Q: How many times do the minute hand & hour hand of a clock make an angle of 90 degree in a day ?

In 24 hours, the minute hand moves around the circle 24 times(in one hour it makes one circle). In 24 hours the hour hand moves around the circle 2 times(every 12 hours it makes one circle)
So relative to the hour hand the minute hand makes 24-2=22 circles. Now , for each circle relative to the hour hand the minute hand makes an angle of 90 degree, 2 times.(for example , from 12 pm to 1 am it appears 2 times : at 12:15 & 12:45 respectively) . For 22 circle right angle are mad 22*2=44 times