$A$ 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 $\,K$)

In a Carnot engine,the temperature of the reservoir is $927\ ^oC$ and that of the sink is $27\ ^oC.$ If the work done by the engine is $12.6 \times 10^6 \ J,$ the quantity of heat absorbed by the engine from the reservoir is:

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

$A$ number of Carnot engines are operated at identical cold reservoir temperatures $(T_{L})$. However,their hot reservoir temperatures are kept different. $A$ graph of the efficiency of the engines versus hot reservoir temperature $(T_{H})$ is plotted. The correct graphical representation is

Which statement is incorrect?

Suppose that two heat engines are connected in series,such that the heat exhaust of the first engine is used as the heat input of the second engine as shown in the figure. The efficiencies of the engines are $\eta_1$ and $\eta_2$,respectively. The net efficiency of the combination is given by