The clock hands will make 90° angles with each other at:

03:30

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06:45

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09:00

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12:15

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Solution

The correct option is C 09:00
At 03:30, the clock hands are not exactly at 90°, because the hour hand has also moved and is not exactly at 3, but between 3 and 4 at the instance.

At 06:45, the clock hands are not exactly at 90°, because the hour hand has also moved and is not exactly at 6, but between 6 and 7 at the instance.

At 09:00, the clock hands are exactly at 90° with each other.

At 12:15, the clock hands are not exactly at 90°, because the hour hand has also moved and is not exactly at 12, but between 12 and 1 at the instance.

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