For minimum height to hold for a tree with given number of nodes , number of nodes per level should be maximised .
Hence ,
Number of nodes possible in height 0 = 1
in height 1 = 7 [ As D = 7 ]
in height 2 = 49
in height 3 = 343
in height 4 = 2401
in height 5 = 16807
Hence total number of nodes = 1 + 7 + 49 + 343 + 2401 + 16807
= 19608 which is given in the question as well.
Hence minimum height possible = 5 . Hence B) should be the correct option .