The efficiency of a Carnot engine is $100\%$ if

Two Carnot engines $A$ and $B$ are operated in succession. The first one,$A$,receives heat from a source at $T_1 = 800 \ K$ and rejects heat to a sink at $T_2 \ K$. The second engine,$B$,receives the heat rejected by the first engine and rejects heat to another sink at $T_3 = 300 \ K$. If the work outputs of the two engines are equal,then the value of $T_2$ is .... $K$.

The Carnot cycle (reversible) of a gas represented by a Pressure-Volume $(P-V)$ curve is shown in the diagram. Consider the following statements:
$I.$ Area $ABCD =$ Work done by the gas
$II.$ Area $ABCD =$ Net heat absorbed
$III.$ Change in the internal energy in the cycle $= 0$
Which of these are correct?

$A$ frictionless heat engine can be $100 \%$ efficient only if its exhaust temperature is ............

$A$ Carnot heat engine works with an ideal diatomic gas and an adiabatic volume expansion ratio of $32$. Then its efficiency is ....... $\%$

The temperature of the sink of a Carnot engine is $300 \,K$ and the efficiency of the engine is $0.25$. If the temperature of the source of the engine is increased by $100 \,K$, the efficiency of the engine increases by: