To maximize power transfer, a lossless transmission line is to be matched to a resistive load impedance via a $$\lambda /4$$ transformer as shown.

Which one of the following field patterns represents a TEM wave traveling in the positive $$x$$ direction?

If the electric field of a plane wave is $$$\overrightarrow E \left( {z,t} \right) = \widehat x3\cos \left( {\omega t - kz + {{30}^ \circ }} \right) - \widehat y4\sin \left( {\omega t - kz + {{45}^ \circ }} \right)\left( {mV/m} \right)$$$

The polarization state of the plane wave is

For a rectangular waveguide of internal dimensions $$a\,\, \times \,\,b$$ (a > b), the cut-off frequency for the $$T{E_{11}}$$ mode is the arithmetic mean of the cut-off frequencies for $$T{E_{10}}$$ mode and $$T{E_{20}}$$ mode. If a $$ = \sqrt 5 \,cm$$, the value of b (in cm) is