Does anyone knows （）the famous writer was born.
分析一下吧,这里was born后面缺少一个介词,in或者on
当是in时,be born in一般表示出生在...地方；
此时Does anyone knows in which the famous writer was born
而in which=where所以可替换.
当是on时,be born on后面一般接具体时间某年某日,指在...时间出生.
此时Does anyone knows on which the famous writer was born
而on which=when所以可替换.
所以说,B和C都讲得通,只是意思不一样而已,一个提问时间,一个提问地点.
所以【B】【C】都可以