At what time between 7 and 8, are the hands of a clock coincides?

$38\frac{2}{11}$ min past 7

At 7:35, Minute Hand is at 7×30º = 210º

       and Hour Hand is at 210º + 35 × 0.5º = 227.5º

After 1 minute that is 7:36, Minute hand is at = 210º + 6º = 216º (Doesn't cross Hour Hand which has moved further from 227.5º)

After 2 minutes that is 7:37, Minute hand is at = 216º + 6º = 222º (Doesn't cross Hour Hand which has moved further from 227.5º)

After 3 minutes that is 7:38, Minute hand is at = 222º + 6º = 228º 

At 7:38 Hour Hand is at 210º + 38 × 0.5º = 229º

Thus Option 2 and 3 have been eliminated

Now both the hands have approached near and do not require 10 more minutes as per the calculations.

Thus option 4 is also eliminated. 

The correct answer is Option (1) → $38\frac{2}{11}$ min past 7