Explanation:

This question tests our knowledge of Sanskrit prefixes, specifically 'निर्' (nir), and how they combine with root words, often involving Sandhi (euphonic conjunction) rules. The prefix 'निर्' generally means 'without', 'out of', or 'away from'. Let's analyze each option: **Option (A): निराकरण (Nirakaran)** This word is formed by combining the prefix 'निर्' with the root 'आकरण' (akaran, meaning 'making' or 'doing'). According to Sandhi rules, when 'निर्' is followed by a vowel, the 'र्' (r) combines with the vowel. So, 'निर् + आकरण' becomes 'निराकरण'. Here, the 'र्' combines with 'आ' to form 'रा'. Thus, 'निराकरण' clearly originates from the 'निर्' prefix. **Option (B): नीरोग (Nirog)** This word means 'healthy' or 'without disease'. It is formed from the prefix 'निर्' and the word 'रोग' (disease). However, its formation involves a specific Vyanjan Sandhi (consonant conjunction) rule. When the prefix 'निर्' (or 'दुस्') is followed by the letter 'र' (r), the 'र्' of the prefix is dropped, and the preceding short vowel 'इ' (i) becomes a long vowel 'ई' (ī). So, 'निर् + रोग' transforms into 'नी + रोग', resulting in 'नीरोग'. While 'नीरोग' is indeed derived from the concept of 'निर्' (without) + 'रोग' (disease), the direct form of the prefix 'निर्' does not visibly appear in the final word; it undergoes a significant phonetic change (dropping of 'र्' and lengthening of 'इ'). This makes it distinct from the other options where 'निर्' is more directly visible or undergoes simpler vowel combination. **Option (C): निरूपण (Nirupan)** This word is formed by combining 'निर्' with 'रूपण' (rūpan, meaning 'description' or 'representation'). Similar to 'निराकरण', the 'र्' of 'निर्' combines with the vowel 'ऊ' (ū) of 'रूपण' to form 'रू'. So, 'निर् + रूपण' becomes 'निरूपण'. This is a straightforward application of the 'निर्' prefix. **Option (D): निरपराध (Niraparadh)** This word means 'innocent' or 'without fault'. It is formed by combining 'निर्' with 'अपराध' (aparādh, meaning 'fault' or 'crime'). Here, the 'र्' of 'निर्' combines with the vowel 'अ' (a) of 'अपराध' to form 'र'. So, 'निर् + अपराध' becomes 'निरपराध'. This is another clear example of a word directly formed with the 'निर्' prefix. **Conclusion:** All options (A), (C), and (D) show a direct and relatively simple combination of the 'निर्' prefix with a root word, where the 'र्' either combines with a following vowel or remains as a half-consonant. However, in option (B), 'नीरोग', the prefix 'निर्' undergoes a specific Sandhi rule where its 'र्' is dropped and the preceding vowel is lengthened. This makes 'नीरोग' the word where the prefix 'निर्' is not 'directly' or 'visibly' present in its original form, but rather through a transformed phonetic rule. Therefore, 'नीरोग' is the word that is *not* formed in the same straightforward manner as the others from the 'निर्' prefix, making it the correct answer in the context of this question.