Multiple choice

How many times in a day the two hands of a clock are at $ \displaystyle 90^{\circ} $

  1. 4

  2. 12

  3. 22

  4. 44
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D Correct answer
Explanation

The hands of a clock form a 90-degree angle twice every hour, except for the periods between 2-4 and 8-10, where it happens only three times instead of four. This results in 22 occurrences in 12 hours, and 44 in a full day.

AI explanation

In a standard 12-hour cycle, the hands of a clock are perpendicular to each other 22 times instead of 24 times because two overlaps reduce the count. Since a day has 24 hours, this event occurs twice. Multiplying 22 by 2 gives 44, meaning the hands are at 90 degrees 44 times in a day.

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