For what value of it, the sum of digits in the number (10n + 1) is 2?

The notation (10n + 1) in this context is commonly interpreted as 10 raised to the power of n, plus 1 (i.e., 10^n + 1). Let's analyze the sum of digits for this expression:

1. For n = 0: The number is (10^0 + 1) = (1 + 1) = 2. The sum of digits in 2 is 2. So, n=0 works.

2. For n = 1: The number is (10^1 + 1) = (10 + 1) = 11. The sum of digits is 1 + 1 = 2. So, n=1 works.

3. For n = 2: The number is (10^2 + 1) = (100 + 1) = 101. The sum of digits is 1 + 0 + 1 = 2. So, n=2 works.

4. For any positive integer n (n >= 1): The number 10^n is a '1' followed by 'n' zeros (e.g., 10, 100, 1000...). Adding 1 to this number results in a number that starts with '1', has (n-1) zeros in the middle, and ends with '1' (e.g., 11, 101, 1001...). The sum of the digits will always be 1 + 0 + ... + 0 + 1 = 2.

Combining these observations, the sum of digits is 2 for n=0 and for any positive integer n. Whole numbers include 0 and all positive integers (0, 1, 2, 3...). Therefore, the condition holds for any whole number n.

Let's analyze the options: A) For n = 0 only: Incorrect, as it also works for any positive integer n. B) For any whole number n: Correct, as demonstrated above (n=0 and all positive integers work). C) For any positive integer n only: Incorrect, as n=0 also satisfies the condition. D) For any real number n: Incorrect. The concept of "sum of digits" is typically applied to integers. For non-integer real numbers, it is not well-defined in this context.

The final answer is B.