The correct answer is: A. Six, viz., Adityapur, Bokaro, Patna, Ranchi, Darbhanga and Muzaffarpur.
Adityapur Industrial Area Development Authority (AIADA) is a statutory body established by the Government of Bihar in 1972 to promote and develop the industrial area of Adityapur in Jamshedpur district. Bokaro Industrial Area Development Authority (BIADA) is a statutory body established by the Government of Bihar in 1967 to promote and develop the industrial area of Bokaro in Bokaro district. Patna Industrial Area Development Authority (PIADA) is a statutory body established by the Government of Bihar in 1972 to promote and develop the industrial area of Patna in Patna district. Ranchi Industrial Area Development Authority (RIADA) is a statutory body established by the Government of Bihar in 1972 to promote and develop the industrial area of Ranchi in Ranchi district. Darbhanga Industrial Area Development Authority (DIADA) is a statutory body established by the Government of Bihar in 1972 to promote and develop the industrial area of Darbhanga in Darbhanga district. Muzaffarpur Industrial Area Development Authority (MIADA) is a statutory body established by the Government of Bihar in 1972 to promote and develop the industrial area of Muzaffarpur in Muzaffarpur district.
The other options are incorrect because they do not list the correct number of industrial area development authorities in Bihar. Option B lists five industrial area development authorities, but there are actually six. Option C lists seven industrial area development authorities, but there are actually only six. Option D lists four industrial area development authorities, but there are actually six.