Is there any exact definition of vegetable and fruit? How can new plant be classified?
A true fruit is a ripened ovary that usually starts ripening when it is fertilized. And vegetable is any vegetative part of the plant which is edible and contains stored food probably in the form of starch.
These definitions are not exact as there are a lot of fruits which are fruits but do not strictly follow the given definition. See Syconus, Composite fruits, Sorosis.etc
Classification is based on several different criteria, for example the mode of reproduction, arrangement and design of flowering parts and flowers and also on the basis of habitat and habit.
From a culinary point of view, the difference between a vegetable and fruit is are they sweet or not.
Hence eggplant, tomatoes and bell peppers which are biologically fruits are considered vegetables.
Potatoes which are tubes, are considered vegetable. Kale which are leaves are considered vegetable. And cauliflower which are flowers are considered vegetables.
The question of fruit and vegetable would be might be tested if somebody made a very sweet and soft carrot, at which point I am not sure what the master chefs of the world might say. Could a soft and sugary sweet carrot be able to graduate into the word of fruits and leave the world of vegetables behind?