Proving undecidability for a language which contains string with certain syntax
It can be thought of a semantic property of the language, and its ok to use Rice's theorem here.

Define $C=\{L|\text{there is a string with exactly 3 zeros in }L\}$

So, $L_1=\{&lt;M&gt;|M \text{ is a turing machine and } L(M)\in C\}$ and because $C\neq\emptyset$ and $C$ is not every language, then by Rice's theorem, $L_1\notin R$.