When will the hour and minute hands of the clock be opposite to each other or make an angle of 180° with each other between 2 and 3 o'clock.

To determine when the hour and minute hands of the clock will be opposite to each other (180° apart) between 2:00 and 3:00.

The minute hand moves 360° in 60 minutes, so it moves 6° per minute.

The hour hand moves 360° in 12 hours, so it moves 30° per hour or 0.5° per minute.

At 2:00, the hour hand is at 60° (since 2 × 30° = 60°)

The minute hand starts at 0°.

Let the number of minutes after 2:00 be x.

The position of the minute hand after x minutes is 6x°.

The position of the hour hand after x minutes is 60 + 0.5x°.

The hands will be 180° apart, so:

|(60 + 0.5x) - (6x)∣ = 180

∣60+0.5x-6x∣ = 180

Solve of x:
5.5x = 240

x = $$\frac {240}{5.5}$$​

x = $$\frac {2400}{55}$$

​

x = $$\frac {480}{11}$$​​

x = 43 $$\frac {7}{11}$$ minutes​

The hands will be opposite each other at 2:43 7/11 (or 2:43 and about 38 seconds).

Thus, correct option is (a).