There are many kind of Korean food.
There are many kind of cars.
There are(you use 'are' as you are refering to plural words here) a lot of fruits.
There are many kind of fruits.
I think the above ones are more sensible than others.But I would also like to know if I am right from the teachers.Also, I would like to know when to use 'kinds of',do people use that in sentences?