Find the angle between the hour hand and the minute hand of a clock when the time is 10.25 hours i.e. 25 minutes past 10 ?

In every hour , hour hand covers $$30^\circ$$.

So, at 10:25 pm , angle covered by hour hand will be ,

$$ \frac{30 \times 125 }{12} = 312.5^\circ$$

In every hour , minute hand will cover $$360^\circ$$

So, at 10:25 pm , angle covered by minute hand will be ,

$$60 \times 25  = 150^\circ$$

angle between the hour hand and the minute hand of a clock = $$312.5^\circ - 150^\circ$$ = $$162\frac{1}{2}°$$

So, the answer would be option c)$$162\frac{1}{2}°$$