The focal length of a concave mirror is $20 \ cm$. Determine where an object must be placed to form an image,magnified two times and real.

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

The distance of an object from a spherical mirror is equal to the focal length of the mirror. Then the image:

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

$A$ concave mirror of focal length $f$ forms an image $n$ times the size of the object. If the image is real, then the distance of the object from the mirror is .......

What can be the largest distance of an image of a real object from a convex mirror of radius of curvature $10\,cm$?