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

(a) For n= 0 only

(b) For any whole number n

(c) For any positive integer n only

(d) For any real number n

Correct Answer: (b) For any whole number n

#### Question from UPSC Prelims 2020 CSAT Paper

**Explanation :**

## Sum of digits in the number (10^n + 1) is 2 for any whole number n.

This is because when you raise 10 to any positive integer power n, you get a number that has a 1 followed by n zeros. For example:

When n = 0, 10^0 = 1

When n = 1, 10^n = 10

When n = 2, 10^n = 100

When n = 3, 10^n = 1000

When you add one to these numbers (10^n +1), you get a number that has a digit sum of two:

When n =0 , (10^n +1) =2

When n =1 , (10^n +1) =11

When n=2 , (10^n +1) =101

When n=3 , (10^n +1) =1001

In each case the sum of digits is equal to two.

**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.