What are the projections of varying lengths protruding out of an amoeba’s body, which can appear and disappear, known as?

Pseudopodia

The correct answer is Option (4)-Pseudopodia

pseudopodium, temporary or semipermanent extension of the cytoplasm, used in locomotion and feeding by all sarcodine protozoans (i.e., those with pseudopodia; see sarcodine) and some flagellate protozoans. Pseudopodia are formed by some cells of higher animals (e.g., white blood corpuscles) and by amoebas. During amoeboid feeding, pseudopodia either flow around and engulf prey or trap it in a fine, sticky mesh.

Amoebas use pseudopodia for movement, feeding, and capturing prey. The term "pseudopodia" means "false feet," reflecting their dynamic and temporary nature.

The other terms:

• Contractile vacuole: A structure in some protists that expels excess water from the cell to maintain osmotic balance.
• Paramecium: A type of single-celled ciliate protist, which moves using cilia instead of pseudopodia.
• Pseudo vacuole: This term is not commonly used in biology. It might be a misinterpretation or a less recognized term for a cellular structure.

In the context of amoebas and their unique mode of movement, the correct term for the protrusions is pseudopodia.