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The modes in a rectangular waveguide are denoted by $\mathrm{TE}_{\mathrm{mn}} / \mathrm{TM}_{\mathrm{mn}}$ where $\mathrm{m}$ and $\mathrm{n}$ are the eigen numbers along the larger and smaller dimensions of the waveguide respectively. Which one of the following statements is TRUE?

1. The $\mathrm{TM}_{10}$ mode of the waveguide does not exist
2. The $\mathrm{TE}_{10}$ mode of the waveguide does not exist
3. The $\mathrm{TM}_{10}$ and the $\mathrm{TE}_{10}$ modes both exist and have the same cut-off frequencies
4. The $\mathrm{TM}_{10}$ and the $\mathrm{TM}_{01}$ modes both exist and have the same cut-off frequencies