The correct option is option 3, Mesozoic era. The Indian desert, also known as Marusthali, is believed to have been under the sea during the Mesozoic era. This era lasted from approximately 252 to 66 million years ago. During this time period, the supercontinent Pangaea began to break apart, leading to the formation of new landmasses and changes in sea levels.

The other options are not correct. Option 1, Cenozoic era, is the current era, which began around 66 million years ago and continues to the present. Option 2, Palaeozoic era, occurred from about 541 to 252 million years ago and is known for the diversification of life on Earth. Option 4, Archaean and Pre-Cambrian era, refers to an extremely long period of time that predates the Paleozoic era, encompassing the formation of the Earth and the earliest forms of life.

Therefore, the Indian desert, Marusthali, is believed to have been under the sea during the Mesozoic era, option 3.