1. The problem asks to verify the correctness of given true/false or multiple-choice statements about integral equations. 2. We will analyze the first question only as per instructions: "The free term of an integral equation is the kernel." 3. Definitions: - The free term (or free function) in an integral equation is the function independent of the unknown function, often denoted as $f(x)$. - The kernel is the function inside the integral that relates the variables, often denoted as $k(x,t)$. 4. Explanation: - The free term and the kernel are distinct components. - The free term is not the kernel. 5. Therefore, the statement "The free term of an integral equation is the kernel" is false. Final answer: a. false ✅