Step 1: Understand the mechanisms of material removal in different machining processes.
- Chemical Machining (A) involves material removal by corrosive action (II).
- Electro-Machining (B) involves fusion and vaporization due to electrical energy (I).
- Electro-chemical discharge Machining (C) involves ion displacement (IV), which is due to electrochemical processes.
- Ultrasonic Machining (D) involves erosion by high-frequency vibrations (III).
Step 2: Conclusion
The correct matching is:
- (A) Chemical Machining → (II) Corrosive
- (B) Electro-Machining → (I) Fusion and vaporization
- (C) Electro-chemical discharge Machining → (IV) Ion displacement
- (D) Ultrasonic Machining → (III) Erosion
Final Answer:
\[
\boxed{(A) (I), (B) (II), (C) (IV), (D) (III)}
\]