Hey Hi... you need to take a ship from Cochin.. there are several passenger ships going to Lakshwadeep and it takes around 15-20 hours.. if you happen to go by ship you will spend around 2 days on the ship ( to and fro).. Also please note that you require a permit to visit Lakshwadeep..
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This might help
What is the permit requirements
You can take the ship/ ferry from Kochi. 5 day trip for 2 should happen in Rs50000
U can book the samundran package it very nice..check it in google for more details
To reach Lakshadweep you can avail ship services from Cochin. Seven passenger ships are operated from Cochin to Lakshadweep such as MV Arabian Sea, MV Dweep Setu, MV Kavaratti, MV Bharat Seema, MV Minicoy, MV Lakshadweep Sea and MV Amindivi Sea. The journey through this route takes around 14 to 20 hours. Different classes of accommodation such as A/C Deluxe Class (with 2 berth cabins), A/C First Class (with 4 berth cabins) and Tourist Class (with A/C seating) can be availed in these ships. The ships are well equipped with an entertainment lounge, walkway, cafeteria, snack bars and video shows, etc. Avail health service or call on a doctor on board. From October to May, boat services from Agatti to Kavaratti and Kadmat can be enjoyed.
You can take the ship/ ferry from Kochi.note that you require a permit to visit Lakshwadeep.