Indicate which one of the following modes do NOT exist in a rectangular resonant cavity.

A rectangular air-filled waveguide has a cross section of $$4\,cm\,\, \times \,\,10cm$$. The minimum frequency which can propagate in the waveguide is

The interior of a $${{20} \over 3}\,\,cm\,\, \times \,\,{{20} \over 4}\,\,cm$$ rectangular waveguide is completely filled with a dielectric of $${ \in _r} = 4$$. Waves of free space wave-lengths shorter than .........can be propagated in the $$T{E_{11}}$$ mode.