
Bond Analysis of 2-formylhex-4-enoic acid
The compound 2-formylhex-4-enoic acid has the molecular structure represented as:
\(H–O–C(=O)–CH(CHO)–CH_2–CH=CH–CH_3\)
Where the numbering of carbon atoms is as follows: \(C_1\) to \(C_6\).
Each single bond is a \(\sigma\) (sigma) bond, and each double bond consists of one \(\sigma\) and one \(\pi\) (pi) bond.
1. The molecule contains both a –COOH (carboxylic acid) group and a –CHO (formyl) group.
2. The C=O bonds in both groups contribute two \(\pi\) bonds.
3. The C=C double bond at position 4–5 adds one more \(\pi\) bond.
4. Adding all sigma and pi bonds, we get:
\[\sigma\text{-bonds} = 19, \quad \pi\text{-bonds} = 3\]Among SO₃, NF₃, NH₃, XeF₂, CIF$_3$, and SF₆, the hybridization of the molecule with non-zero dipole moment and one or more lone-pairs of electrons on the central atom is:
Given below are two statements: 
Statement (II): Structure III is most stable, as the orbitals having the lone pairs are axial, where the $ \ell p - \beta p $ repulsion is minimum. In light of the above statements, choose the most appropriate answer from the options given below:
Match list-I with list-II and choose the correct option.
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 ___________.