What is the angle between the minute and the hour hand of the clock wh

From the position of hands on 12:00 (both hands are vertical) hour hands moves \(\frac{360}{12*60}=0.5\) degrees in 1 minute and minute hands moves \(\frac{360}{60}=6\) degrees in 1 minute.

Hence at 12:24, after 24 minutes from 12:00, when both hands are vertical, hour hand will move \(24*0.5=12\) degrees from the vertical position and minute hand will move \(24*6=144\) degrees from vertical position. So the angle between them will be \(144-12=132\) degrees.

Answer: E.

There is general formula for this, (though no need to memorize):

\(|\frac{11}{2}m - 30h|\)

If the result is greater than 180 degrees, subtract it from 360 to get the included angle.

The above can be derived from the fact that:
In 1 minute:
Hour hand moves 0.5 degrees,
Minute hand moves 6 degrees.

AND

In an hour:
Hour hand moves 30 degrees,
Minute hand moves 360 degrees.

For our original question:
12:24 --> \(h=0\) (not 12) and \(m=24\) --> \(|\frac{11}{2}m - 30h|=|\frac{11}{2}24 - 30*0|=132\)

Answer: E.

Hope it's clear.