. How many times do the two hands of a clock are exactly opposite to each other in a day?  a.22  b.36  c.4  d.8

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 in 60 minutes, which means it moves 360 degrees per hour.
2. The hour hand takes 12 hours to complete a full revolution, which means it moves 30 degrees per hour.

Now, let's calculate the times when the two hands are exactly opposite:

3. The first time the two hands are opposite is at 12:00. At this time, the hour hand is at 0 degrees, and the minute hand is at 180 degrees.

4. The second time the two hands are opposite is when the minute hand has moved 180 degrees from the 12:00 position. Since the minute hand moves 360 degrees per hour, it takes 30 minutes for the minute hand to move 180 degrees. Therefore, the second time is at 12:30.

5. The third time the two hands are opposite is when the minute hand has moved another 180 degrees from the 12:30 position. Again, it takes 30 minutes for the minute hand to move 180 degrees, so the third time is at 1:00.

6. Following the same pattern, the fourth time is at 1:30, the fifth time is at 2:00, and so on.

7. We can observe that the two hands are opposite every 30 minutes. In a 12-hour period, there are 24 intervals of 30 minutes each.

8. Therefore, the two hands are exactly opposite to each other 24 times in a day.

So, the correct answer is not provided in the options given.