Step 1: Understand the Hydrolysis Reactions of Xenon Fluorides
When xenon fluorides ($ \text{XeF}_2 $, $ \text{XeF}_4 $, and $ \text{XeF}_6 $) undergo complete hydrolysis, they produce different products depending on their oxidation states and reactivity with water. Let's analyze each case:
 Step 2: Analyze Each Reaction
 % Option
 (I) Complete Hydrolysis of $ \text{XeF}_2 $
 $ \text{XeF}_2 $ undergoes hydrolysis to form xenon gas ($ \text{Xe} $) and hydrogen fluoride ($ \text{HF} $):
$$
\text{XeF}_2 + 2\text{H}_2\text{O} \rightarrow \text{Xe} + 4\text{HF}
$$
 No $ \text{XeO}_3 $ is formed.
 % Option
 (II) Complete Hydrolysis of $ \text{XeF}_4 $
 $ \text{XeF}_4 $ undergoes hydrolysis to form $ \text{XeO}_3 $, hydrogen fluoride ($ \text{HF} $), and oxygen ($ \text{O}_2 $):
$$
\text{XeF}_4 + 2\text{H}_2\text{O} \rightarrow \text{XeO}_3 + 4\text{HF} + \frac{1}{2}\text{O}_2
$$
 $ \text{XeO}_3 $ is formed.
 % Option
 (III) Complete Hydrolysis of $ \text{XeF}_6 $
 $ \text{XeF}_6 $ undergoes hydrolysis to form $ \text{XeO}_3 $, hydrogen fluoride ($ \text{HF} $), and oxygen ($ \text{O}_2 $):
$$
\text{XeF}_6 + 3\text{H}_2\text{O} \rightarrow \text{XeO}_3 + 6\text{HF} + \frac{3}{2}\text{O}_2
$$
 $ \text{XeO}_3 $ is formed.
 Step 3: Identify the Correct Option
From the analysis:
 I) Complete hydrolysis of $ \text{XeF}_2 $ does not produce $ \text{XeO}_3 $.
 II) Complete hydrolysis of $ \text{XeF}_4 $ produces $ \text{XeO}_3 $.
 III) Complete hydrolysis of $ \text{XeF}_6 $ produces $ \text{XeO}_3 $.
Thus, the correct reactions that give $ \text{XeO}_3 $ as a product are II and III.
 Step 4: Match with Options
 Option (1): I& II only  
  Incorrect — $ \text{XeF}_2 $ does not produce $ \text{XeO}_3 $.
 Option (2): II& III only  
   Correct — matches the analysis.
 Option (3): I& III only  
  Incorrect — $ \text{XeF}_2 $ does not produce $ \text{XeO}_3 $.
 Option (4): I, II, III  
  Incorrect — $ \text{XeF}_2 $ does not produce $ \text{XeO}_3 $.