Answer
a.
paper burns over wood.
b.
II is best
Work Step by Step
Steel has high thermal conductivity, while wood has low thermal conductivity.
a.
The heat received by the paper from the flame is passed (conducted) onto the material it is in contact with. If that material is steel, a good conductor, a good part of the heat is given by the paper to the steel, keeping the rise of its temperature relatively low, so it doesn't burn.
If it is wood, no heat (or little heat) is conducted away, so the temperature rises, and the paper burns.
b.
I is incorrect, the metal gets hot due to the heat received from the paper.
II is correct.
III is incorrect for the same reason as I.
Thus, II is best.