An object is placed at a distance of $f$ from the pole of a convex mirror of focal length $f$. Where will the image be formed?

An object placed in front of a concave mirror at a distance of $x \ cm$ from the pole gives a $3$ times magnified real image. If it is moved to a distance of $(x+5) \ cm$, the magnification of the image becomes $2$. The focal length of the mirror is: (in $cm$)

An object of length $f/3$ is placed on the principal axis of a concave mirror of focal length $f$. The image of the end of the object farthest from the mirror is formed at the same position. Find the length of the image.

An object is placed at a distance of $20 \ cm$ from the pole of a concave mirror of focal length $10 \ cm$. The distance of the image formed is

$A$ square cardboard of side $3\, cm$ is placed $25\, cm$ from a concave mirror of focal length $10\, cm$. What is the area enclosed by the image of the cardboard? (The plane of the cardboard is perpendicular to the principal axis.)

Consider the following statements regarding an object placed between the pole and the focus of a concave mirror: $I$. The image is real. $II$. The image is magnified. $III$. The image is erect. Which of the following is correct?