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

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

1. For n = 0 only
2. For any whole number n
3. For any positive integer n only
4. For any real number n

• Answer: The correct option is B
• Explanation:

  Given number, N = (10ⁿ + 1)

  On putting n = 0, we get:

  N = 10⁰ + 1

  = 1 + 1 = 2 {sum of digits is 2}

  On putting n = 1, we get:

  N = 10¹ + 1

  = 10 + 1 = 11 {sum of digits is 2}

  On putting n = 2, we get:

  N = 10² + 1

  = 100 + 1 = 101 {sum of digits is 2}

  On putting n = 3, we get:

  N = 10³ + 1

  = 1000 + 1 = 1001 {sum of digits is 2}

  Hence, sum of digits of number N will always be 2 if n = 0, 1, 2, 3, …

  The sum of digits of number N will always be 2 if n is any whole number.

• Exam Year: 2020