Consider a solution of CO$_2$(g) dissolved in water in a closed container. Which one of the following plots correctly represents variation of $\log$ (partial pressure of CO$_2$ in vapour phase above water) [y-axis] with $\log$ (mole fraction of CO$_2$ in water) [x-axis] at
$25^\circ$C? 
Which one of the following graphs accurately represents the plot of partial pressure of CS₂ vs its mole fraction in a mixture of acetone and CS₂ at constant temperature?

Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.