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