Final answer:
B-cell receptors are specific and bind only to unique epitopes; the statement claiming that BCRs lack specificity and can bind to various antigens is incorrect. BCRs are membrane-bound IgD and IgM and undergo affinity maturation.
Step-by-step explanation:
The statement that does not describe B-cell receptors (BCRs) is "B-cell receptors lack specificity and can bind to a number of different antigens." This statement is incorrect because BCRs are highly specific and can bind only to unique epitopes. B-cell receptors indeed have both a variable region and a constant region, with the variable region being responsible for the specificity of antigen binding. Each B-cell has receptors that are specific to a particular antigenic determinant. Furthermore, BCRs are membrane-bound IgD and IgM and can undergo affinity maturation as a result of somatic hypermutation, which makes them more effective at binding their specific antigen over time.