To determine the correctness of the statements provided, let's analyze each reaction separately.
Statement-I:
The sequence of reactions is \(\text{KMnO}_4 \xrightarrow{\Delta} \text{NH}_2\) followed by \(\text{Br}_2/\text{KOH} \rightarrow \text{NH}_2\).
The first part of the reaction suggests heating with \(\text{KMnO}_4\). However, there seems to be a typographical error or inconsistency as \(\text{KMnO}_4\) doesn't directly lead to an \(\text{NH}_2\) group. The second part is related to the Hofmann bromamide reaction where an amide reacts with \(\text{Br}_2/\text{KOH}\) to form an amine with one less carbon atom. Assuming the initial compound that reacts with \(\text{Br}_2/\text{KOH}\) is already an amide, the reaction could indeed yield an \(\text{NH}_2\) group.
Thus, we can consider the statement constructively correct under these assumptions.
Statement-II:
The reaction \(\text{CH}_3\text{NH}_2 \xrightarrow{(i) \text{ Br}_2/\text{H}_2\text{O}, (ii) \text{ NaNO}_2/\text{HCl}, (iii) \text{ H}_3\text{PO}_2/\Delta} \text{CH}_3\text{Br}\) describes a multi-step transformation:
This sequence correctly converts \(\text{CH}_3\text{NH}_2\) to \(\text{CH}_3\text{Br}\) through formation and substitution of the diazonium group.
Thus, both statements are describing valid chemical transformations, making both statements correct. Therefore, the correct answer is:
Statement-I and Statement-II both are correct.