Which of the following molecule has large extent of back bonding?

The right answer is A. $\mathrm{O}{\left({\mathrm{SiH}}_3\right)}_2$.
a) In $\mathrm{O}{\left({\mathrm{SiH}}_3\right)}_2$, Si has empty d-orbitals while oxygen has a single pair in the p-orbital. $\mathrm{O}{\left({\mathrm{SiH}}_3\right)}_2$ thus has a 2p–3d back bonding.

In comparison to $\mathrm{O}{\left({\mathrm{SiH}}_3\right)}_2$, the given alternative $\mathrm{OCl}$has less back bonding.