Step 1: Matching P, Gas hydrate:
Gas hydrates are ice like crystalline solids formed when natural gas molecules, mostly methane, get trapped inside cage like structures built by hydrogen bonded water molecules under low temperature and high pressure conditions. This matches description (IV), gas is present inside the cages formed by water molecules. So P pairs with IV.
Step 2: Matching Q, Oil shale:
Oil shale is a fine grained sedimentary rock that contains kerogen, an organic material that has not yet matured into conventional oil. This matches description (II), sedimentary rock contains kerogen. So Q pairs with II.
Step 3: Matching R, Coal bed methane:
In coal bed methane reservoirs, the gas generated during coalification is held mainly on the internal surface of the coal matrix in an adsorbed state, with only a small fraction present as free gas in the cleats and fractures. This matches description (I), gas is mostly present in adsorbed state. So R pairs with I.
Step 4: Matching S, Shale oil:
Shale oil refers to the liquid oil that is recovered from oil shale, either by mining and retorting the rock or by in situ heating, converting the kerogen into a synthetic crude. This matches description (III), oil recovered from shale. So S pairs with III.
Step 5: Assembling the full match and checking options:
Putting all four pairs together gives P-IV, Q-II, R-I, S-III. Comparing with the given options, option A gives Q-III and S-II which is wrong, option B gives P-I and R-IV which is wrong, option D also gives P-I and S-II which is wrong. Only option C, P-IV; Q-II; R-I; S-III, matches the derived pairing exactly.
Final Answer:
\[ oxed{ ext{(C) P - IV; Q - II; R - I; S - III}} \]