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)
Which one of the following graphs accurately represents the plot of partial pressure of CS₂ vs its mole fraction in a mixture of acetone and CS₂ at constant temperature?

Consider the following two reactions A and B: 
The numerical value of [molar mass of $x$ + molar mass of $y$] is ___.
Consider the following reaction sequence: 
Given: Compound (x) has percentage composition \(76.6%\ \text{C}\), \(6.38%\ \text{H}\) and vapour density \(=47\). Compound (y) develops a characteristic colour with neutral \(\mathrm{FeCl_3}\) solution. Identify the {INCORRECT statement.}
Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.