A

Step 1: Analyze the nature of images formed by different optical devices based on their characteristics.

(i) Virtual image for all positions of real object:
- A concave mirror can produce a virtual image only when the object is located between the focal point and the mirror. But the question specifies 'for all positions of real object'.
- A convex lens, however, can create a virtual image regardless of the object's position as long as it is within a specific range.
Thus, the correct match is Convex lens.

(ii) Always diminished image for virtual object:
- A convex lens produces a diminished virtual image when the object is between the focus and the lens itself. Thus, the answer is Convex lens.

(iii) Always real image for virtual objects:
- A convex mirror will always produce a virtual image, while a concave mirror can produce a real image, but only with real objects. This points to a Convex mirror.

(iv) Real object at focus; image at finite distance:
- A concave mirror can produce a real image at finite distance when the object is located at the focal point, which further implies Concave mirror.

After matching, the connections appear as follows:
(i) Convex lens (B), (ii) Convex lens (B), (iii) Convex mirror (C), (iv) Concave lens (D). Therefore, the first match concludes with option A.