$A$ concave mirror has a focal length of $30 \, cm$. If the image formed is erect (virtual),at what distance from the mirror should an object be placed so that the image is three times the size of the object (in $, cm$)?

$A$ student performed the experiment of determination of focal length of a concave mirror by $u-v$ method using an optical bench of length $1.5 \ m$. The focal length of the mirror used is $24 \ cm$. The maximum error in the location of the image can be $0.2 \ cm$. The $5$ sets of $(u, v)$ values recorded by the student (in $cm$) are: $(42, 56), (48, 48), (60, 40), (66, 33), (78, 39)$. The data set$(s)$ that cannot come from the experiment and is (are) incorrectly recorded,is (are):
$(A) (42, 56)$
$(B) (48, 48)$
$(C) (66, 33)$
$(D) (78, 39)$

The distance of an object from the pole of a concave mirror is equal to its radius of curvature. The image must be:

An object ' $O$ ' is placed at a distance of $100\,cm$ in front of a concave mirror of radius of curvature $200\,cm$ as shown in the figure. The object starts moving towards the mirror at a speed of $2\,cm/s$. The position of the image from the mirror after $10\,s$ will be at ...... $cm$.

$A$ 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 longitudinal magnification of the image is

Two objects $A$ and $B$ are placed at $15\,cm$ and $25\,cm$ from the pole in front of a concave mirror having a radius of curvature $40\,cm$. The distance between the images formed by the mirror is $..........\,cm$.