A common example of alpha decay is

Energy released \( Q \) is given by the equation: \[ Q = (\Delta m)_{\text{amu}} \times 931.5 \, \text{MeV}. \] Here, the mass defect \( \Delta m \) is: \[ \Delta m = m_u - m_{\text{Th}} - m_{\text{He}} = 238.05060 \, u - 234.04360 \, u - 4.00260 \, u = 0.0044 \, u. \] Thus, \[ Q = 0.0044 \times 931.5 \, \text{MeV} = 4.0986 \, \text{MeV}. \] Therefore, the energy released during the alpha decay of \( ^{238}_{92} U \) is 4.0986 MeV.

Potential energy (V) versus distance (x) is given by the graph. Rank various regions as per the magnitudes of the force (F) acting on a particle from high to low. 
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 ___________.