At what time between 7 and 8 o'clock will the hands of a clock be at right angle?

The angle between the hands of the clock at 7 o'clock = 210 degrees.
The hands will form a right angle when the minute hand covers a distance of 210 - 90 = 120 degrees towards the hour hand.
The relative speed of the minute hand with hour hand = 6 - 0.5 = 5.5 degrees per minute.
Time taken to cover 120 degrees = $$\frac{120}{5.5}=21\frac{9}{11}\ $$mins.
So, the hands will form a right angle at $$21\frac{9}{11}\ $$mins. past 7.