A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.
Question: Is rⁿ less than 1, where r is a real number and n is a positive integer?
Statement-I: 0 < r² < 1
Statement-II: 0 < r³ < 2
A.The Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone✓ Correct
B.The Question can be answered by using either Statement alone
C.The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
D.The Question cannot be answered even by using both the Statements together
Explanation
Statement I: 0 < r² < 1 implies −1 < r < 1 and r ≠ 0. So |r| < 1, which means rⁿ < 1 for any positive integer n (since |rⁿ| < 1). Hence I alone is sufficient. Statement II: 0 < r³ < 2 means 0 < r < 2^(1/3), so r could be greater than 1 (e.g., r = 1.2 gives r³ ≈ 1.728 < 2 but rⁿ for large n exceeds 1). So II alone is not sufficient. Hence only one statement answers the question.
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