Which of the following(s) is/are true?
I. `(sqrt9-sqrt6) gt (sqrt6-sqrt3)`
II. `(sqrt6-sqrt9) gt (sqrt3-sqrt5)`

Options

A. a)Only I
B. b)Only II
C. c)Both I and II
D. d)Neither I nor II

Answer

To determine which of the statements is true, we will analyze each statement step by step.

### Statement I: \( \sqrt{9} - \sqrt{6} > \sqrt{6} - \sqrt{3} \)

1. **Calculate \( \sqrt{9} \), \( \sqrt{6} \), and \( \sqrt{3} \)**:
- \( \sqrt{9} = 3 \)
- \( \sqrt{6} \approx 2.45 \)
- \( \sqrt{3} \approx 1.73 \)

2. **Substitute the values into the inequality**:
- Left side: \( 3 - 2.45 = 0.55 \)
- Right side: \( 2.45 - 1.73 = 0.72 \)

3. **Compare the two sides**:
- \( 0.55 > 0.72 \) is **false**.

Thus, Statement I is **not true**.

### Statement II: \( \sqrt{6} - \sqrt{9} > \sqrt{3} - \sqrt{5} \)

1. **Calculate \( \sqrt{5} \)**:
- \( \sqrt{5} \approx 2.24 \)

2. **Substitute the values into the inequality**:
- Left side: \( 2.45 - 3 = -0.55 \)
- Right side: \( 1.73 - 2.24 = -0.51 \)

3. **Compare the two sides**:
- \( -0.55 > -0.51 \) is **false**.

Thus, Statement II is also **not true**.

### Conclusion:
Both statements are false.