The reaction for decolourisation of KMnO\(_4\) with H\(_2\)O\(_2\) is:
\[
2KMnO_4 + 3H_2O_2 + 4H_2O \rightarrow 2MnO_2 + 3O_2 + 4KOH
\]
From the stoichiometry, 3 moles of H\(_2\)O\(_2\) are required for every 2 moles of KMnO\(_4\). Therefore, for 1 mole of KMnO\(_4\), the required moles of H\(_2\)O\(_2\) will be \( \frac{3}{2} \).
Thus, the correct answer is Option (C).