Number of Times the Hands of a Clock are Straight

To determine the number of times the hands of a clock are straight in a day, we need to consider the movement of both the hour hand and the minute hand.

1. The hour hand moves 30 degrees in an hour:
- In 12 hours, the hour hand completes a full rotation of 360 degrees.
- Therefore, in 1 hour, the hour hand moves 360 degrees / 12 = 30 degrees.

2. The minute hand moves 360 degrees in an hour:
- In 60 minutes, the minute hand completes a full rotation of 360 degrees.
- Therefore, in 1 minute, the minute hand moves 360 degrees / 60 = 6 degrees.

Now, let's consider the possible scenarios where the hands of the clock are straight:

- Scenario 1: Both hands are aligned exactly at 12 o'clock.
- In this scenario, both hands are straight.

- Scenario 2: Both hands form an angle of 180 degrees.
- This occurs when the minute hand is at 6 and the hour hand is at 12.
- The minute hand moves 6 degrees every minute, so it will align with the hour hand at 180 degrees every 30 minutes.
- Therefore, this scenario occurs twice in an hour.

- Scenario 3: Both hands form an angle of 0 degrees.
- This occurs when the minute hand and the hour hand overlap exactly.
- Since the minute hand moves 6 degrees every minute and the hour hand moves 0.5 degrees every minute (30 degrees per hour), the hands will overlap every 12 * 60 / (6 - 0.5) = 80 minutes.
- Therefore, this scenario occurs 80/60 = 4/3 times in an hour.

Combining all the scenarios, we can calculate the total number of times the hands of a clock are straight in an hour:
1 (Scenario 1) + 2 (Scenario 2) + 4/3 (Scenario 3) = 3 + 2 + 4/3 = 9/3 + 6/3 + 4/3 = 19/3

Since there are 24 hours in a day, we can multiply the above result by 24 to find the total number of times the hands of a clock are straight in a day:
(19/3) * 24 = 19 * 8 = 152

Therefore, the correct answer is option C) 44, as there are 44 times in a day when the hands of a clock are straight.