In a closed insulated container a liquid is stirred with a paddle...

System is in a closed container. So there will be no heat transfer. Therefore the heat is $q=0$. Now liquid is stirred with a paddle to increase the temperature which increases the internal energy $\Delta E$ of the system. $$\begin{aligned}& \Delta \mathrm{E}=n \mathrm{C} \Delta \mathrm{T}\\ & \Delta \mathrm{E} \neq0 \end{aligned}$$Work is also done on$ the system when started with a paddle.\begin{gathered}\mathrm{W} \neq0 \\ \Delta \mathrm{E}=q+\mathrm{W}=0+\mathrm{W}, \Delta \mathrm{E}=\mathrm{W}\\ \Delta \mathrm{E}=\Delta \mathrm{W} \neq0, q=0 \end{gathered}