The first operation involved in a Carnot cycle is

An engine has an efficiency of $1/6$. When the temperature of the sink is reduced by $62^{\circ}C$,its efficiency is doubled. The temperature of the source is ....... $^{\circ}C$.

$A$ diatomic ideal gas is used in a Carnot engine as a working substance. If during the adiabatic expansion part of the cycle,the volume of the gas increases from $V$ to $32V$,the efficiency of the engine is:

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

Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures $T_{1}$ and $T_{2}$. The temperature of the hot reservoir of the first engine is $T_{1}$ and the temperature of the cold reservoir of the second engine is $T_{2}$. $T$ is the temperature of the sink of the first engine,which is also the source for the second engine. How is $T$ related to $T_{1}$ and $T_{2}$,if both engines perform equal amounts of work?

This question has Statement $1$ and Statement $2.$ Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement $1 :$ An inventor claims to have constructed an engine that has an efficiency of $30\%$ when operated between the boiling and freezing points of water. This is not possible.
Statement $2:$ The efficiency of a real engine is always less than the efficiency of a Carnot engine operating between the same two temperatures.