Which statement is incorrect?

$A$ Carnot engine,whose efficiency is $40\%$,takes in heat from a source maintained at a temperature of $500\ K$. It is desired to have an engine of efficiency $60\%$. Then,the intake temperature for the same exhaust (sink) temperature must be ....... $K$.

The $p-V$ diagram of a Carnot's engine is shown in the graph below. The engine uses $1$ mole of an ideal gas as the working substance. From the graph,the area enclosed by the $p-V$ diagram is equal to the net work done by the engine. Given that the heat supplied to the gas is $8000 \ J$,calculate the net work done by the engine. (Note: The efficiency of a Carnot engine is $\eta = 1 - \frac{T_2}{T_1} = \frac{W}{Q_1}$) (in $J$)

The ratio of the efficiencies of two Carnot engines $A$ and $B$ is $1.25$. The temperature difference between the source and the sink is the same in both engines. The ratio of the absolute temperatures of the sources of engines $A$ and $B$ is

$A$ Carnot engine absorbs heat from a reservoir maintained at temperature $1000 \,K$. The engine rejects heat to a reservoir whose temperature is $T$. If the magnitude of absorbed heat is $400 \,J$ and work performed is $300 \,J$, then the value of $T$ is (in $\,K$)

$Assertion :$ The Carnot cycle is useful in understanding the performance of heat engines.
$Reason :$ The Carnot cycle provides a way of determining the maximum possible efficiency achievable with reservoirs of given temperatures.