Predict the major product of the following reaction sequence: 




The given sequence starts with methylcyclohexane and involves the following reagents:
(1) \( \mathrm{Br_2}/h\nu \)
(2) Alcoholic \( \mathrm{KOH} \)
(3) \( \mathrm{HBr} \) / \( \mathrm{ROOR} \), \( h\nu \)
The reaction proceeds through three distinct stages:
1. Free-radical bromination at the most substituted carbon (tertiary position) under photochemical conditions.
2. β-Elimination (E2) by alcoholic \( \mathrm{KOH} \) to form an alkene (Zaitsev product).
3. Anti-Markovnikov addition of \( \mathrm{HBr} \) in the presence of peroxides (\( \mathrm{ROOR} \)), where bromine adds to the less substituted carbon.
Step 1: Radical bromination.
\[ \text{CH}_3\text{-C}_6\text{H}_{11} \xrightarrow{\mathrm{Br_2},\,h\nu} \text{1-Bromo-1-methylcyclohexane} \]Bromine substitutes the tertiary hydrogen (attached to the carbon bearing the methyl group), forming a tertiary alkyl bromide.
Step 2: Elimination using alcoholic \( \mathrm{KOH} \).
\[ \text{1-Bromo-1-methylcyclohexane} \xrightarrow[\Delta]{\mathrm{alc.\ KOH}} \text{1-Methylcyclohexene} \]Dehydrohalogenation gives the more substituted alkene (Zaitsev product).
Step 3: Radical addition of \( \mathrm{HBr} \) in the presence of peroxide.
\[ \text{1-Methylcyclohexene} \xrightarrow[\mathrm{ROOR},\,h\nu]{\mathrm{HBr}} \text{2-Bromo-1-methylcyclohexane} \]Under peroxide conditions, the addition follows the anti-Markovnikov rule. Bromine attaches to the less substituted carbon of the double bond, forming 2-bromo-1-methylcyclohexane.
The major product is 2-bromo-1-methylcyclohexane.
Correct Option: (2)
A solution of aluminium chloride is electrolyzed for 30 minutes using a current of 2A. The amount of the aluminium deposited at the cathode is _________
If \( z \) is a complex number and \( k \in \mathbb{R} \), such that \( |z| = 1 \), \[ \frac{2 + k^2 z}{k + \overline{z}} = kz, \] then the maximum distance from \( k + i k^2 \) to the circle \( |z - (1 + 2i)| = 1 \) is: