# 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?

(a) At 7:00 hours

(b) Between 7:00 hours and 7:05 hours

(c) At 7:05 hours

(d) Between 7:05 hours and 7:10 hours

Correct Answer: (d) Between 7:05 hours and 7:10 hours

#### Question from UPSC Prelims 2021 CSAT Paper

**Explanation : **

The hour hand and the minute hand of a clock make an angle of 180° with each other when they are exactly opposite to each other. At 7:00 hours, the hour hand is at 7 and the minute hand is at 12. The angle between them is less than 180°. At 7:05 hours, the minute hand has moved to 1 and the hour hand has moved slightly past 7. The angle between them is still less than 180°.

Between 7:05 hours and 7:10 hours, the minute hand moves from position 1 to position 2 while the hour hand moves slightly further past position 7. At some point between these two times, the two hands will be exactly opposite to each other and will make an angle of 180° with each other. So the correct answer is (d) Between 7:05 hours and 7:10 hours.