Explanation:

The term 'binary' itself provides the answer to this question. In the context of computing and mathematics, 'binary' refers to a system or choice involving two distinct possibilities or states. \nOption (b) Two: This is the correct answer. A binary choice fundamentally refers to the two possible states or values that a bit can take: $0$ or $1$. These two states represent the basic 'on' or 'off' electrical signals that computers use to process and store information. The prefix 'bi-' means two. \nOption (a) One: This is incorrect. If there were only one choice, it would not be a 'binary' system; it would be a unary system, which cannot represent varying information or choices. \nOption (c) It depends upon the amount of memory in a computer.: This is incorrect. The number of choices in a binary system ($0$ or $1$) is a fundamental characteristic of the system itself, not dependent on the amount of memory. Memory capacity affects how many bits can be stored, but not the nature of a single bit's choice. \nOption (d) It depends upon the speed of the processor of a computer.: This is incorrect. Similar to memory, processor speed affects how quickly binary operations can be performed, but it does not alter the fact that a binary choice fundamentally involves two options. \nOption (e) None of these: This is incorrect because 'Two' accurately describes the number of choices in a binary system.