The correct matching between the equipment and their functions in municipal solid waste treatment is as follows:
Step 1: Trommel
A trommel is used for screening, which is the process of separating materials based on their size. Therefore, \( P \) matches with (iii) Screening.
Step 2: Magnetic separator
A magnetic separator is used to recover ferrous metals from the waste. Therefore, \( Q \) matches with (iv) Ferrous metal recovery.
Step 3: Hammer mill
A hammer mill is a machine used for size reduction of materials, breaking them down into smaller pieces. Therefore, \( R \) matches with (i) Size reduction.
Step 4: Eddy current separator
An eddy current separator is used for separating non-ferrous metals, especially aluminium, from other materials. Therefore, \( S \) matches with (ii) Aluminium separation.
Final Answer:
\[
\boxed{\text{(A) P-(iii), Q-(iv), R-(i), S-(ii)}}
\]