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Match List-I with List-II

List IList II
(Time)(Angle between the hour hand and minute hand of a clock)
(A) 2:20 p.m.(I) 35∘35^{\circ}
(B) 3:10 p.m.(II) 40∘40^{\circ}
(C) 5:30 p.m.(III) 50∘50^{\circ}
(D) 6:40 p.m(IV) 15∘15^{\circ}

Choose the correct answer from the options given below:

Solution

✅ Correct Option: 3

The angle between the hour hand and minute hand of a clock can be found using the formula:

Angle =∣11M/2−30H∣= \left|11M/2 - 30H\right|

where MM = minutes and HH = hours (in 12-hour format)


For (A) 2:20 p.m., H=2H = 2 and M=20M = 20:

Angle =∣11(20)2−30(2)∣= \left|\frac{11(20)}{2} - 30(2)\right|

=∣110−60∣= |110 - 60|

=50°= 50°

This matches with (III)


For (B) 3:10 p.m., H=3H = 3 and M=10M = 10:

Angle =∣11(10)2−30(3)∣= \left|\frac{11(10)}{2} - 30(3)\right|

=∣55−90∣= |55 - 90|

=35°= 35°

This matches with (I)


For (C) 5:30 p.m., H=5H = 5 and M=30M = 30:

Angle =∣11(30)2−30(5)∣= \left|\frac{11(30)}{2} - 30(5)\right|

=∣165−150∣= |165 - 150|

=15°= 15°

This matches with (IV)


For (D) 6:40 p.m., H=6H = 6 and M=40M = 40:

Angle =∣11(40)2−30(6)∣= \left|\frac{11(40)}{2} - 30(6)\right|

=∣220−180∣= |220 - 180|

=40°= 40°

This matches with (II)


The correct matching is:

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

Therefore, the correct answer is Option 3.

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