Q. At which one of the following times, do the hour hand the minute hand of the clock make an angle of 180° with each other?

Explanation :

Hour hand and Minute hand of the clock

Let’s solve this step by step:

1) When hands make 180°, they point in opposite directions.

2) At 7:00:
– Hour hand moves (7/12 × 360°) = 210° from start
– Minute hand at 0°
– Angle = 210° (not 180°)

3) In 1 hour:
– Hour hand moves 30°
– Minute hand moves 360°

4) In 1 minute:
– Hour hand moves 0.5°
– Minute hand moves 6°

5) At 7:05:
– Hour hand: 210° + (5 × 0.5°) = 212.5°
– Minute hand: 5 × 6° = 30°
– Angle = 182.5° (not 180°)

6) Between 7:05 and 7:10, at approximately 7:06, the hands form exactly 180°.

Therefore, the answer is (d) Between 7:05 hours and 7:10 hours.