Let \( 0 < z < y < x \) be three real numbers such that \( \frac{1}{x}, \frac{1}{y}, \frac{1}{z} \) are in an arithmetic progression and \( x, \sqrt{2}y, z \) are in a geometric progression. If \( xy + yz + zx = \frac{3}{\sqrt{2}} xyz \), then \( 3(x + y + z)^2 \) is equal to ____________.
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 ___________.