$A$ thin rod of length $f/3$ lies along the axis of a concave mirror of focal length $f$. One end of its magnified image touches an end of the rod. The length of the image is

Match the corresponding entries of Column-$I$ with Column-$II$. [Where $m$ is the magnification produced by the mirror]

Column-$I$	Column-$II$
$1$. $m = -2$	a. Convex mirror
$2$. $m = -1/2$	b. Concave mirror
$3$. $m = +2$	c. Real image
$4$. $m = +1/2$	d. Virtual image

Which of the following graphs represents the magnification of a real image against the distance from the focus of a concave mirror?

$A$ short straight object of height $100\, cm$ lies before the central axis of a spherical mirror whose focal length has absolute value $|f|=40\, cm$. The image of the object produced by the mirror is of height $25\, cm$ and has the same orientation as the object. One may conclude from the information:

$A$ concave mirror gives an image three times as large as the object placed at a distance of $20\,cm$ from it. For the image to be real,the focal length should be........$cm$

$A$ straight metal rod of length $6 \ cm$ is placed along the principal axis of a concave mirror of focal length $9 \ cm$ such that the end of the rod closer to the mirror is at a distance of $15 \ cm$ from the pole of the mirror. The length of the image of the rod is (in $cm$)