At which one of the following times, do the hour hand and the minute hand of the clock make an angle of 180° with each other ?

Correct Answer: (D) Between 7:05 hours and 7:10 hours

At 7:00, the angle between the hour and minute hands is $210^$$\circ$. For the two hands to be directly opposite each other ($180^$$\circ$ apart), the minute hand must gain $210^$$\circ$ - 180^$\circ$ = 30^$\circ$ on the hour hand. At a relative speed of $5.5^$$\circ$ per minute, the time taken is $\frac{{30}^{\circ }}{{5.5}^{\circ }}=\frac{60}{11}=5\frac{5}{11}\text{ minutes}$$\frac{30^\circ}{5.5^\circ}$ = $\frac{60}{11}$ = 5$\frac{5}{11}$$\text{ minutes}$. Thus, they form a straight line of $180^$$\circ$ at approximately 7 hours $5$$\frac{5}{11}$ minutes, which lies between 7:05 hours and 7:10 hours.