Consider the following reaction :

$$ \begin{aligned} & 2 \mathrm{~A}(\mathrm{~g})+\mathrm{B}(\mathrm{~g}) \rightarrow 2 \mathrm{D}(\mathrm{~g}) \\ & \Delta \mathrm{U}^{\ominus}=-10 \mathrm{~kJ} \mathrm{~mol}^{-1} \text { and } \Delta \mathrm{S}^{\ominus}=-44 \mathrm{JK}^{-1} \text { at } 298 \mathrm{~K} . \end{aligned} $$

Identify the correct option with $\Delta \mathrm{G}^{\ominus}$ for the reaction and spontaneity of the reaction at 298 K .

(Given : $\mathrm{R}=8.31 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ )

At a certain temperature, $\mathrm{T}(\mathrm{K})$, during a process, 500 J is absorbed by the system and work of 200 J is done by the system. Then change in internal energy of the system is :

The standard heat of formation, in $\mathrm{kcal} / \mathrm{mol}$ of $\mathrm{Ba}^{2+}$ is : [Given : standard heat of formation of $\mathrm{SO}_4^{2-}$ ion $(\mathrm{aq})=-216 \mathrm{kcal} / \mathrm{mol}$, standard heat of crystallisation of $\mathrm{BaSO}_4(\mathrm{~s})=-4.5 \mathrm{kcal} / \mathrm{mol}$, standard heat of formation of $\left.\mathrm{BaSO}_4(\mathrm{~s})=-349 \mathrm{kcal} / \mathrm{mol}\right]$

$\mathrm{C}(\mathrm{s})+2 \mathrm{H}_2(\mathrm{~g}) \rightarrow \mathrm{CH}_4(\mathrm{~g}) ; \Delta \mathrm{H}=-74.8 \mathrm{~kJ} \mathrm{~mol}^{-1}$. Which of the following diagrams gives an accurate representation of the above reaction? [ $\mathrm{R} \rightarrow$ reactants; $\mathrm{P} \rightarrow$ products]