The maximum possible efficiency of a heat engine is ...........

In a Carnot engine,as the gas absorbs heat energy from the source,the temperature of the source

$A$ Carnot engine whose efficiency is $40 \%$, receives heat at $500 \ K$. If the efficiency is to be $50 \%$, the source temperature for the same exhaust temperature is (in $K$)

Two Carnot engines $A$ and $B$ are operated in series. Engine $A$ receives heat from a reservoir at $600\,K$ and rejects heat to a reservoir at temperature $T$. Engine $B$ receives heat rejected by engine $A$ and in turn rejects it to a reservoir at $100\,K$. If the efficiencies of the two engines $A$ and $B$ are equal,what is the value of the intermediate temperature $T$ and the ratio of their efficiencies $\frac{\eta_A}{\eta_B}$?

In a Carnot engine,if the temperatures of the source and the sink are decreased by $100 \ K$ each,then the efficiency of the engine:

$A$ Carnot engine,whose efficiency is $40 \%$,takes heat from a source maintained at a temperature of $600 \ K$. If it is desired to have an efficiency of $60 \%$,then the intake temperature for the same exhaust (sink) temperature should be: (in $K$)