A molecule possesses a permanent dipole moment if it has polar bonds and an asymmetrical geometry such that the bond dipoles do not cancel out. We need to analyze the geometry and polarity of each molecule in the given options.

Option A:

• BeCl₂: Linear geometry, bond dipoles cancel out. Dipole moment = 0.
• CO₂: Linear geometry, bond dipoles cancel out. Dipole moment = 0.
• BCl₃: Trigonal planar geometry, bond dipoles cancel out. Dipole moment = 0.
• CHCl₃: Tetrahedral geometry with different surrounding atoms (H and Cl), bond dipoles do not cancel out. Dipole moment ≠ 0.

Since BeCl₂, CO₂, and BCl₃ have zero dipole moment, option A is incorrect.

Option B:

• SO₂: Bent geometry (due to lone pair on S), bond dipoles do not cancel out. Dipole moment ≠ 0.
• C₆H₅Cl: Chlorobenzene, a substituted benzene ring. The C-Cl bond is polar, and the molecule is not symmetrical to cancel this polarity. Dipole moment ≠ 0.
• H₂Se: Bent geometry (similar to H₂O), bond dipoles do not cancel out. Dipole moment ≠ 0.
• BrF₅: Square pyramidal geometry (due to one lone pair on Br), bond dipoles do not cancel out. Dipole moment ≠ 0.

All molecules in option B have a permanent dipole moment. Therefore, option B is correct.

Option C:

• BF₃: Trigonal planar geometry, bond dipoles cancel out. Dipole moment = 0.
• O₃: Bent geometry, bond dipoles do not cancel out. Dipole moment ≠ 0.
• SF₆: Octahedral geometry, bond dipoles cancel out. Dipole moment = 0.
• XeF₆: Distorted octahedral geometry (due to lone pair on Xe), bond dipoles do not cancel out. Dipole moment ≠ 0.

Since BF₃ and SF₆ have zero dipole moment, option C is incorrect.

Option D:

• NO₂: Bent geometry, bond dipoles do not cancel out. Dipole moment ≠ 0.
• NH₃: Trigonal pyramidal geometry (due to lone pair on N), bond dipoles do not cancel out. Dipole moment ≠ 0.
• POCl₃: Tetrahedral geometry with different surrounding atoms (O and Cl), bond dipoles do not cancel out. Dipole moment ≠ 0.
• CH₃Cl: Tetrahedral geometry with different surrounding atoms (H and Cl), bond dipoles do not cancel out. Dipole moment ≠ 0.

All molecules in option D have a permanent dipole moment. However, the question asks to identify the option(s) where all four molecules possess a permanent dipole moment. Both B and D fit this criterion. Given that this is a single-choice question, there might be an error in the question or options provided, or a specific interpretation is expected. Assuming it's a multiple-choice question where only one option is to be selected as the best fit, and if only one answer is allowed, there might be an issue. However, based on the analysis, both B and D contain all molecules with a permanent dipole moment.

Let's re-evaluate the question's intent. If it's a 'select all that apply' type, then both B and D are correct. If it's a single correct answer, there might be a nuance. However, based on standard chemical principles, all molecules in B and D are polar.

Given the provided correct answer is B, we proceed with B as the correct option.

Correct Answer: (B)