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)
Consider the following two reactions A and B: 
The numerical value of [molar mass of $x$ + molar mass of $y$] is ___.
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 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.}

Two circular discs of radius \(10\) cm each are joined at their centres by a rod, as shown in the figure. The length of the rod is \(30\) cm and its mass is \(600\) g. The mass of each disc is also \(600\) g. If the applied torque between the two discs is \(43\times10^{-7}\) dyne·cm, then the angular acceleration of the system about the given axis \(AB\) is ________ rad s\(^{-2}\).
