A combination of two thin lenses with focal length $f_1$ and $f_2$ respectively forms an image of distant object at distance $60 \mathrm{cm}$ when lenses are in contact. The position of this image shifts by $35 \mathrm{cm}$ towards the combination when two lenses are separated by $10 \mathrm{cm}.$ The corresponding values of $f_1$ and $f_2$ are:

A plano-convex thin lens of focal length $10 \mathrm{cm}$ is silvered at its plane face. The distance $d$ at which an object must be placed in order to get its image on itself is:

In the figure $\left(\mathrm{i}\right)$ a thin lens of focal length $10 \mathrm{cm}$ is shown. The lens is cut into two equal parts and arranged as shown in the figure $\left(\mathrm{ii}\right).$ An object $AB$ of height $1 \mathrm{cm}$ is placed at a distance of $7.5 \mathrm{cm}$ then, height of the final image will be