Step 1: The name of the antigen group is itself the clue. If an antigen is labelled T cell independent, then by definition it does its work without leaning on T lymphocytes.
Step 2: So which cell does it engage instead? These antigens are usually big repetitive structures, like the polysaccharide coats and endotoxin of bacteria. Their repeating epitopes simultaneously clamp many B cell receptors on a single B cell, and that strong cross-linking is enough to switch the B cell on by itself. The pathway therefore runs through the B cell, which is option b.
Step 3: Since no helper T cell or antigen presenting cell processing is involved, the macrophage, the helper T cell and the cytotoxic CD8 T cell options are all off the mark. The antibody produced is largely IgM with weak memory.
Step 4: The direct line from repeating antigen to B cell receptor confirms the route.
\[\boxed{\text{B-cell}}\]