2026 · Q76
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 natural number?
Statement I0 < r² < 1.
Statement II0 < r³ < 2.
Which one of the following is correct in respect of the above Question and the Statements?
Elementary MathematicsNumber System
- AThe Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
- BThe Question can be answered by using either Statement alone
- CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
- DThe Question cannot be answered even by using both the Statements together
Explanation
Statement I: 0<r²<1 gives |r|<1, whence r^n≤|r|^n<1 for every natural n — the question is answered (Yes) by I alone. Statement II: 0<r³<2 permits r>1 (e.g. r=1.2), for which r^n can exceed 1 — inconclusive. One statement alone suffices, option A.