Should be 图书馆在哪里 or 图书馆在哪儿。
The multiple choice didn't include either 里 or 儿, making "图书馆在哪" the only possible solution. Which I have sometimes heard, but just seems a bit like "street language" or like the speaker is just in a rush and can't bother with the "extra word".
It doesn't matter. I think people in the North tend to use 哪儿. While people in the South tend to use 哪里.