The work done by all the forces (external and Internal) on a system equals the change in

${\mathrm{W}}_{\mathrm{c}}+{\mathrm{W}}_{\mathrm{nc}}+{\mathrm{W}}_{\mathrm{ext}}={\mathrm{K}}_{\mathrm{f}}-{\mathrm{K}}_{\mathrm{i}}$

According to work – Energy theorem work done by all the forces (conservative, Non conservative, external) on a system is equals the change in KE.

Option a, c, d are wrong because

$\begin{array}{r}{\mathrm{W}}_{\mathrm{c}}+{\mathrm{W}}_{\mathrm{nc}}+{\mathrm{W}}_{\mathrm{ext}}\ne {\mathrm{u}}_{\mathrm{f}}-{\mathrm{u}}_{\mathrm{i}}\\ {\mathrm{W}}_{\mathrm{c}}+{\mathrm{W}}_{\mathrm{nc}}+{\mathrm{W}}_{\mathrm{ext}}\ne \mathrm{\Delta E}\end{array}$