Explanation:

Cis-1,3-dibromo-trans-2,4-dichlorocyclobutane is a cyclobutane compound with two bromine atoms and two chlorine atoms attached. Let's analyze the given statements one by one.

a) It has a plane of symmetry:
A plane of symmetry is an imaginary plane that can be drawn through a molecule, dividing it into two parts that are mirror images of each other. If a molecule has a plane of symmetry, it is achiral. Cis-1,3-dibromo-trans-2,4-dichlorocyclobutane does not have a plane of symmetry, as it cannot be divided into two identical halves by any plane passing through it. Hence, statement a) is incorrect.

b) It has a center of symmetry:
A center of symmetry is a point in a molecule where there is an inversion center and all atoms are equidistant from it. If a molecule has a center of symmetry, it is achiral. Cis-1,3-dibromo-trans-2,4-dichlorocyclobutane has a center of symmetry, which is located at the center of the cyclobutane ring. All atoms are equidistant from this point, and if the molecule is inverted through this center, it becomes superimposable on its mirror image. Therefore, statement b) is correct.

c) It has no chiral carbon:
A chiral carbon is a carbon atom that is attached to four different groups. If a molecule has a chiral carbon, it can exist in two mirror-image forms called enantiomers, which are non-superimposable. Cis-1,3-dibromo-trans-2,4-dichlorocyclobutane does not have a chiral carbon, as all four substituents on each carbon atom are the same. Hence, statement c) is correct.

d) It has a total of three stereoisomers:
Stereoisomers are molecules that have the same molecular formula and connectivity but differ in the arrangement of their atoms in space. Cis-1,3-dibromo-trans-2,4-dichlorocyclobutane has only one stereoisomer, as it does not have any chiral centers. Therefore, statement d) is incorrect.

In conclusion, statement b) is correct, while statements a), c), and d) are incorrect.