UPSC CDS 2 2022 Math Paper

Concept:The angle between clock hands is found using the formula: Angle = $|30H - 11 \times \frac{m}{2}|$, where $H$ is the hour (in 12-hour format) and $m$ is the minutes.Explanation:For 4 hours 40 minutes, $H = 4$ and $m = 40$.Substitute into the formula: Angle = $|30 \times 4 - 11 \times \frac{40}{2}|$Simplify: $30 \times 4 = 120$, and $11 \times \frac{40}{2} = 11 \times 20 = 220$.Thus, Angle = $|120 - 220| = |-100| = 100^\circ$.The hour hand moves $0.5^\circ$ per minute, so at 4:40 it has moved $40 \times 0.5 = 20^\circ$ from the 4 mark, adding to $120^\circ$ total from 12 o'clock. Minute hand at 40 minutes is at $240^\circ$. Difference is $120^\circ - 240^\circ = -120^\circ$? Wait, careful: $30 \times 4 = 120^\circ$ for hour hand at 4 exactly, but plus $0.5 \times 40 = 20^\circ$ gives $140^\circ$. Minute hand at $6 \times 40 = 240^\circ$. Difference $|140-240| = 100^\circ$.The formula gives the correct result directly.So the required angle is $100^\circ$.Answer:$100^\circ$ (Option B)