let \(\lambda\neq 0\) be in r.If \(\alpha\) and \(\beta\) are the roots of the equation, then x2-x+2\(\lambda\)=0 and \(\alpha\) and \(\gamma\) are the roots of the equation, 3x2-10x+27\(\lambda\)=0,then \(\frac{\beta\gamma}{\lambda}=?\)
36
27
9
18
The correct answer is option (D) : 18
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 ___________.