Hydrocarbon (P) on reductive ozonolysis gives products which give positive iodoform test and on acidification produces the compound shown. Identify the structure of (P). 
Concept:
Ozonolysis cleaves carbon–carbon double bonds to form carbonyl compounds. Reductive ozonolysis (\(O_3/Zn/H_2O\)) converts alkenes into aldehydes and ketones. If one of the resulting products contains a methyl ketone (\(-COCH_3\)), it gives a positive iodoform test. 
Step 1: Ozonolysis reaction. \[ \text{Alkene} \xrightarrow{O_3/Zn,H_2O} \text{Carbonyl compounds} \] The ozonolysis products include a methyl ketone which gives a positive iodoform test. Step 2: Iodoform test condition. Compounds containing the group \[ -COCH_3 \] give yellow precipitate of \(CHI_3\). Step 3: Formation of intermediate products. The ozonolysis of structure (1) produces carbonyl compounds capable of undergoing aldol condensation under basic conditions. \[ \text{Carbonyl compound} \xrightarrow{OH^- / \Delta} \text{Aldol product} \] Step 4: Acidification step. After iodoform reaction: \[ RCOCH_3 \xrightarrow{I_2/NaOH} RCOO^- + CHI_3 \] On acidification: \[ RCOO^- \xrightarrow{H^+} RCOOH \] The final product shown in the question matches the product obtained from alkene structure (1). Step 5: Conclusion. \[ \boxed{\text{Structure (1) is the correct hydrocarbon}} \]
The % increase in oxygen in steam volatile product with respect to phenol is ____ \(10^{-1}\%\).
Benzene reacts with propyl chloride in presence of \(AlCl_3\) to give product \(X\). Mark correct statement(s) for the given reaction. 
(a) One of the intermediate is formed due to rearrangement.
(b) Major product is n-propylbenzene.
(c) Polysubstitution of substrate is also possible.
(d) Electron releasing group decreases rate of reaction.
Let the lines $L_1 : \vec r = \hat i + 2\hat j + 3\hat k + \lambda(2\hat i + 3\hat j + 4\hat k)$, $\lambda \in \mathbb{R}$ and $L_2 : \vec r = (4\hat i + \hat j) + \mu(5\hat i + + 2\hat j + \hat k)$, $\mu \in \mathbb{R}$ intersect at the point $R$. Let $P$ and $Q$ be the points lying on lines $L_1$ and $L_2$, respectively, such that $|PR|=\sqrt{29}$ and $|PQ|=\sqrt{\frac{47}{3}}$. If the point $P$ lies in the first octant, then $27(QR)^2$ is equal to}
As shown in the figure, the ratio of \(T_1\) and \(T_2\) is 