Which type of process is performed in an ideal engine?

The temperature of the sink of a Carnot engine is $250 \ K$. In order to increase the efficiency of the Carnot engine from $25 \%$ to $50 \%$,the temperature of the sink should be increased by

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 ....... $^{\circ}C$.

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 operates with the cold reservoir at a temperature of $324 \; K$. If the heat engine takes $300 \; J$ of heat from the hot reservoir and delivers $180 \; J$ of heat to the cold reservoir per cycle,what is the minimum temperature of the hot reservoir in $K$?

Two heat engines $X$ and $Y$ of same efficiency are connected in series in such a way that the sink of $X$ works as the source of $Y$. $X$ receives heat at $900 \,K$ and rejects some heat to its sink at $T \,K$, and in turn, $Y$ rejects heat to its sink at $400 \,K$. Then the temperature $T$ is: (in $\,K$)