A convex lens (of focal length 20 cm) and a concave mirror, having their principal axes along the same lines, are kept 80 cm apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of 30 cm to the left of the convex lens, its image remains at the same position even if the concave mirror is removed. The maximum distance of the object for which this concave mirror, by itself would produce a virtual image would be :

Correct option is B. 10cm
Image formed by lens
1/v - 1/u = 1/f
1/v + 1/30 = 1/20
v = +60cm
If image position does not change even when the mirror is removed, it means the image formed by the lens is formed at the center of curvature of the spherical mirror.
Radius of curvature of mirror = 80 - 60 = 20cm ⇒ focal length of mirror f = 10cm
For a virtual image, the object is to be kept between the focus and the pole.
⇒ maximum distance of the object from the spherical mirror for which a virtual image is formed, is 10cm.