Under which of the following conditions will a convex mirror of focal length $f$ produce an image that is erect,diminished and virtual?

$A$ 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 $.... \ cm$.

An object is placed at a distance of $20 \ cm$ from the pole of a concave mirror of focal length $10 \ cm$. The distance of the image formed is

$A$ ray of light is incident on a convex mirror along a vector $3\hat i + 4\hat j + 12\hat k$. The normal to the convex mirror at the point of incidence is along $3\hat i + 4\hat j$. The unit vector along the reflected ray is:

$A$ small candle,$2.5\; cm$ in size,is placed at $27\; cm$ in front of a concave mirror of radius of curvature $36\; cm$. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror,how would the screen have to be moved?

$A$ mirror is used to produce an image with magnification of $\frac{1}{4}$. If the distance between the object and its image is $40 \ cm$,then the focal length of the mirror is . . . . . . . (in $cm$)