All of the following statements are correct except (for a real object):

$A$ 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.....$cm$.

Suppose that the lower half of the concave mirror's reflecting surface in the figure is covered with an opaque (non-reflective) material. What effect will this have on the image of an object placed in front of the mirror?

$A$ concave mirror has a focal length $20\,cm$. The distance between the two positions of the object for which the image size is double of the object size is......$cm$

The distance between an object and its image (magnified by $-\frac{1}{3}$) is $30 \ cm$. The focal length of the mirror used is $\left(\frac{x}{4}\right) \ cm$,where the magnitude of the value of $x$ is . . . . . . .

$A$ concave mirror of radius of curvature $R$ has a circular outline of radius $r$. $A$ circular disc is to be placed normal to the axis at the focus,so that it collects all the light that is reflected from the mirror from a beam parallel to the axis. For $r \ll R$,the area of this disc has to be at least