Which of the following statements is correct ?

The statement that is correct is: Fusion of protoplasms between two motile on non‑motile gametes is called plasmogamy.

In the life cycle of many fungi and some algae, the first stage of sexual reproduction involves the merging of the cytoplasmic contents of two gametes while their nuclei remain separate. This process is specifically termed plasmogamy. During plasmogamy, the cell walls (or membranes) of the two gametes break down, allowing their protoplasm— the living, fluid portion of the cell—to mix. The nuclei, however, do not fuse at this stage; they will later combine in a separate event called karyogamy.

Gametes can be motile (capable of movement, often via flagella) or non‑motile (stationary). The definition of plasmogamy does not depend on the motility of the gametes; it simply describes the fusion of their protoplasm. Therefore, the statement correctly identifies plasmogamy as the process that occurs when the protoplasm of two gametes—one motile and one non‑motile—merge.

Why the other options are incorrect:

• Organisms that depend on living plants are called saprophytes. This is false; saprophytes obtain nutrients from dead organic matter, not from living plants. Organisms that depend on living plants are typically called parasites or phytopathogens.
• Some of the organisms can fix atmospheric nitrogen in specialized cells called sheath cells. The term “sheath cells” is not associated with nitrogen fixation. Nitrogen‑fixing organisms (e.g., certain cyanobacteria) use specialized cells called heterocysts, not sheath cells.
• Fusion of two cells is called karyogamy. Karyogamy specifically refers to the fusion of two nuclei, not the entire cells. The general fusion of whole cells, including their cytoplasm, is plasmogamy.

Thus, among the given statements, only the description of plasmogamy accurately matches the biological terminology.