Step 1: Understand equivalent weight concept of KMnO\(_4\).
The equivalent weight of KMnO\(_4\) depends on the number of electrons exchanged in redox reaction, which changes with the reaction medium. Hence, the same compound has different equivalent weights in acidic, neutral, and basic media.
Step 2: Determine oxidation states and reduction behavior.
In acidic medium, MnO\(_4^-\) reduces to Mn\(^{2+}\) (gain of 5 electrons).
In neutral medium, it reduces to MnO\(_2\) (gain of 3 electrons).
In strongly basic medium, it reduces to MnO\(_4^{2-}\) (gain of 1 electron).
Step 3: Compute equivalent weight formula basis.
Equivalent weight is given by:
\[
\text{Eq. wt.} = \frac{Molecular\ weight}{n\text{-factor}}
\]
Molecular weight of KMnO\(_4\) = 158.
Step 4: Calculate values in each medium.
Acidic medium: \(n = 5\), so
\[
\frac{158}{5} = 31.6
\]
Neutral medium: \(n = 3\), so
\[
\frac{158}{3} \approx 52.7
\]
Basic medium: \(n = 1\), so
\[
\frac{158}{1} = 158
\]
Step 5: Match with given list.
So,
A (acidic) → 31.6 → (ii)
B (neutral) → 52.7 → (iii)
C (basic) → 158 → (i)
Step 6: Final conclusion.
Thus, correct matching is:
\[
A \to ii,\; B \to iii,\; C \to i
\]
\[
\boxed{(2)}
\]