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According to the Air India hand luggage restrictions, the maximum length of hand luggage is 22 inches. A skateboard is not on the Air India restricted items list nor is it in the list of special items, although it is banned as hand luggage on some other airlines. Sometimes the airline will allow you to carry longer items such as musical instruments or sporting equipment on board but this is at the discretion of the check-in or gate agent.
There is an article here travel restrictions on carrying skateboards which also does not specifically mention restrictions in Asia.
I'd recommend asking if you'd be allowed to carry it on board at check-in and perhaps if you're not allowed, you could tape it, suitably protected, to one of your check-in bags?