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.
Concept:
This reaction is an example of Friedel–Crafts alkylation. In this reaction, an alkyl halide reacts with benzene in presence of a Lewis acid catalyst such as \(AlCl_3\) to generate a carbocation intermediate which then attacks the benzene ring. 
Step 1: Formation of carbocation intermediate. \[ CH_3CH_2CH_2Cl + AlCl_3 \rightarrow CH_3CH_2CH_2^+ + AlCl_4^- \] The primary carbocation formed is unstable and rearranges to a more stable secondary carbocation. \[ CH_3CH_2CH_2^+ \rightarrow (CH_3)_2CH^+ \] Thus, rearrangement occurs. Step 2: Electrophilic substitution on benzene. The rearranged secondary carbocation attacks benzene to form isopropylbenzene (cumene) as the major product. \[ \text{Benzene} + (CH_3)_2CH^+ \rightarrow \text{Isopropylbenzene} \] Therefore, the major product is not n-propylbenzene. Step 3: Polysubstitution possibility. The alkyl group introduced into benzene is electron-donating and activates the ring toward further substitution. Hence polysubstitution can occur. Step 4: Effect of substituents. Electron-releasing groups increase the rate of electrophilic substitution rather than decrease it. Step 5: Final evaluation of statements. (a) True — rearrangement occurs.
(b) False — major product is isopropylbenzene.
(c) True — polysubstitution is possible.
(d) False — electron releasing groups increase reaction rate. \[ \boxed{\text{Correct statements: a and c}} \]
Styrene undergoes the following sequence of reactions Molar mass of product (P) is:
The % increase in oxygen in steam volatile product with respect to phenol is ____ \(10^{-1}\%\).
Hydrocarbon (P) on reductive ozonolysis gives products which give positive iodoform test and on acidification produces the compound shown. Identify the structure of (P). 
Styrene undergoes the following sequence of reactions Molar mass of product (P) is:
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}