At 9 : 38 A.M. through how many degrees the hour hand of a clock moved since noon the previous day ?

Answer: Option D

Time from 12 noon to 9 : 38 A.M.
= 12 hours + 9 hours 38 minutes
= 21 hours 38 minutes
$$\begin{array}{rl}& \text{ = 21}\frac{38}{60}\text{ hours}\\ & \text{ = 21}\frac{19}{30}\text{ hours}\\ & \text{ = }\frac{649}{30}\text{hours}\end{array}$$
Angle traced by the hour hand in 12 hours = 360°
Angle traced by the minute hand in
$$\begin{array}{rl}& \iff \frac{649}{30}\text{hours}\\ & ={\left(\frac{360}{12}\times \frac{649}{30}\right)}^{\circ }\\ & =649^{\circ }\end{array}$$