Alice answering Bob without knowing the question
You can use Oblivious transfer protocol for the answers: https://en.wikipedia.org/wiki/Oblivious_transfer

Here is an example with only 2 answers ($m0$ and $m1$) and uses RSA ($e,d,N$) :



In your case Alice would have to send $x_0 \ldots x_9$ and Bob would have to pick $b \in \{0,\ldots,9\}$ where $b$ is the number of his question. The operation $m + k$ can be considered as a symmetric encryption of $m$ with the key $k$.