An object $O$ is placed at a distance of 20 cm from a thin Plano-convex lens of focal length 15 cm. The plane surface of the lens is silvered as shown in Fig. The image is formed at a distance of

The word KVPY is written on $\mathrm{a}$ board and viewed through different lenses such that board is at a distance beyond the focal length of the lens.

Ignoring magnification effects, consider the following statements.
$\left(\mathrm{I}\right)$ First image has been viewed from the planar side of a plano-concave lens and second image from the planar side of a plano-convex lens.
$\left(\mathrm{II}\right)$ First image has been viewed from the concave side of a plano-concave lens and second image from the convex side of a plano-convex lens.
$\left(\mathrm{III}\right)$ First image has been viewed from the concave side of a plano-concave lens and second image from the planar side of a plano-convex lens.
$\left(\mathrm{IV}\right)$ First image has been viewed from the planar side of a plano-concave lens and second image from the convex side of a plano-convexlens.

Which of the above statements are correct?

A small object is placed $50 \mathrm{cm}$ to the left of thin convex lens of focal length $30 \mathrm{cm}$. A convex spherical mirror of radius of curvature $100 \mathrm{cm}$ is placed to the right of the lens at a distance of $50 \mathrm{cm}$. The mirror is tilted such that the axis of the mirror is at an angle $\theta =30°$ to the axis of the lens, as shown in the figure. If the origin of the coordinate system is taken to be at the centre of the lens, the coordinates (in $\mathrm{cm}$) of the point $(x, y)$ at which the image is formed are: