The correct option is (a) 7.786 x10^-3
For explanation I would say: For a sparged vessel, the diameter of the bubble = (2.344 x10^-3)/(Relative velocity of the liquid upwards)^0.67
The relative velocity of the liquid upward= liquid flow rate/ (1- gas holdup)
Relative velocity = 0.15/0.9
Diameter = 7.786 x10^-3.