The efficiency of a Carnot heat engine is $25 \%$ and the temperature of its source is $127^{\circ} C$. Without changing the temperature of the source,if the absolute temperature of the sink is decreased by $10 \%$,the new efficiency of the engine is: (in $\%$)

$A$ Carnot engine with efficiency $\eta$ operates between two heat reservoirs with temperatures $T_1$ and $T_2$,where $T_1 > T_2$. If only $T_1$ is changed by $0.4 \%$,the change in efficiency is $\Delta \eta_1$,whereas if only $T_2$ is changed by $0.2 \%$,the efficiency is changed by $\Delta \eta_2$. The ratio $\frac{\Delta \eta_1}{\Delta \eta_2}$ is approximately,

Match the temperatures of the source and sink ($T_1$ and $T_2$ respectively) of a Carnot heat engine given in List-$I$ with the corresponding efficiencies given in List-$II$.

List-$I$	List-$II$
$A$. $T_1 = 500 \text{ K}, T_2 = 300 \text{ K}$	$i$. $0.2$
$B$. $T_1 = 500 \text{ K}, T_2 = 350 \text{ K}$	$ii$. $0.3$
$C$. $T_1 = 800 \text{ K}, T_2 = 400 \text{ K}$	$iii$. $0.4$
$D$. $T_1 = 450 \text{ K}, T_2 = 360 \text{ K}$	$iv$. $0.5$

$A$ heat engine receives $200 \, cal$ of heat and rejects $150 \, cal$ of heat. If the temperature of the source is $400 \, K$,what is the temperature of the sink in $K$ (in $, K$)?

When the absolute temperature of the source of a Carnot heat engine is increased by $25 \%$,its efficiency increases by $80 \%$. The new efficiency of the engine is (in $\%$)

$A$ scientist claims that their heat engine has an efficiency of $26\%$ when operating between a source temperature of $127^{\circ}C$ and a sink temperature of $27^{\circ}C$. This implies that: