Under which ideal condition does the efficiency of a Carnot engine become $100 \%$?

When the temperature difference between the source and sink increases,the efficiency of the heat engine

$A$ Carnot engine with efficiency $\eta$ operates between two heat reservoirs with temperatures $T_1$ and $T_2$,where $T_1 > T_2$. If only $T_1$ is changed by $0.4 \%$,the change in efficiency is $\Delta \eta_1$,whereas if only $T_2$ is changed by $0.2 \%$,the efficiency is changed by $\Delta \eta_2$. The ratio $\frac{\Delta \eta_1}{\Delta \eta_2}$ is approximately,

The efficiency of a Carnot cycle is $\frac{1}{6}$. By lowering the temperature of the sink by $65 \ K$,it increases to $\frac{1}{3}$. The initial and final temperatures of the sink are:

What is a Carnot cycle?

For which of the following options will the efficiency of a Carnot engine be the highest?