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 ______ .

When potassium iodide is added to an aqueous solution of potassium ferricyanide, a reversible reaction is observed in which a complex $\mathbf{P}$ is formed. In a strong acidic medium, the equilibrium shifts completely towards $\mathbf{P}$. Addition of zinc chloride to $\mathbf{P}$ in a slightly acidic medium results in a sparingly soluble complex Q.

The number of moles of potassium iodide required to produce two moles of $\mathbf{P}$ is _______.

When potassium iodide is added to an aqueous solution of potassium ferricyanide, a reversible reaction is observed in which a complex $\mathbf{P}$ is formed. In a strong acidic medium, the equilibrium shifts completely towards $\mathbf{P}$. Addition of zinc chloride to $\mathbf{P}$ in a slightly acidic medium results in a sparingly soluble complex Q.

The number of zinc ions present in the molecular formula of $\mathbf{Q}$ is _______.

Considering only the principal values of the inverse trigonometric functions, the value of

$$ \tan \left(\sin ^{-1}\left(\frac{3}{5}\right)-2 \cos ^{-1}\left(\frac{2}{\sqrt{5}}\right)\right) $$

is