Introduction:
In the field of computer science, there are various tools and techniques used to process and manipulate different types of languages. One such tool is a machine, which can be a compiler, interpreter, loader, or linker. Each of these tools serves a specific purpose and has its own characteristics. In the given question, we are asked to identify which tool would give a finite solution to an infinite language when passed through it.

Explanation:
To understand the answer to this question, let's first define the terms mentioned in the options:

1. Compiler: A compiler is a software tool that translates a high-level programming language into machine code or an intermediate representation known as object code. It typically takes the entire program as input and generates a compiled executable file.

2. Interpreter: An interpreter is a program that directly executes the instructions of a programming language without the need for prior compilation. It reads the source code line by line and executes it immediately.

3. Loader: A loader is a program that loads executable programs or object code into the computer's memory and prepares them for execution.

4. Linker: A linker is a program that takes one or more object files generated by a compiler and combines them into a single executable file. It resolves dependencies between different modules of a program.

Solution:
Based on the given options, the correct answer is Option A - Compiler. Here's why:

1. An infinite language refers to a language that has an infinite number of possible inputs or strings. It is not possible to process or handle an infinite language directly.

2. Both interpreters and compilers can handle finite languages, which means they can process a finite number of inputs or strings.

3. However, an interpreter executes the program line by line, and therefore, it cannot handle an infinite language as it would require an infinite amount of time and resources to execute all possible inputs.

4. On the other hand, a compiler translates the entire program into machine code or object code in a single pass. It does not need to execute the program line by line, and it can handle finite languages efficiently.

5. Therefore, when an infinite language is passed to a machine, the subsidiary that gives a finite solution to the infinite input tape is a compiler. The compiler can analyze the program and generate the corresponding machine code without the need for executing each input individually.

Conclusion:
In conclusion, the correct option is A - Compiler. A compiler is capable of handling finite languages efficiently and can provide a finite solution to an infinite input tape. Unlike interpreters, compilers do not need to execute the program line by line, allowing them to process and translate the entire program at once.