Which of the following statement is correct ?

Options

A. Dipole moment :

B. Stability of free radical :

C. Basic strength : `CH_3 O^(Ө) gt overset (Ө) O H gt R S^(Ө)`
D. Basic and nucleophilic strength : `I^(Ө) gt Br^(Ө) gt C1^(Ө) gt F^(Ө)`

Explanation

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

### Step 1: Analyze Statement A
**Statement A** discusses the dipole moments of certain compounds. The dipole moment (μ) is influenced by the angle (θ) between the dipoles. The formula for dipole moment is given by:

\[ \mu = \sqrt{\mu_1^2 + \mu_2^2 + 2\mu_1\mu_2\cos\theta} \]

- The larger the angle (θ), the smaller the contribution of the cos(θ) term, leading to a higher dipole moment.
- In this case, the angles provided are 30°, 120°, and 180°.
- The order of dipole moments can be inferred as follows:
- 30° will have the highest dipole moment.
- 120° will have a moderate dipole moment.
- 180° will have the lowest dipole moment.

**Conclusion for A**: The statement regarding dipole moments is correct.

### Step 2: Analyze Statement B
**Statement B** pertains to the stability of free radicals.

- Free radicals are more stable when they have resonance stabilization.
- We analyze the structures:
- The first structure has two resonance forms.
- The second structure has one resonance form.
- The third structure has no resonance.

**Conclusion for B**: Since resonance increases stability, the first structure is the most stable, followed by the second, and the third is the least stable. Thus, this statement is also correct.

### Step 3: Analyze Statement C
**Statement C** compares the basic strength of CH3O⁻, OH⁻, and RS⁻.

- The acidity of the corresponding acids determines the basicity of their conjugate bases.
- The order of acidity is: RSH > H2O > CH3OH.
- Therefore, the order of basicity of the conjugate bases would be the reverse: CH3O⁻ > OH⁻ > RS⁻.

**Conclusion for C**: The statement regarding the basic strength is incorrect as the order provided does not match the expected order.

### Step 4: Analyze Statement D
**Statement D** discusses the basic and nucleophilic strength of halides.

- As we move down the group in the periodic table, basicity decreases due to the increase in atomic size and the delocalization of the negative charge.
- However, nucleophilicity increases down the group because larger ions can better stabilize the negative charge and are more effective at attacking electrophiles.

**Conclusion for D**: The statement is incorrect as it suggests that basicity and nucleophilicity behave similarly along the group, which is not the case.

### Final Conclusion
The correct statements are A and B. However, the question asks for which statement is correct, and since both A and B are correct, we can conclude that the statements A and B are valid.