Match List-I with List-II
| List I | List II | ||
|---|---|---|---|
| (Time) | (Angle between the hour hand and minute hand of a clock) | ||
| (A) | 2:20 p.m. | (I) | 35° |
| (B) | 3:10 p.m. | (II) | 40° |
| (C) | 5:30 p.m. | (III) | 50° |
| (D) | 6:40 p.m. | (IV) | 15° |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A)-(III), (B)-(I), (C)-(IV), (D)-(II)
The minute hand turns 6° a minute and the hour hand 0.5° a minute (30° an hour). At H hours M minutes the angle between them is therefore \(\theta=|30H-5.5M|\); if this comes out above 180°, it is subtracted from 360°.
(A) 2:20 p.m. — this matches (III) 50°.
\(\theta=|30\times2-5.5\times20|=|60-110|=50^\circ\)
(B) 3:10 p.m. — this matches (I) 35°.
\(\theta=|30\times3-5.5\times10|=|90-55|=35^\circ\)
(C) 5:30 p.m. — this matches (IV) 15°.
\(\theta=|30\times5-5.5\times30|=|150-165|=15^\circ\)
At half past five the hour hand is halfway between 5 and 6, just 15° short of the minute hand on 6.
(D) 6:40 p.m. — this matches (II) 40°.
\(\theta=|30\times6-5.5\times40|=|180-220|=40^\circ\)