The correct options are
B the magnetic field at the axis of the conductor is zero
D the electric field in the vicinity of the conductor is zero
If a current passes through any conductor, net charge through any section is zero. hence electric field in the vicinity of the conductor is zero. hence, electric field in the vicinity of the conductor is zero. we can observe using biot and savart law that the magnetic field at the axis of the cylindrical wire will be zero .electric field at the axis of the wire cannot be zero otherwise the current through the wire cannot flow.