`{:("Column I","Column II"),((A)" As object is approaches from x = oo to x = R ,the image approaches the pole . The mirror must be",(p)"convex"),((B)"As object approches from x = R//2 to x=0 , then the image approaches the pole. The mirror may be",(q)" concave"),((C) "The speed of the object is u , then if mirror is concave the speed of the image is " , (r) ((R)/(R + 2x))^(2)u) , ((D) " The speed of the object is u , then if mirror is convex then speed of the image is " , (s) ((R)/(R-2x))^(2)u):}`

Explanation

To solve the problem, we need to match the statements in Column I with the appropriate statements in Column II based on the properties of concave and convex mirrors.

### Step-by-Step Solution:

1. **Analyzing Statement A**:
- The statement says: "As the object approaches from x = ∞ to x = R, the image approaches the pole."
- This behavior is characteristic of a **convex mirror**. In a convex mirror, as the object moves from infinity towards the mirror, the image formed moves closer to the mirror's pole.
- **Match**: A → p (convex)

2. **Analyzing Statement B**:
- The statement says: "As the object approaches from x = R/2 to x = 0, then the image approaches the pole."
- This behavior can occur in a **concave mirror**. As the object moves from R/2 (between the focus and the pole) to the mirror, the image also moves towards the pole.
- **Match**: B → q (concave)

3. **Analyzing Statement C**:
- The statement says: "The speed of the object is u, then if the mirror is concave, the speed of the image is..."
- For a concave mirror, the speed of the image can be calculated using the magnification formula. The magnification (m) is given by the ratio of the image distance (v) to the object distance (u). The speed of the image can be derived as \( v = \left(\frac{R}{R - 2x}\right)^2 u \).
- **Match**: C → r \(\left(\frac{R}{R - 2x}\right)^2 u\)

4. **Analyzing Statement D**:
- The statement says: "The speed of the object is u, then if the mirror is convex, the speed of the image is..."
- For a convex mirror, the speed of the image can similarly be derived using the magnification formula. The speed of the image is given by \( v = \left(\frac{R}{R + 2x}\right)^2 u \).
- **Match**: D → s \(\left(\frac{R}{R + 2x}\right)^2 u\)

### Final Matches:
- A → p (convex)
- B → q (concave)
- C → r \(\left(\frac{R}{R - 2x}\right)^2 u\)
- D → s \(\left(\frac{R}{R + 2x}\right)^2 u\)