Step 1: Recall what each NDT method is best suited for.
Each non-destructive testing (NDT) method in Column II has a specific strength: some find internal flaws, some track cracks while a component stays in service, and some find only surface-breaking defects.
Step 2: Match P (Internal flaws in a railroad wheel).
Ultrasonic testing sends high-frequency sound waves through the thickness of a part and picks up reflections from internal discontinuities. A railroad wheel is a thick, solid steel component, so ultrasonic testing is the standard method for checking internal flaws deep inside it. So P matches entry (1), Ultrasonic.
Step 3: Match Q (In-service monitoring of a crack).
Acoustic emission testing listens for the transient elastic stress waves released when a crack grows or a defect moves under load. Since it can run continuously while the part is in service and under load, it is the method used for real-time, in-service crack monitoring. So Q matches entry (4), Acoustic Emission.
Step 4: Match R (Inclusion in mild steel).
Radiography passes X-rays or gamma rays through a part and records the image on film or a detector; a subsurface inclusion, being denser or less dense than the surrounding steel, shows up as a contrast change on the radiograph. This makes radiography the natural choice for finding an internal inclusion in mild steel. So R matches entry (2), Radiography.
Step 5: Match S (Surface crack in an Al-based alloy).
Dye penetrant testing lets a colored or fluorescent liquid seep into a surface-breaking crack by capillary action and then draws it back out with a developer, making the crack visible. It can only find defects open to the surface, which fits a surface crack in an aluminum-based alloy. So S matches entry (3), Dye Penetrant.
Step 6: Combine and check against the options.
The complete match is P-1, Q-4, R-2, S-3, which is exactly option (A).
\[ \boxed{P\text{-}1,\ Q\text{-}4,\ R\text{-}2,\ S\text{-}3} \]