Translation:Do they have a radio or a television?
Reported: "Do they have a radio or television?" should be accepted. It shows the understanding of the Finnish sentence that the question wants to test.
This source explains the difference very well: https://uusikielemme.fi/finnish-vocabulary/interesting-words/the-difference-between-tai-and-vai/
Yes, the basic partitive adds a "ta" instead of an "a" when a noun ends in two vowels (like "radio"): https://uusikielemme.fi/finnish-grammar/finnish-cases/grammatical-cases/the-partitive-case-partitiivi#formation .