Answer:
To find the number of times the hands of a clock are at a right angle in a day, we need to understand the relationship between the hour hand and the minute hand.

Explanation:
- The minute hand of a clock completes a full rotation in 60 minutes, which is 360 degrees.
- The hour hand of a clock completes a full rotation in 12 hours, which is 360 degrees.
- In one hour, the minute hand moves 360/60 = 6 degrees.
- In one hour, the hour hand moves 360/12 = 30 degrees.
- Let's assume that the minute hand moves x degrees in one minute.
- The relative speed of the hour hand with respect to the minute hand is 6 - x degrees per minute.

Approach:
To find the number of times the hands of a clock are at a right angle in a day, we need to consider all possible positions where the relative speed of the hour hand and the minute hand is zero or 90 degrees per minute.

Calculation:
- At 12:00, both the hour hand and the minute hand coincide. The relative speed is zero.
- At 3:15, the minute hand is at 15 minutes and the hour hand is at 3. The relative speed is zero.
- At 6:30, the minute hand is at 30 minutes and the hour hand is at 6. The relative speed is zero.
- At 9:45, the minute hand is at 45 minutes and the hour hand is at 9. The relative speed is zero.

Conclusion:
Therefore, in a day, the hands of a clock are at a right angle 4 times. Hence, the correct answer is option C) 44.