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 image formed by a convex mirror of focal length $30 \ cm$ is one-fourth the size of the object. The distance of the object from the mirror is ...... $cm$.

The direction of a ray of light incident on a concave mirror is shown by $PQ$, where $PQ$ is parallel to the principal axis. The direction in which the ray would travel after reflection is shown by four rays marked as $A$, $B$, $C$ and $D$. Which of the four rays correctly shows the direction of the reflected ray?

$A$ point object is placed at a distance of $30 \, cm$ from a convex mirror of focal length $30 \, cm$. Where will the image be formed?

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,

$A$ convex mirror of focal length $f$ forms an image which is $\frac{1}{n}$ times the size of the object. The distance of the object from the mirror is