How many times do the hour-hand and the minute-hand of a clock coincide between 10:00 a.m. and 2:00 p.m. (on the same day)?

The hour and minute hands coincide 11 times in every 12 hours. Between 10:00 a.m. and 2:00 p.m. (a 4-hour interval), coincidences occur at approximately 10:54:33, 12:00:00, and 1:05:27. That gives 3 coincidences.