- Buna-N rubber is categorized as an Elastomer, making \( A \) match with III.
- Terylene is a Fibre polymer, which aligns \( B \) with I.
- Polystyrene falls under Thermoplastic polymers, so \( C \) corresponds to IV.
- Urea-Formaldehyde resin is a Thermosetting polymer, thus \( D \) aligns with II.
Therefore, the correct answer is Option (1): \( A - III, B - I, C - IV, D - II \).