$6)($a$)$ Consider the $3$ dB directional coupler shown in Fig$\mathrm{.}1.$ The third port is matched and not available for measurement. Construct a four port $6$ dB directional coupler using the mentioned directional coupler.

$($b$)$ Calculate the resonant frequency of an air$-$filled rectangular cavity with width $3$ cm $,$ height $1\mathrm{.}5$ cm and length $3\mathrm{.}5$ cm operating in $\backslash (\backslash$mathrm$\{$TE$\}\_\{105\}\backslash )$ and $\backslash (\backslash$mathrm$\{$TM$\}\_\{113\}\backslash )$ modes.

$[4][$CO$02][$BTL $3]6)($a$)$ Consider the $3$ dB directional coupler shown in Fig$\mathrm{.}1.$ The third port is matched and not available for measurement. Construct a four port $6$ dB directional coupler using the mentioned directional coupler.

$($b$)$ Calculate the resonant frequency of an air$-$filled rectangular cavity with width $3$ cm $,$ height $1\mathrm{.}5$ cm and length $3\mathrm{.}5$ cm operating in $\backslash (\backslash$mathrm$\{$TE$\}\_\{105\}\backslash )$ and $\backslash (\backslash$mathrm$\{$TM$\}\_\{113\}\backslash )$ modes.

$[4][$CO$02][$BTL $3]$