$A$ concave mirror of focal length $f$ in air is dipped in a liquid of refractive index $\mu$. Its focal length in the liquid will be $:$

Consider the following statements regarding an object placed between the pole and the focus of a concave mirror: $I$. The image is real. $II$. The image is magnified. $III$. The image is erect. Which of the following is correct?

An object is placed on the principal axis of a concave mirror at a distance of $1.5 f$ ($f$ is the focal length). The image will be at ....... $f$.

An object is placed $40\;cm$ from a concave mirror of focal length $20\;cm.$ The image formed is

The radius of curvature of a concave mirror is $40 \ cm$ and the size of the image is twice that of the object. The object distance is $... \ cm$.

$A$ thin cylindrical rod of length $10\,cm$ is placed horizontally on the principal axis of a concave mirror of focal length $20\,cm$. The rod is placed in such a way that the midpoint of the rod is at $40\,cm$ from the pole of the mirror. The length of the image formed by the mirror will be $\frac{x}{3}\,cm$. The value of $x$ is $............$.