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

Answer: (b) For any whole number n

For any positive integer n, 10ⁿ + 1 is 1 followed by zeros and a final 1, so its digit sum is 2. For n = 0 it is 1 + 1 = 2, whose digit sum is also 2. So it holds for every whole number 0, 1, 2, …, but not for fractional n, where 10ⁿ + 1 is not a whole number.

1. n = 1, 2, 3 …: 11, 101, 1001 … — digit sum 2.
2. n = 0: 10⁰ + 1 = 2 — digit sum 2.
3. n = 1/2: 10ⁿ + 1 = √10 + 1 ≈ 4·16, not a whole number, so 'any real number' fails.
4. So the statement holds for any whole number n.

Remember · Always test the edge value n = 0 before choosing 'positive integers only'.

Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). · Report an error