A steady current I flows along an infinitely long hollow cylindrical conductor of radius R. This cylinder is placed coaxially inside an infinite solenoid of radius 2R. The solenoid has n turns per unit length and carries a steady    current I. Consider a point P at a distance r from the common axis. The correct statement(s) is (are)
I.  In the region $0<r<R,$ the magnetic field is non-zero
II. In the region $R<r<2R,$ the magnetic field is along the common axis
III. In the region $R<r<2R,$ the magnetic field is tangential to the circle of radius r, centred on the axis
IV. In the region $r>2R,$ the magnetic field is non-zero