The correct answer is option 2, which states that there are 18 designated Biosphere Reserves in India. Let`s analyze each option to understand why the others are not correct.

Option 1 states that the idea of Biosphere Reserve was initiated by UNESCO in 1973-74. This statement is incorrect because while UNESCO did contribute to the establishment and designation of Biosphere Reserves, the concept of Biosphere Reserves was introduced by the International Union for Conservation of Nature (IUCN) in the 1960s. UNESCO later adopted and further developed the concept.

Option 3 states that all Biosphere Reserves in India have been included in the world network of Biosphere Reserves of UNESCO. This statement is incorrect because not all of the Biosphere Reserves in India are included in the world network of Biosphere Reserves of UNESCO. While Biosphere Reserves have to meet certain criteria to be included, not all of them are automatically included.

Therefore, the correct answer is option 2, which states that there are 18 designated Biosphere Reserves in India.