The correct answer is Option 4: Gulf of Kachchh.

Biosphere reserves are designated areas that aim to conserve biodiversity, promote sustainable development, and provide a platform for scientific research, monitoring, and education. They are established under the Man and the Biosphere (MAB) program of UNESCO.

Let`s analyze each option to understand why Option 4 does not belong to the biosphere reserves set-up so far:

1. Great Nicobar: Great Nicobar is the largest of the Nicobar Islands, located in the Indian Ocean. It is home to diverse ecosystems, including rainforests and mangroves, and supports rich biodiversity. In 2013, the Great Nicobar Biosphere Reserve was established, covering an area of 885 square kilometers. It is recognized for its unique flora and fauna, including several endemic species.

2. Sunderbans: The Sunderbans is a vast mangrove forest located in the delta region of the Ganges, Brahmaputra, and Meghna rivers in India and Bangladesh. It is recognized as a UNESCO World Heritage Site and is also a biosphere reserve. The Sundarbans Biosphere Reserve was established in 1989 and covers approximately 10,000 square kilometers. It is renowned for its Royal Bengal Tigers and a wide range of flora and fauna.

3. Nanda Devi: Nanda Devi is a mountain located in the state of Uttarakhand, India. It is part of the Nanda Devi Biosphere Reserve, which was established in 1988. The reserve spans an area of about 2,236 square kilometers and includes the Nanda Devi National Park, which is a UNESCO World Heritage Site. The region is known for its alpine meadows, high-altitude flora, and rare animal species like the snow leopard.

4. Gulf of Kachchh: The Gulf of Kachchh, also known as the Gulf of Kutch, is an inlet of the Arabian Sea located in the state of Gujarat, India. While the region is ecologically significant and supports a unique marine ecosystem, there is currently no designated biosphere reserve in the Gulf of Kachchh. However, it is important to note that the Gulf of Kachchh is a part of the larger transboundary Gulf of Kachchh and the adjacent marine area, which has been recognized as a marine biosphere reserve under the World Network of Biosphere Reserves by UNESCO. But as per the given options, there is no specific mention of a biosphere reserve in the Gulf of Kachchh.

In conclusion, among the options provided, Option 4: Gulf of Kachchh does not belong to the biosphere reserves set-up so far. While it is part of a larger marine biosphere reserve, there is no distinct biosphere reserve established solely in the Gulf of Kachchh.