How many times are an hour hand and a minute hand of a clock at right angles during their motion from 1.00 p.m. to 10.00 p.m.?

The minute hand and the hour hand of a clock form a right angle 2 times in every hour.

The duration from 1:00 p.m. to 10:00 p.m. is exactly 9 hours.

Number of right angles = 9 × 2 = 18.

Therefore, the answer is C (18).