The correct options are
A The terminal carbon atoms are sp2-hybridized.
B The planes containing the CH2 groups are mutually perpendicular to permit the formation of two separate π-bonds.
D The central carbon is sp-hybridized.
In the allene molecule, the central C atom is sp hybridized and other two C atoms are sp2 hybridized.
Thus, the central C atom has two double bonds whereas other two C atoms have on double bond each.
There are two unhybridized p orbitals present on the central carbon atom which are mutually perpendicular. These two unhybridized p orbitals are used to form two pi bonds with two adjacent C atoms.
Hence, the planes containing the CH2 groups are mutually perpendicular.
Thus, the statements A, B and C are correct.