In 24 hours how many times minute hand & hour hand-will coincide each other? 

Given: A day → 24 hours

In one day, total minutes is ⇒ 24 hr ×  60 min = 1440 minutes. 

As, hour hand and minute hand coincides every 65 minutes 

⇒ 1440 ÷ 65 = 22.15

So, In 24 Hours it coincide 22 times. 

Hence, "Option 2" is the correct answer.

Alternate MethodHands coincide in 12 hours

⇒ The hands of a clock (hour hand and minute hand) coincide once every 1 hour and 5 minutes (or 1 hour + 5/11 of an hour).

⇒ In 12 hours, the hands coincide 11 times, because the first coincidence occurs at 12:00, and the next at approximately 1:05, 2:10, and so on.

Hands coincide in 24 hours

⇒  Since there are two 12-hour cycles in a day (one for AM and one for PM), the total number of coincidences is: 11(coincidences in 12 hours) × 2 = 22.

Important Points The reason it is 11 coincidences per 12 hours instead of 12 is that the hands coincide at the very start of the cycle and not again until the next cycle begins.