The correct option is B A and B have equal speeds but opposite velocities
Since shell is initially at rest, it means initially the momentum is zero.
So after the explosion, the resultant momentum of its fragments A & B must also be equal to zero.
Let the mass of fragments be m1&m2 and since the fragments A & B are equal therefore, m1=m2
Hence the conservation of linear momentum:
m1v1+m2v2=0⇒m1v1+m1v2=0⇒v1=−v2
Therefore, A and B have equal speeds but opposite velocities.