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

Explanation :

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

Let’s solve step by step.

1) The question asks for what value(s) of n, sum of digits in (10^n + 1) is 2.

2) Testing values systematically:

For n = 0:
10^0 + 1 = 1 + 1 = 2
Sum of digits = 2

For n = 1:
10^1 + 1 = 10 + 1 = 11
Sum of digits = 1 + 1 = 2

For n = 2:
10^2 + 1 = 100 + 1 = 101
Sum of digits = 1 + 0 + 1 = 2

For n = 3:
10^3 + 1 = 1000 + 1 = 1001
Sum of digits = 1 + 0 + 0 + 1 = 2

3) Key observations:
– For n = 0, sum is 2
– For positive integers, number is always in form 1(n zeros)1, so sum is always 2
– For negative integers, not applicable
– For non-integer values, not applicable

4) Checking options:
(a) For n = 0 only – False as works for other values too
(b) For any whole number n – True as works for n = 0 and all positive integers
(c) For any positive integer n only – False as also works for n = 0
(d) For any real number n – False as not applicable for non-integers

The answer is (b).

Note: Whole numbers are non-negative integers, including zero (0, 1, 2, 3, …). They represent whole things without fractions or decimals. Real numbers include all the numbers on the number line: rational numbers (fractions, integers) and irrational numbers (numbers that cannot be expressed as fractions, like √2). They encompass all possible magnitudes and their opposites, describing quantities in the real world.