$A$ Carnot engine operating between two reservoirs has an efficiency of $\frac{1}{3}$. When the temperature of the cold reservoir is raised by $x$,its efficiency decreases to $\frac{1}{6}$. The value of $x$,if the temperature of the hot reservoir is $99^{\circ} C$,will be $........ K$.

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: Efficiency of a reversible heat engine will be highest at $-273^{\circ} C$ temperature of cold reservoir.
Reason $R$: The efficiency of Carnot's engine depends not only on the temperature of the cold reservoir but it depends on the temperature of the hot reservoir too and is given as $\eta = (1 - \frac{T_2}{T_1})$.
In the light of the above statements,choose the correct answer from the options given below:

Give the basic features of a heat engine based on a cyclic process and obtain the formula for its efficiency.

An ideal heat engine exhausts heat at $77\,^{\circ}C$. To have a $30\%$ efficiency,it must take heat at what temperature in $^{\circ}C$?

Even a Carnot engine cannot give $100\%$ efficiency because we cannot

The efficiency of a Carnot cycle is $\frac{1}{6}$. By lowering the temperature of the sink by $65 \ K$,it increases to $\frac{1}{3}$. The initial and final temperatures of the sink are: