"Kind" means type or class, which is just a unit of a logical division, so your sentences sound a bit strange to me. You can say:«Truck is a kind of vehicle», and «Hatchback is a kind of car». It absolutely OK not to use the definite article before "vehicle" and "car" because these nouns do not refer to any specific vehicle or car.
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zazzexWhich is correct? And why?A. is correct, because that's how English works: No article after [one / another / the other / a different / a certain ...] kind of.
A. He has one kind of car.
B. He has one kind of a car.
zazzex"Girls are usually afraid of cockroach." Plural is not typically needed because you are referring cockroach as a collective noun.These are wrong. Singular concrete countable nouns must have articles.
The same can be said "Cockroach is the most amazingly adaptable insect in the world".