For a double strand DNA, one strand is given below:

The amount of energy required to split the double strand DNA into two single strands is _______ kcal $\operatorname{mol}^{-1}$.

[Given: Average energy per H-bond for A-T base pair $=1.0 ~\mathrm{kcal}~ \mathrm{mol}^{-1}$, G-C base pair $=1.5 ~\mathrm{kcal}$ $\mathrm{mol}^{-1}$, and A-U base pair $=1.25 ~\mathrm{kcal} ~\mathrm{mol}^{-1}$. Ignore electrostatic repulsion between the phosphate groups.]

A sample initially contains only U-238 isotope of uranium. With time, some of the U-238 radioactively decays into $\mathrm{Pb}-206$ while the rest of it remains undisintegrated.

When the age of the sample is $\mathbf{P} \times 10^8$ years, the ratio of mass of $\mathrm{Pb}-206$ to that of $\mathrm{U}-238$ in the sample is found to be 7. The value of $\mathbf{P}$ is _______.

[Given: Half-life of $\mathrm{U}-238$ is $4.5 \times 10^9$ years; $\log _e 2=0.693$ ]

Among $\left[\mathrm{Co}(\mathrm{CN})_4\right]^{4-},\left[\mathrm{Co}(\mathrm{CO})_3(\mathrm{NO})\right], \mathrm{XeF}_4,\left[\mathrm{PCl}_4\right]^{+},\left[\mathrm{PdCl}_4\right]^{2-},\left[\mathrm{ICl}_4\right]^{-},\left[\mathrm{Cu}(\mathrm{CN})_4\right]^{3-}$ and $\mathrm{P}_4$ the total number of species with tetrahedral geometry is _______.

An organic compound $\mathbf{P}$ having molecular formula $\mathrm{C}_6 \mathrm{H}_6 \mathrm{O}_3$ gives ferric chloride test and does not have intramolecular hydrogen bond. The compound $\mathbf{P}$ reacts with 3 equivalents of $\mathrm{NH}_2 \mathrm{OH}$ to produce oxime $\mathbf{Q}$. Treatment of $\mathbf{P}$ with excess methyl iodide in the presence of $\mathrm{KOH}$ produces compound $\mathbf{R}$ as the major product. Reaction of $\mathbf{R}$ with excess iso-butylmagnesium bromide followed by treatment with $\mathrm{H}_3 \mathrm{O}^{+}$gives compound $\mathbf{S}$ as the major product.

The total number of methyl $\left(-\mathrm{CH}_3\right)$ group(s) in compound $\mathbf{S}$ is ___.