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 ...... $cm$.

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?

$A$ 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 $cm$)

Incident parallel rays make an angle of $5^{\circ}$ with the axis of a concave mirror of focal length $20 \ cm$. The perpendicular distance of the image from the axis is nearly $-$ (in $cm$)

An image formed by a concave mirror of focal length $6 \, cm$ is $3$ times the size of the object. The distance of the object from the mirror is......$cm$.

In a car,a rear-view mirror having a radius of curvature $1.50 \, m$ forms a virtual image of a bus located $10.0 \, m$ from the mirror. The factor by which the mirror magnifies the size of the bus is close to