$A$ thin rod of $5 \, cm$ length is kept along the axis of a concave mirror of $10 \, cm$ focal length such that its image is real and magnified. If one end of the rod is at a distance of $2f$ from the mirror,what will be its magnification?

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

$A$ ray of light is incident on a concave mirror. It is parallel to the principal axis and its height from the principal axis is equal to the focal length of the mirror. The ratio of the distance of point $B$ (where the reflected ray intersects the principal axis) to the distance of the focus from the centre of curvature is ($AB$ is the reflected ray).

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 ...... $cm$.

An object of height $3.6 \ cm$ is placed normally on the principal axis of a concave mirror of radius of curvature $30 \ cm$. If the object is at a distance of $10 \ cm$ from the principal focus of the mirror, then the height of the real image formed due to the mirror is (in $cm$)

Incident parallel rays make an angle of $5^{\circ}$ with the axis of a concave mirror of focal length $20 \ cm$. The perpendicular distance of the image from the axis is nearly $-$ (in $cm$)