Step 1: Know what each shaft sinking method actually does.
Piling system uses timber or steel piles driven ahead of the excavation to hold back the ground. It works only in shallow, loose ground close to the surface, because piles cannot be driven very deep.
Caisson (drum) method sinks a rigid cylindrical curb, called a caisson, under its own weight. The cutting edge of the caisson bites into loose ground while the strong bands of strata support the caisson's weight as it goes down, so this method suits strata with alternating strong and loose layers.
Cementation seals the ground by pumping cement grout under pressure into the fissures and cracks of the rock, so it works on fissured, water bearing strata, but only when there is no running or quick sand, because a fast flow of sand and water would wash the grout away before it sets.
Freezing turns the water in the ground into ice around the shaft, forming a temporary ice wall strong enough to sink through. It is kept for the worst conditions, heavily watery ground that includes running or quick sand, where cementation cannot be trusted.
Step 2: Match P, Q, R, S against 1, 2, 3, 4.
P (Piling system) needs shallow, loose ground near the surface, which is description (2).
Q (Caisson method) needs alternating strong and loose soil with the drum sinking under its own weight, which is description (1).
R (Cementation) needs fissured water bearing strata without running sand, which is description (4).
S (Freezing) needs heavily watery strata including quick sand, which is description (3).
Step 3: Check why the other options fail.
Option (A) sends P to (2) correctly but puts Q against (3), which is freezing's job, not caisson's.
Options (B) and (D) both put P against (4), but piling cannot handle fissured water bearing strata, that needs cementation.
Final Answer:
The correct match is P to 2, Q to 1, R to 4, S to 3.
\[ \boxed{P \rightarrow 2,\ Q \rightarrow 1,\ R \rightarrow 4,\ S \rightarrow 3} \]