• What is the angle between the hour hand and the minute hand when the clock strikes 3:15 ?

Careful! It is very tempting to say 0 degrees. Remember what I told you here. What you see is NOT what you get!

When it strikes 3:15, the hour hand moves ahead a little and is no more pointing at 3 thus the angle is definitely more than zero. You can mention to your interviewer that the solution is definitely not zero.

Once you identified this caveat the rest of the question is just maths. Here's the math. The hour hand moves 360 degrees for 12 hours.

Degree the hour hand moves in 1 hour = 360/12
= 30 degrees

Now note that the minute hand has done 15 minutes. If it does the entire 60 minutes the hour hand would have moved by 30 degrees. Also note that 15 is 1/4th of 60 or a quarter.

You now have your solution. If the minute hand moves by a quarter then the hour hand would advance for a quarter of the value for which it would have advanced had the minute hand done all the 60 minutes.