What is the time at 2 and 3 o'clock when both the hands of the clock (minute and hour) are pointing towards each other make an angle of 180° with each other?

Formula to calculate the time when both hands of the clock make an angle of 180°:

Time = $$\frac {60}{11} \times$$ | Initial angle between hands - 180°|

Initial angle at 2:00:

Angle = 30 $$\times$$ 2 = 60°

Time after 2:00 when the make 180°:

Time = $$\frac {60 \times (180 - 60)}{11 \times 30}$$

= $$\frac {60 \times 120}{330}$$

= $$\frac {7200}{330}$$

= $$\frac {240}{11}$$

= 21$$\frac {9}{11}$$

Exact time:
2:43$$\frac {7}{11}$$minutes

Thus, correct option is (c).