The hour hand and minute hand coincide approximately once every hour and 5 minutes (or 65 minutes).

Between 10:00 a.m. and 2:00 p.m., the coincidence occurs at the following times:

• Between 10:00 a.m. and 11:00 a.m.
• Between 11:00 a.m. and 1:00 p.m.
• Between 1:00 p.m. and 2:00 p.m.

Thus, the hands coincide 3 times during this period.

Answer: A. 3 times.