Step 1: Analyze Each Molecule's Hybridization and Geometry
- I. \(\mathrm{SiH_4}\): Silicon forms four single bonds with hydrogen, with no lone pairs. Hybridization is \(\mathrm{sp^3}\) and geometry is tetrahedral. This is correct.
- II. \(\mathrm{BeCl_2}\): Beryllium dichloride is linear with \(\mathrm{sp}\) hybridization and no lone pairs on Be. Given \(\mathrm{sp^2}\) and 1 lone pair is incorrect.
- III. \(\mathrm{SF_4}\): Sulfur tetrafluoride has \(\mathrm{dsp^3}\) hybridization, geometry is seesaw, and has 1 lone pair on sulfur. This is correct.
However, the question asks for the correct set, so partial incorrectness in other options matters.
- IV. \(\mathrm{SnCl_2}\): Tin dichloride is bent with \(\mathrm{sp^2}\) hybridization and 1 lone pair, not 2.
- V. \(\mathrm{CH_4}\): Methane is \(\mathrm{sp^3}\) hybridized, tetrahedral, with zero lone pairs, which is correct.
Step 2: Conclusion
Only set I correctly matches hybridization, geometry, and lone pairs. Other options have errors in hybridization or lone pairs.
Hence, the correct answer is I.