If a plant that we eat has seeds, it is a fruit. If it doesn't it's a vegetable. So a vegetable would never be a fruit. Bananas don't look like they have seeds but they actually do. Some people think...
A cucumber is a plant which bears fruit. When you eat a cucumber, you are technically eating a fruit. Legally, they are sold as vegetables due to how consumers view them. This is similar to a tomato.
There aren't any vegetables with seeds on the outside because no vegetables have seeds. But there are fruits with seeds on the outside like strawberries.