A concave mirror for face viewing has focal length of \(0.4~\text{m}\). The distance at which you hold the mirror from your face in order to see your image upright with a magnification of \(5\) is:
1. \(1.60~\text{m}\)
2. \(0.16~\text{m}\)
3. \(0.32~\text{m}\)
4. \(0.24~\text{m}\)

A concave mirror has a radius of curvature of \(40~\text{cm}\). It is at the bottom of a glass that has water filled up to \(5~\text{cm}\) (see figure). If a small particle is floating on the surface of the water, its image as seen, from directly above the glass, is at a distance \(d\) from the surface of the water. The value of \(d\) is close to: ( Refractive index of water \(1.33\)) 

1. \(11.7~\text{cm}\)
2. \(6.7~\text{cm}\)
3. \(13.4~\text{cm}\)
4. \(8.8~\text{cm}\)

A spherical mirror is obtained as shown in the figure from a hollow glass sphere. If an object is positioned in front of the mirror, what will be the nature and magnification of the image of the object? (Figure drawn as schematic and not to scale)
      

When an object is kept at a distance of \(30~\text{cm}\) from a concave mirror, the image is formed at a distance of \(10~\text{cm}\) from the mirror. If the object is moved with a speed of \(9~\text{cms}^{-1}\), the speed (\(\text{in cms}^{-1}\)) with which image moves at that instant is:
1. \(4\)
2. \(3\)
3. \(2\)
4. \(1\)

A short straight object of height \(100\) cm lies before the central axis of a spherical mirror whose focal length has absolute value \(|f|=40~\mathrm{cm}\). The image of object produced by the mirror is of height \(25\) cm and has the same orientation of the object. One may conclude from the information: