To determine which set of molecules has zero dipole moment, we need to analyze the molecular geometry and symmetry of each molecule.$\\$1. Boron trifluoride (BF$_3$):$\\$• BF$_3$ is a trigonal planar molecule.$\\$• The three B-F bonds are symmetrically arranged at 120° angles.$\\$• The dipoles cancel each other out, resulting in a net dipole moment of zero.$\\$2. Hydrogen fluoride (HF):$\\$• HF is a linear diatomic molecule.$\\$• It has a significant dipole moment due to the difference in electronegativity between H and F.$\\$• Therefore, HF does not have a zero dipole moment.$\\$3. Carbon dioxide (CO$_2$):$\\$• CO$_2$ is a linear molecule.$\\$• The two C=O bonds are equal and opposite, canceling each other out.$\\$• Thus, CO$_2$ has a zero dipole moment.$\\$4. 1,3-Dichlorobenzene:$\\$• In 1,3-dichlorobenzene, the chlorine atoms are positioned at the 1 and 3 positions on the benzene ring.$\\$• The dipoles do not cancel out completely due to the asymmetrical arrangement.$\\$• Therefore, it does not have a zero dipole moment.$\\$5. Nitrogen trifluoride (NF$_3$):$\\$• NF$_3$ is a trigonal pyramidal molecule.$\\$• It has a net dipole moment due to the lone pair on nitrogen.$\\$• Therefore, NF$_3$ does not have a zero dipole moment.$\\$6. Beryllium difluoride (BeF$_2$):$\\$• BeF$_2$ is a linear molecule.$\\$• The two Be-F bonds are equal and opposite, canceling each other out.$\\$• Thus, BeF$_2$ has a zero dipole moment.$\\$7. Water (H$_2$O):$\\$• H$_2$O is a bent molecule.$\\$• It has a significant dipole moment due to the bent shape and electronegativity difference.$\\$• Therefore, H$_2$O does not have a zero dipole moment.$\\$8. 1,4-Dichlorobenzene:$\\$• In 1,4-dichlorobenzene, the chlorine atoms are positioned at the 1 and 4 positions on the benzene ring.$\\$• The dipoles cancel out due to the symmetrical arrangement.$\\$• Therefore, it has a zero dipole moment.$\\$Based on the analysis, the set of molecules with zero dipole moment is:$\\$Boron trifluoride, beryllium difluoride, carbon dioxide, 1,4-dichlorobenzene.$\\$This corresponds to Option 3.