An object is placed at $20 \, cm$ from a convex mirror of focal length $10 \, cm$. The image formed by the mirror is

The image formed by a convex mirror of focal length $30 \,cm$ is a quarter of the size of the object. The distance of the object from the mirror is (in $\,cm$)

$A$ driver sitting inside a parked car is watching vehicles approaching from behind with the help of a side-view mirror,which is a convex mirror with a radius of curvature $R = 2 \ m$. Another car approaches from behind with a uniform speed of $90 \ km/h$. When the car is at a distance of $24 \ m$ from the mirror,the magnitude of the acceleration of the image in the side-view mirror is $a$. The value of $100a$ is $m/s^2$.

The shape of the image formed of an object $AB$ due to the concave mirror shown in the figure is best represented by (assume point $A$ is at the centre of curvature of the mirror):-

$STATEMENT-1$: The formula connecting $u, v$ and $f$ for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature. because
$STATEMENT-2$: Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.

$A$ candle of height $3 \ cm$ is placed at $300 \ cm$ 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 $.... \ cm$.