Given Molecules and Their Hybridization:
Correct Answer: The correct answer is 4.
• \(NH_3\): The nitrogen atom is surrounded by three bonded atoms and one lone pair, resulting in an sp3 hybridization due to the tetrahedral arrangement.
• \(SO_2\): Sulfur in \(SO_2\) is sp2 hybridized because it forms two sigma bonds and has one lone pair, giving a bent structure.
• \(SiO_2\): Each silicon atom forms four sigma bonds with oxygen atoms. However, due to its extended lattice structure, we consider the local bonding, indicating sp3 hybridization for the central Si atom.
• \(BeCl_2\): The beryllium atom is sp hybridized as it forms two sigma bonds with chlorine atoms, leading to a linear geometry.
• \(CO_2\): Carbon in \(CO_2\) is sp hybridized since it forms two sigma bonds with oxygen atoms, resulting in a linear structure.
• \(H_2O\): The oxygen atom has two sigma bonds and two lone pairs, leading to sp3 hybridization, resulting in a bent structure.
• \(CH_4\): Carbon in \(CH_4\) is sp3 hybridized as it forms four sigma bonds, resulting in a tetrahedral geometry.
• \(BF_3\): Boron in \(BF_3\) is sp2 hybridized, as it forms three sigma bonds with fluorine atoms, resulting in a planar triangular structure.
From the given following (A to D) cyclic structures, those which will not react with Tollen's reagent are : 
Compound 'P' undergoes the following sequence of reactions : (i) NH₃ (ii) $\Delta$ $\rightarrow$ Q (i) KOH, Br₂ (ii) CHCl₃, KOH (alc), $\Delta$ $\rightarrow$ NC-CH₃. 'P' is : 

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 ___________.