Liquids A and B form ideal solution over the entire range of composition. At temperature $$T,$$ equimolar binary solution of liquids $$A$$ and $$B$$ has vapor pressure $$45$$ $$Torr.$$ At the same temperature, a new solution of $$A$$ and $$B$$ having mole fractions $${X_A}$$ and $${X_B}$$, respectively, has vapour pressure of $$22.5$$ $$Torr.$$ The value of $${x_A}/{x_B}$$ in the new solution is ___________.

(given that the vapor pressure of pure liquid $$A$$ is $$20$$ $$Torr$$ at temperature $$T$$)

In the following reaction sequence, the correct structure(s) of $$X$$ is (are)

The reaction (s) leading to the formation of $$1,3,5$$-trimethylbenzene is (are)

A reversible cyclic process for an ideal gas is shown below. Here, $$P, V,$$ and $$T$$ are pressure, volume and temperature, respectively. The thermodynamic parameters $$q,w, H$$ and $$U$$ are heat, work, enthalpy and internal energy, respectively.



The correct option(s) is (are)