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 __________.
Among $\mathrm{V}(\mathrm{CO})_6, \mathrm{Cr}(\mathrm{CO})_5, \mathrm{Cu}(\mathrm{CO})_3, \mathrm{Mn}(\mathrm{CO})_5, \mathrm{Fe}(\mathrm{CO})_5,\left[\mathrm{Co}(\mathrm{CO})_3\right]^{3-},\left[\mathrm{Cr}(\mathrm{CO})_4\right]^{4-}$, and $\operatorname{Ir}(\mathrm{CO})_3$, the total number of species isoelectronic with $\mathrm{Ni}(\mathrm{CO})_4$ is _________.
[Given, atomic number: $\mathrm{V}=23, \mathrm{Cr}=24, \mathrm{Mn}=25, \mathrm{Fe}=26, \mathrm{Co}=27, \mathrm{Ni}=28, \mathrm{Cu}=29, \mathrm{Ir}=77$ ]
In the following reaction sequence, the major product $\mathbf{P}$ is formed.
Glycerol reacts completely with excess $\mathbf{P}$ in the presence of an acid catalyst to form $\mathbf{Q}$. Reaction of $\mathbf{Q}$ with excess $\mathrm{NaOH}$ followed by the treatment with $\mathrm{CaCl}_2$ yields Ca-soap $\mathbf{R}$, quantitatively. Starting with one mole of $\mathbf{Q}$, the amount of $\mathbf{R}$ produced in gram is __________.
[Given, atomic weight: $\mathrm{H}=1, \mathrm{C}=12, \mathrm{~N}=14, \mathrm{O}=16, \mathrm{Na}=23, \mathrm{Cl}=35, \mathrm{Ca}=40$ ]
Among the following complexes, the total number of diamagnetic species is ___________.
$\left[\mathrm{Mn}\left(\mathrm{NH}_3\right)_6\right]^{3+},\left[\mathrm{MnCl}_6\right]^{3-},\left[\mathrm{FeF}_6\right]^{3-},\left[\mathrm{CoF}_6\right]^{3-},\left[\mathrm{Fe}\left(\mathrm{NH}_3\right)_6\right]^{3+}$, and $\left[\mathrm{Co}(\mathrm{en})_3\right]^{3+}$
[Given, atomic number: $\mathrm{Mn}=25, \mathrm{Fe}=26, \mathrm{Co}=27$;
$$ \text { en } \left.=\mathrm{H}_2 \mathrm{NCH}_2 \mathrm{CH}_2 \mathrm{NH}_2\right] $$