Find the angle traced by hour hand of a correct clock between 7 pm 0’ clock and 2 am 0’ clock.

The correct option is 210^◦.

To find the angle traced by the hour hand of a correct clock between 7:00 PM and 2:00 AM, we can break down the calculation step-by-step:

1. Calculate the total hours elapsed:
From 7:00 PM to 12:00 midnight is 5 hours.
From 12:00 midnight to 2:00 AM is 2 hours.
Total time duration = 5 hours + 2 hours = 7 hours.

2. Determine the rate of rotation of the hour hand:
A complete rotation of a clock dial is 360^◦, which corresponds to 12 hours.
Therefore, the angle traced by the hour hand in 1 hour is:

$$\frac{{360}^{\circ }}{12}={30}^{\circ }$$

3. Calculate the angle traced in 7 hours:
Since the hour hand traces 30^◦ in 1 hour, the angle traced in 7 hours is:

$$7\times {30}^{\circ }={210}^{\circ }$$

Thus, the hour hand traces an angle of 210^◦.