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 that the hour hand and the minute hand of a clock move at different speeds.

The minute hand completes a full revolution around the clock in 60 minutes, while the hour hand takes 12 hours to complete a full revolution.

In a day, there are 24 hours. Therefore, the hour hand will pass the 12 o'clock position twice in a day.

To calculate the number of times the two hands are exactly opposite, we need to find the number of times the minute hand and the hour hand align perfectly.

When the minute hand is at the 12 o'clock position, the hour hand can be at any of the 12 positions. So, there are 12 possible alignments in this case.

When the minute hand is at the 1 o'clock position, the hour hand will be 1/12th of the way between the 1 and 2 positions. Similarly, for each hour, the hour hand will be 1/12th of the way between two consecutive hour positions.

Therefore, for each hour, there is one alignment between the minute hand and the hour hand.

In total, there are 12 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 24 alignments in a day.

However, we need to divide this number by 2 because the question asks for the number of times the two hands are exactly opposite to each other.

Therefore, the correct answer is 24 / 2 = 12.

So, the correct option is not listed among the given choices.

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

The minute hand completes a full revolution around the clock in 60 minutes, while the hour hand takes 12 hours to complete a full revolution.

In a day, there are 24 hours. Therefore, the hour hand will pass the 12 o'clock position twice in a day.

To calculate the number of times the two hands are exactly opposite, we need to find the number of times the minute hand and the hour hand align perfectly.

When the minute hand is at the 12 o'clock position, the hour hand can be at any of the 12 positions. So, there are 12 possible alignments in this case.

When the minute hand is at the 1 o'clock position, the hour hand will be 1/12th of the way between the 1 and 2 positions. Similarly, for each hour, the hour hand will be 1/12th of the way between two consecutive hour positions.

Therefore, for each hour, there is one alignment between the minute hand and the hour hand.

In total, there are 12 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 24 alignments in a day.

However, we need to divide this number by 2 because the question asks for the number of times the two hands are exactly opposite to each other.

Therefore, the correct answer is 24 / 2 = 12.

So, the correct option is not listed among the given choices.

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

The minute hand completes a full revolution around the clock in 60 minutes, while the hour hand takes 12 hours to complete a full revolution.

In a day, there are 24 hours. Therefore, the hour hand will pass the 12 o'clock position twice in a day.

To calculate the number of times the two hands are exactly opposite, we need to find the number of times the minute hand and the hour hand align perfectly.

When the minute hand is at the 12 o'clock position, the hour hand can be at any of the 12 positions. So, there are 12 possible alignments in this case.

When the minute hand is at the 1 o'clock position, the hour hand will be 1/12th of the way between the 1 and 2 positions. Similarly, for each hour, the hour hand will be 1/12th of the way between two consecutive hour positions.

Therefore, for each hour, there is one possible alignment of the two hands.

In total, there are 12 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 24 possible alignments in a day.

However, we need to divide this number by 2 because the question asks for the number of times the two hands are exactly opposite to each other.

Therefore, the correct answer is 24 / 2 = 12.

So, the correct option is a. 12.