76. A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : Is r^n less than 1, where r is a real number and n is a natural number ? Statement-I : 0 < r^2 < 1 Statement-II : 0 < r^3 < 2

  1. A. The Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone ✓
  2. B. The Question can be answered by using either Statement alone
  3. C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
  4. D. The Question cannot be answered even by using both the Statements together

Correct Answer: A. The Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone

Explanation

Statement I implies -1 < r < 1 (and r \neq 0). For any natural number n, |r|^n < 1, guaranteeing r^n < 1. Statement II allows r to be greater than 1 (e.g., r = 1.1), which would make r^n > 1 for some n, so it is insufficient.

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