The correct option is
C I and III
Analogous organs are the organs which differ in basic structural design but they perform similar functions. For example, wings of insects and wings of bats perform the same function, helping animals to fly but they have different internal structures.
Potato and sweet potato are analogous organs in plants as potato is a stem tuber whereas sweet potato is a root tuber. Their origin is different but function is the same i.e., storage of food in the form of starch. Hence, statements I and III are correct.
Homologous organs are those organs where the basic structure and origin are similar but differ in the functions they perform. For example, the forelimbs of man and frog have the same origin and structural design of bones but they carry out different functions.
Cats, lizards and whales are vertebrates. They indicate common ancestry. The function of forelimbs in all these animals is different, but the basic structure and developmental pattern is similar. Hence, they are examples of homologous organs.
Thorns of Citrus and tendrils of Cucurbita are homologous organs as both of them are stem modifications developed from the axillary buds. The thorns provide protection against predators whereas tendrils help plants with weak stems to climb.
So, statements II and IV are incorrect.