An organic compound $\mathbf{P}$ with molecular formula $\mathrm{C}_9 \mathrm{H}_{18} \mathrm{O}_2$ decolorizes bromine water and also shows positive iodoform test. $\mathbf{P}$ on ozonolysis followed by treatment with $\mathrm{H}_2 \mathrm{O}_2$ gives $\mathbf{Q}$ and $\mathbf{R}$. While compound $\mathbf{Q}$ shows positive iodoform test, compound $\mathbf{R}$ does not give positive iodoform test. $\mathbf{Q}$ and $\mathbf{R}$ on oxidation with pyridinium chlorochromate (PCC) followed by heating give $\mathbf{S}$ and $\mathbf{T}$, respectively. Both $\mathbf{S}$ and $\mathbf{T}$ show positive iodoform test.

Complete copolymerization of 500 moles of $\mathbf{Q}$ and 500 moles of $\mathbf{R}$ gives one mole of a single acyclic copolymer $\mathbf{U}$.

[Given, atomic mass: $\mathrm{H}=1, \mathrm{C}=12, \mathrm{O}=16$ ]

The molecular weight of $\mathbf{U}$ is ______ .

Complete reaction of acetaldehyde with excess formaldehyde, upon heating with conc. $\mathrm{NaOH}$ solution, gives $\mathbf{P}$ and $\mathbf{Q}$. Compound $\mathbf{P}$ does not give Tollens' test, whereas $\mathbf{Q}$ on acidification gives positive Tollens' test. Treatment of $\mathbf{P}$ with excess cyclohexanone in the presence of catalytic amount of $p$-toluenesulfonic acid (PTSA) gives product $\mathbf{R}$.

Sum of the number of methylene groups $\left(-\mathrm{CH}_2-\right)$ and oxygen atoms in $\mathbf{R}$ is __________.

In the reaction given below, the total number of atoms having sp² hybridization in the major product P is _________.

In the following reaction, compound Q is obtained from compound P via an ionic intermediate



What is the degree of unsaturation of Q?