To determine which set of molecules will have zero dipole moment, we need to consider the individual dipole moments of each molecule.

Dipole moment is a measure of the separation of positive and negative charges within a molecule. It occurs when there is an uneven distribution of electrons due to differences in electronegativity between atoms.

Molecules with zero dipole moment have a symmetrical arrangement of atoms or have polar bonds that cancel each other out.

Let's analyze each set of molecules:

a) Nitrogen trifluoride (NF3): Nitrogen is more electronegative than fluorine, resulting in a polar bond. However, the molecule is pyramidal in shape, which means it is not symmetrical. As a result, it has a dipole moment.
Beryllium difluoride (BeF2): Beryllium is less electronegative than fluorine, so the bond is polar. However, the molecule has a linear shape, which means the bond dipoles cancel each other out. Therefore, it has no dipole moment.
Water (H2O): Oxygen is more electronegative than hydrogen, resulting in polar bonds. The molecule is bent in shape, which makes it asymmetrical. Therefore, it has a dipole moment.
1,3-dichlorobenzene: The molecule is symmetrical and has no polar bonds. Therefore, it has no dipole moment.

b) Boron trifluoride (BF3): Boron is less electronegative than fluorine, resulting in polar bonds. However, the molecule is trigonal planar in shape, which means the bond dipoles cancel each other out. Therefore, it has no dipole moment.
Beryllium difluoride (BeF2): As mentioned earlier, it has no dipole moment.
Carbon dioxide (CO2): The molecule is linear in shape, and the bond dipoles cancel each other out. Therefore, it has no dipole moment.
1,4-dichlorobenzene: The molecule is symmetrical and has no polar bonds. Therefore, it has no dipole moment.

c) Ammonia (NH3): Nitrogen is more electronegative than hydrogen, resulting in polar bonds. The molecule is pyramidal in shape, which means it is not symmetrical. As a result, it has a dipole moment.
Beryllium difluoride (BeF2): As mentioned earlier, it has no dipole moment.
Water (H2O): As mentioned earlier, it has a dipole moment.
1,4-dichlorobenzene: As mentioned earlier, it has no dipole moment.

d) Boron trifluoride (BF3): As mentioned earlier, it has no dipole moment.
Hydrogen fluoride (HF): The molecule is polar due to the difference in electronegativity between hydrogen and fluorine. It is linear in shape, so it does not cancel out the dipole moment. Therefore, it has a dipole moment.
Carbon dioxide (CO2): As mentioned earlier, it has no dipole moment.
1,3-dichlorobenzene: As mentioned earlier, it has no dipole moment.

From the analysis above, it can be concluded that option B (Boron trifluoride, beryllium difluoride,