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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 . 

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