The Correct answer is Option 4. 

Key Points

Express each hand’s angle from 12 o’clock:

Minute hand speed: 6° per minute.

Hour hand speed: 0.5° per minute, with a 60° head start at 2:00.

Set up the equation for coincidence:

Let t be the number of minutes after 2:00. We want the minute hand’s angle to equal the hour hand’s angle:

6t  =  60  +  0.5t

Simplifying:

6t − 0.5t = 60 → 5.5t = 60 → t = 60 / 5.5 = 120 / 11 = 10 10⁄11 minutes

Therefore, the hands coincide at 10 10⁄11 minutes past 2, 

Hence Correct answer is Option 4.