The minute hand moves 360° in 60 minutes, giving a rate of 6° per minute.
The hour hand moves 360° in 12 hours (720 minutes), giving a rate of 0.5° per minute.
At 2 o'clock, the hour hand is at 60° from 12 o'clock position (since 2×30°=60°), while the minute hand is at 0°.
Let t be the number of minutes past 2 o'clock when the hands coincide.
Position of minute hand = 6t degrees
Position of hour hand = 60+0.5t degrees
For the hands to be together:
6t=60+0.5t
6t−0.5t=60
5.5t=60
t=5.560
t=21160
t=11120
t=101110 minutes
Therefore, the hour and minute hands coincide at 101110 minutes past 2 o'clock.
The answer is Option 3: 101110 min past 2.