Final answer:
In programming terms, option (c) 4 and 4.125, and option (d) 4 and 5 share the same data type -- both pairs consist of numeric values. Option (a) undefined and null are different data types, and option (b) 4 and "4" involve a number and a string, respectively.
Step-by-step explanation:
Understanding data types is crucial in programming and computer science. When comparing whether two values are of the same data type, we must consider their intrinsic nature rather than just their appearance.
For option (a), undefined and null might seem similar, but they are in fact different data types in languages like JavaScript. Undefined represents a variable that has been declared but not assigned a value, while null is an assignment value that represents the intentional absence of any object value.
For option (b), the number 4 and the string "4" might look the same, but they are of different data types. The first is a number, while the second is a string because it is enclosed in quotation marks.
In option (c), both 4 and 4.125 are numbers, and more specifically, they are considered as floating-point numbers in many programming languages.
Finally, option (d) also consists of numbers: 4 and 5. Both are integers, which is a subset of numbers.
Therefore, options (c) and (d) are examples of values that share the same data type.