How many times do the two hands of a clock are exactly opposite to each other in a day?

To determine how many times the two hands of a clock are exactly opposite to each other in a day, we need to consider the relative speeds of the hour and minute hands.

1. The minute hand completes a full revolution around the clock in 60 minutes.
2. The hour hand completes a full revolution around the clock in 12 hours, which is equivalent to 720 minutes.

Now, let's calculate the time it takes for the two hands to be exactly opposite to each other.

Since the minute hand moves 12 times faster than the hour hand (60 minutes vs. 720 minutes), it will take the minute hand 720/12 = 60 minutes to catch up to the hour hand.

Therefore, the two hands will be exactly opposite to each other once every 60 minutes.

In a day, there are 24 hours, which is equivalent to 1440 minutes. So, the two hands will be exactly opposite to each other 1440/60 = 24 times in a day.