To solve this question, the user needs to have knowledge about characters from the Indian epic Mahabharata. The question describes a character who is the son of river Ganga and remained unmarried throughout his life. Additionally, the character supported the Kauravas despite knowing that they were at fault.
Now let's go through each option and explain why it is right or wrong:
A. Bhishma: This option is correct. Bhishma was a prominent character in the Mahabharata and was the son of river Ganga, also known as the goddess Ganga. He was known for his vow of celibacy, due to which he remained unmarried throughout his life. Despite knowing that the Kauravas were at fault, he chose to remain loyal to Hastinapur and fought for the Kauravas in the Kurukshetra war.
B. Ved Vyas: This option is wrong. Ved Vyas was a sage who compiled the Mahabharata and other important Hindu texts. However, he was not the son of river Ganga, nor did he stay loyal to the Kauravas.
C. Kripacharya: This option is wrong. Kripacharya was a warrior who fought for the Kauravas in the Kurukshetra war. However, he was not the son of river Ganga and did not remain unmarried throughout his life.
D. Vidur: This option is wrong. Vidur was a wise minister who supported the Pandavas in the Mahabharata. He was not the son of river Ganga and did not remain unmarried throughout his life.
Therefore, the answer is: A. Bhishma.