A Mendelian experiment consisted of breeding tall pea plants bearing violet flowers with short pea plants bearing white flowers. The progeny all bore violet flowers, but almost half of them were short. This suggests that the genetic make-up of the tall parent can be depicted as

The correct option is B TtWW
The appearance of the recessive trait in $F_1$ generation (dwarfism) confirms the presence of one recessive allele in the dominant parent and makes it heterozygous for plant height (Tt). Since all $F_1$ generation has a violet flower, the dominant parent is homozygous for flower color. If the dominant parent was double heterozygous (TtWw), the $F_1$ generation would exhibit recessive traits of both plant height and flower color. But all $F_1$ generation exhibits violet flowers which confirm that the dominant parent is homozygous for flower color.

Thus the correct answer is option C.