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A visa is not required to stay in the transit zone:
A visa is not required to transit through the Ukraine. The traveler must be in possession of a passport valid for 6 months beyond travel dates, a round-trip or onward ticket, and a valid visa for the next destination (if required).
(Source: Travisa)
If you want to exit the airport, you need a visa. You can apply in the embassy of Ukraine in India.
Upvote:0
If you have an Indian passport, you will need to apply for Ukrainian visa here. Unfortunately for you, they don't provide e-visas for Indian nationals.