`{:(,"Column I",,"Column II",),((A),"Elastic collision",(p),KE " is conserved",),((B),"Inelastic collision",(q),KE "after collision = KE before collision" ,),((C ),"Perfectly inelastic collision",(r ),"KE after collision" != "KE before collision",),(,,(s),"particles stick after collision",),(,,(t),"Linear momentum is conserved",),(,,(u),"Relative velocity of separation after is zero",):}`

Answer

To solve the problem of matching the types of collisions with their characteristics, we will analyze each type of collision and its corresponding properties.

### Step-by-Step Solution:

1. **Identify the Types of Collisions:**
- **Elastic Collision (A)**: In this type of collision, both momentum and kinetic energy are conserved.
- **Inelastic Collision (B)**: In this collision, momentum is conserved, but kinetic energy is not conserved.
- **Perfectly Inelastic Collision (C)**: This is a specific type of inelastic collision where the colliding bodies stick together after the collision. Momentum is conserved, but kinetic energy is not.

2. **Match Elastic Collision (A):**
- **Characteristic**: Kinetic energy is conserved.
- **Match**: A → p (KE is conserved).

3. **Match Inelastic Collision (B):**
- **Characteristic**: Kinetic energy after collision is not equal to kinetic energy before collision.
- **Match**: B → r (KE after collision ≠ KE before collision).

4. **Match Perfectly Inelastic Collision (C):**
- **Characteristic**: The particles stick together after the collision.
- **Match**: C → s (particles stick after collision).

5. **Additional Characteristics:**
- For all types of collisions, linear momentum is conserved (t).
- In perfectly inelastic collisions, the relative velocity of separation after the collision is zero (u).

### Final Matches:
- A → p (Elastic Collision: KE is conserved)
- B → r (Inelastic Collision: KE after collision ≠ KE before collision)
- C → s (Perfectly Inelastic Collision: particles stick after collision)

### Summary of Matches:
- A (Elastic collision) → p (KE is conserved)
- B (Inelastic collision) → r (KE after collision ≠ KE before collision)
- C (Perfectly inelastic collision) → s (particles stick after collision)