Match List-I with List-II

Choose the correct answer from the options given below:

(A)-(III), (B)-(I), (C)-(IV), (D)-(II)

The correct answer is Option (3) → (A)-(III), (B)-(I), (C)-(IV), (D)-(II)

To find the angle between the hour hand and the minute hand, we use the standard formula:

$\text{Angle} = \left| 30H - \frac{11}{2}M \right|$

where $H$ is the hour and $M$ is the minutes.

Step-by-Step Calculations

(A) 2:20 p.m.

• $H = 2, M = 20$
• $\text{Angle} = |30(2) - 5.5(20)| = |60 - 110| = |-50| = \mathbf{50^\circ}$
• Match: (A) $\rightarrow$ (III)

(B) 3:10 p.m.

• $H = 3, M = 10$
• $\text{Angle} = |30(3) - 5.5(10)| = |90 - 55| = \mathbf{35^\circ}$
• Match: (B) $\rightarrow$ (I)

(C) 5:30 p.m.

• $H = 5, M = 30$
• $\text{Angle} = |30(5) - 5.5(30)| = |150 - 165| = |-15| = \mathbf{15^\circ}$
• Match: (C) $\rightarrow$ (IV)

(D) 6:40 p.m.

• $H = 6, M = 40$
• $\text{Angle} = |30(6) - 5.5(40)| = |180 - 220| = |-40| = \mathbf{40^\circ}$
• Match: (D) $\rightarrow$ (II)