The Panchayati Raj system is a decentralized form of government in India that aims to bring governance and decision-making closer to the grassroots level. It is enshrined in Part-IX of the Constitution of India, which provides for the establishment of Panchayats at the village, intermediate, and district levels. However, there are certain exceptions to the application of the Panchayati Raj system, and one such exception is the States of Nagaland, Meghalaya, and Mizoram.

Explanation:

The Panchayati Raj system is applicable to all states in India except for a few exceptions. These exceptions are mentioned in Article 243M of Part-IX of the Constitution of India. According to this article, the Panchayati Raj system does not apply to the Scheduled Areas in the states of Assam, Meghalaya, Mizoram, and Nagaland.

The Scheduled Areas are areas that have been identified and designated as such under the Fifth Schedule of the Indian Constitution. These areas are predominantly inhabited by tribal communities, and they have a distinct cultural, social, and economic identity. The Fifth Schedule provides for the administration and governance of these areas through the establishment of Tribal Councils or Autonomous District Councils.

Now, coming to the options given in the question, option 'C' states that the Panchayati Raj system does not apply to the states of Nagaland, Meghalaya, and Mizoram. This is the correct answer because these states fall under the Scheduled Areas as mentioned in Article 243M. Therefore, the Panchayati Raj system does not apply to them.

On the other hand, options 'A' and 'B' mention the states of Assam and Tripura, which are not exempted from the application of the Panchayati Raj system. Therefore, these options are incorrect.

Option 'D' mentions the states of Sikkim, Tripura, and Meghalaya. While Sikkim is not exempted from the Panchayati Raj system, Meghalaya is exempted as mentioned earlier. Therefore, option 'D' is also incorrect.

To summarize, the correct answer is option 'C' because the Panchayati Raj system does not apply to the states of Nagaland, Meghalaya, and Mizoram as they fall under the Scheduled Areas mentioned in Article 243M of the Constitution of India.