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

$A$ candle flame of $3 \, cm$ is placed at $300 \, cm$ from a wall. $A$ concave mirror is kept at distance $x$ from the wall in such a way that the image of the flame on the wall is $9 \, cm$. Then $x$ is......$cm$.

Use the mirror equation to deduce that:
$(a)$ an object placed between $f$ and $2f$ of a concave mirror produces a real image beyond $2f$.
$(b)$ a convex mirror always produces a virtual image independent of the location of the object.
$(c)$ the virtual image produced by a convex mirror is always diminished in size and is located between the focus and the pole.
$(d)$ an object placed between the pole and focus of a concave mirror produces a virtual and enlarged image.

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.

$A$ square wire frame of side length $3.0 \, cm$ is placed $25 \, cm$ away from a concave mirror of focal length $10 \, cm$. The center of the wire frame is on the axis of the mirror,with two of its sides perpendicular to the axis. The area of the image will be $..... \, cm^2$.

In an experiment to determine the focal length $(f)$ of a concave mirror by the parallax method,a student places the object pin $\text{A}$ on the principal axis at a distance $x$ from the pole $\text{P}$. The student looks at the pin and its inverted image from a distance,keeping his/her eye in line with $\text{PA}$. When the student shifts his/her eye towards the left,the image appears to the right of the pin. Then: