Let a plano-convex lens of focal length 10 cm be silvered at its plane face. What will be the distance d at which an object must be placed in order to get its image on itself ? 

The object should be placed at the radius of curvature for it to form image at the same place.

So, Focal length is half of radius of curvature.

Applying this in power formula for combination of lens and mirror:

$\begin{array}{l}{\mathrm{P}}_{\text{tot }}=2\times {\mathrm{P}}_{\text{lens }}+{\mathrm{P}}_{\text{mirror }}\\ {\mathrm{P}}_{\text{tot }}=\frac{1}{\mathrm{\alpha }/2}=\frac{2}{\mathrm{d}}\\ {\mathrm{P}}_{\mathrm{lens}}=\frac{1}{0.1\mathrm{m}}=10\mathrm{D}\end{array}$

Equating both :

$\begin{array}{l}\frac{2}{\mathrm{d}}=2\times 10\mathrm{D}\\ \Rightarrow \frac{2}{\mathrm{d}}=20\mathrm{D}\\ \mathrm{d}=\frac{1}{10}\mathrm{m}=10\mathrm{cm}\end{array}$