How many times in a day, are the hands of a clock in straight line but opposite in direction?

### Concept & Logic The question asks for the number of times the hands form a $180^\circ$ angle (pointing in opposite directions). In a 12-hour period, this happens 11 times. The loss of one occurrence happens between 5 o'clock and 7 o'clock, where they are opposite only exactly at 6:00. ### Step-by-Step Solution 1. **Half-day Analysis:** In 12 hours, the hands point in opposite directions 11 times. 2. **Full-day Analysis:** A full day has 24 hours, which is two 12-hour cycles. Number of times in 24 hours = $11 \times 2 = 22$ times. ### Exam Strategy & Shortcut Direct fact recall: - Straight but opposite ($180^\circ$) = 22 times/day. - Coincide ($0^\circ$) = 22 times/day. ### Common Pitfall Selecting 24 by assuming it happens exactly once every hour without accounting for the shared occurrence at 6:00. Another pitfall is confusing this with just "straight line" which would be 44. The phrase "but opposite in direction" restricts it to 22. ### Final Answer Therefore, the correct answer is **22**.