$ , the minute hand will fall and hence, they will be on same side.
Thus, total number of times they are opposite and in straight line is $11$ .

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Q. A 12 dial clock has its minute hand defective. Whenever it touches dial 12, it immediately falls down to 6 instead of running smoothly (the hour hand remains unaffected during that fall). It was set right at 12 '0' clock in the noon. How many times the two hands of a watch form right angle from 12 O' clock noon to 6 O'clock evening.

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