with regard turnip , carrot , sweet potato and potato , three belong to the same category. identify those three modifications which are homologous or analogous and mention fourth why  modifications do not belong to the same category

Dear student, 

Carrot, turnip and sweet potato are modified roots. While potato are stem tuber-swollen tip of an underground stem. The three grouped vegetable which are modified roots and potato show similar characteristics but have different origin. Since the function of all of them is to store food therefore they describe as analogous structures. 

Regards