Which of the following statements is/are correct?

Question

Let x be a real number between 0 and 1.

Which of the following statements is/are correct?

I. x² x³.

II. x √x.

1. A. I only (Correct answer)
2. B. II only
3. C. Both I and II
4. D. Neither I nor II

Correct Answer

Option A — I only

Detailed Solution & Explanation

The correct answer is I only.

Key Points

• For 0 < x < 1: Statement I: x² > x³?
• Divide by x² (positive): 1 > x. True for 0<x<1. ✓ Statement II: x > √x?
• For 0<x<1, √x > x (e.g., x=0.25: √0.25=0.5 > 0.25). So x > √x is FALSE.
• Only Statement I is correct. Answer: I only.