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) | 70° |
| (C) | 4:30 p.m. | (III) | 50° |
| (D) | 5:40 p.m. | (IV) | 45° |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(III), (B)-(I), (C)-(IV), (D)-(II)
The minute hand turns \(6^\circ\) a minute and the hour hand \(\frac{1}{2}^\circ\) a minute, starting from \(30^\circ\) for every hour. At \(H\) hours \(M\) minutes the hour hand is at \(30H+\frac{M}{2}\) degrees and the minute hand at \(6M\) degrees from 12, so the angle between the hands \(=\left|30H-\frac{11}{2}M\right|\).
(A) 2:20 p.m. — this matches (III) 50°.
\(\left|30\times2-\frac{11}{2}\times20\right|=|60-110|=50^\circ\)
(B) 3:10 p.m. — this matches (I) 35°.
\(\left|30\times3-\frac{11}{2}\times10\right|=|90-55|=35^\circ\)
(C) 4:30 p.m. — this matches (IV) 45°.
\(\left|30\times4-\frac{11}{2}\times30\right|=|120-165|=45^\circ\)
(D) 5:40 p.m. — this matches (II) 70°.
\(\left|30\times5-\frac{11}{2}\times40\right|=|150-220|=70^\circ\)