National Botanical Garden:
- The National Botanical Garden is not the correct answer because it is not specifically known for its collection of tropical plants.

The Indian Botanical Garden:
- The Indian Botanical Garden, also known as the Acharya Jagadish Chandra Bose Indian Botanic Garden, is a botanical garden located in Shibpur, Howrah, near Kolkata, West Bengal, India.
- It is one of the oldest and largest botanical gardens in India, covering an area of about 273 acres.
- The garden was established in 1787 by Colonel Robert Kyd, a British army officer, with the aim of growing and studying various plants for scientific research and educational purposes.
- The Indian Botanical Garden is known for its extensive collection of plants, including rare and endangered species from different parts of India and other tropical regions of the world.
- It serves as a center for conservation, research, and education on plant diversity and ecology.
- The garden is divided into various sections, such as the Palm House, the Orchid House, the Cactus House, and the Economic Plant Section, each showcasing different types of plants and their unique characteristics.
- It also houses a herbarium, containing a large collection of plant specimens preserved for botanical studies and reference purposes.
- The Indian Botanical Garden attracts numerous visitors, including botanists, researchers, students, and nature enthusiasts, who come to explore its diverse plant collections and learn about the importance of plant conservation and biodiversity.

Lloyd Botanical Garden:
- The Lloyd Botanical Garden, located in Darjeeling, West Bengal, is another famous botanical garden in India.
- Although it is known for its beautiful collection of plants, it is not the correct answer to the given question.

Lalbag Garden:
- Lalbag Garden, also known as Lalbagh Botanical Garden, is a popular botanical garden located in Bangalore, Karnataka, India.
- While it is a renowned botanical garden, it is primarily known for its collection of plants native to India and not specifically for tropical plants from around the world.
- Therefore, it is not the correct answer to the question.

In conclusion, the correct answer is option 'b) The Indian Botanical Garden' as it is one of the oldest and largest botanical gardens in India, known for its extensive collection of tropical plants from around the world.