The error that cannot be caught at compile time is accessing an array out-of-bound. This is because the action of bounds checking is performed at runtime, not during the compilation of the program.
The type of error that cannot be caught at compile time among the options provided is b. An array being accessed out-of-bound. This is because bounds checking is a runtime activity. Accessing an element outside the bounds of an array yields undefined behavior, and compilers typically do not check for such errors during compilation. These errors only become apparent when the program is executed and tries to access a memory location that is not allowed, which could potentially lead to a runtime crash or unwanted behavior.
Other errors like adding an integer with a string or casting a value to an unrelated type can often be detected at compile time in statically typed languages because they violate type safety rules of the language's type system. Similarly, an attempted division by zero can sometimes be caught if the zero is a literal and the operation is not part of a more complex expression that the compiler cannot evaluate.
Null pointer dereference can also be detected by some static analysis tools during the compile-time if the value is statically known to be null, but it's commonly a runtime error.
Array out-of-bound access errors are tricky because they do not manifest at compile time. They are runtime errors that require diligent coding practices and, oftentimes, runtime checks to prevent.