\(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{3} \stackrel{(\mathrm{A})}{\longrightarrow} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{Br} \stackrel{(\mathrm{B})}{\longrightarrow} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{CN} \stackrel{(\mathrm{C})}{\longrightarrow} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{COOH}\) \((\mathrm{A}),(\mathrm{b})\) and \((\mathrm{c})\) are respectively, (a) \(\mathrm{NBS}, \mathrm{KCN}\) and \(\mathrm{H}_{\mathrm{y}} \mathrm{O}^{+}\) (b) \(\mathrm{Br}_{2} / \mathrm{Fe}, \mathrm{KCN}\) and \(\mathrm{H}_{3} \mathrm{O}^{+}\) (c) \(\mathrm{Br}_{2} / \mathrm{Fe}, \mathrm{HCN}\) and \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) (d) \(\mathrm{NBS}, \mathrm{AgCN}\) and \(\mathrm{H}_{3} \mathrm{O}^{+}\)

Step by step solution

01

Option (a)

The reagents are NBS, KCN, and H3O+. NBS (N-bromosuccinimide) can be used for the bromination of alkyl groups, so it's suitable for the first step. KCN promotes nucleophilic substitution to replace Br with CN, making it appropriate for the second step. The last step requires an acidic environment to hydrate the nitrile group to a carboxylic acid, and H3O+ provides the necessary hydronium ions. Therefore, option (a) has the correct set of reagents for the given reactions.

02

Option (b)

The reagents are Br2/Fe, KCN, and H3O+. Br2/Fe can cause bromination of aromatic rings, which is not needed in our case as we need the bromination of the alkyl group. Hence, option (b) is not suitable.

03

Option (c)

The reagents are Br2/Fe, HCN, and C2H5OH. Similar to option (b), Br2/Fe is not right for the first step. Also, while HCN can introduce a CN group, it's not the best choice for nucleophilic substitution. Lastly, C2H5OH (ethanol) will not provide the necessary acidic conditions for converting the nitrile to a carboxylic acid. So, option (c) is not the right choice.

04

Option (d)

The reagents are NBS, AgCN, and H3O+. While NBS can be used for the first step and H3O+ for the last step, AgCN is not suitable for the second step as it's not a good nucleophile. Therefore, option (d) is not correct. Based on our analysis, the correct answer is:

05

Answer

The correct set of reagents \((\mathrm{A}),(\mathrm{B})\) and \((\mathrm{C})\) is given in option (a): \(\mathrm{NBS}, \mathrm{KCN}\) and \(\mathrm{H}_{\mathrm{y}} \mathrm{O}^{+}\).

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