The weak band near 1750 cm-1 in the IR spectrum of benzoyl chloride is formed due to Fermi resonance between the C=O band and the first overtone.

Explanation:
IR Spectrum and Benzoyl Chloride:
- The infrared (IR) spectrum is a useful tool in identifying functional groups in organic compounds.
- It shows the absorption of infrared light by the compound as a function of wavelength or frequency.
- Benzoyl chloride (C6H5COCl) is an organic compound with a benzene ring attached to a carbonyl group (C=O) and a chlorine atom (Cl).

Fermi Resonance:
- Fermi resonance occurs when two vibrational modes of a molecule are close in energy and interact with each other.
- In the case of benzoyl chloride, the carbonyl (C=O) stretching vibration is the primary mode of interest.
- The first overtone is the second harmonic of the original vibration, occurring at twice the frequency.
- In benzoyl chloride, the first overtone of the C=O stretching vibration is close in energy to the C-Cl stretching vibration.
- This close energy proximity leads to a Fermi resonance interaction between the two vibrations.

Effects of Fermi Resonance:
- Fermi resonance can result in the splitting or broadening of the absorption band in the IR spectrum.
- In the case of benzoyl chloride, the interaction between the C=O stretching vibration and the first overtone of the C-Cl stretching vibration causes the weak band near 1750 cm-1 to form.
- The interaction between the two vibrations redistributes the energy, resulting in the formation of a new absorption band.

Other Options:
- The inductive effect refers to the electron-withdrawing or electron-donating effects of nearby groups, but it does not explain the formation of the weak band in the IR spectrum.
- The conjugation effect refers to the delocalization of electrons in a molecule, but it is not directly related to the formation of the weak band.
- The hyperconjugation effect is a stabilizing interaction between a filled σ orbital and an adjacent empty or partially filled π orbital. It does not explain the formation of the weak band.

Conclusion:
The formation of the weak band near 1750 cm-1 in the IR spectrum of benzoyl chloride is best explained by Fermi resonance between the C=O band and the first overtone. This interaction between the two vibrations leads to the redistribution of energy and the formation of a new absorption band.