Step 1: Approach the matching from the test side instead of the person side.
Instead of asking "what test did each person invent," flip it around and ask "who is associated with each test in Column 2." This cross-check avoids mixing up similar sounding in-situ tests.
Step 2: Identify the person behind each test.
(P) Dilatometer test: this flat-blade membrane test in geotechnical practice is named after its inventor, Marchetti, so (P) traces back to (II) Marchetti.
(Q) Pressuremeter test: the radial-expansion borehole probe test was developed by Menard, so (Q) traces back to (I) Menard.
(R) Compaction test: the standard laboratory test relating water content to dry density was developed by Proctor, so (R) traces back to (IV) Proctor.
(S) Liquid limit test: the grooved-cup device used to find the liquid limit of soil was designed by Casagrande, so (S) traces back to (III) Casagrande.
Step 3: Assemble the full match.
Reading the four test-to-person links back as person-to-test pairs gives:
(I) Menard $\to$ (Q) Pressuremeter test
(II) Marchetti $\to$ (P) Dilatometer test
(III) Casagrande $\to$ (S) Liquid limit test
(IV) Proctor $\to$ (R) Compaction test
Step 4: Final Answer.
This set of pairs, (I)-(Q); (II)-(P); (III)-(S); (IV)-(R), is exactly option (A).
\[ \boxed{\text{Option (A)}} \]