The correct option is
A II and III only
Lymphocytes are the white blood cells which have a non-granular cytoplasm and are produced in the bone marrow (soft spongy tissue present in the central cavity of long bones) from special pluripotent (the ability of a cell to divide and differentiate into a few cell types) lymphoid progenitor cells.
All lymphocytes are produced in the bone marrow but based on where they mature, lymphocytes can be B-lymphocytes, the ones which mature in the bone marrow, and T-lymphocytes, the ones which mature in the thymus (a lobed organ located near the heart and beneath the breastbone).
Thus, B-lymphocytes are a type of white blood cells that originate and mature in the bone marrow. Mature B- lymphocytes travel to the secondary lymphoid organs that allow them to interact with the trapped antigens (foreign substances capable of triggering an immunogenic response) and proliferate (divide and differentiate into specific cell types). Tonsils, lymph nodes, spleen, etc act as secondary lymphoid organs in the body.
Antigens trigger the B cells to divide and differentiate into plasma cells and memory B cells. The plasma cells produce antibodies and secrete them into the lymph. These antibodies are proteins which have specific sites for binding to particular antigens. Once the antibodies bind to the antigens, they are eliminated from the body. This response of the body after its first encounter with the antigen is known as the primary response.
The memory B cells are the lymphocytes which are capable of memorising their first encounter with the antigen and can launch a very fast second response in case of subsequent encounters with the same antigen in future. They remain in the body for a long time and in the subsequent encounters, these cells start dividing and differentiating into plasma cells to release antibodies against the antigen. This secondary response is faster and stronger compared to the primary response.
Thus, only statements II and III are correct.
Figure: Differentiation of B cells