(A) $(i)$ In satellite communication,microwaves are used,so ${\lambda _1}$ is the wavelength of microwaves.
$(ii)$ Ultraviolet radiations are used to kill germs in water purifiers,so ${\lambda _2}$ is the wavelength of $UV$ rays.
$(iii)$ $X$-rays are used to detect leakage of oil in underground pipelines,so ${\lambda _3}$ is the wavelength of $X$-rays.
$(iv)$ Infrared rays are used to improve visibility on runways during fog and mist conditions,so ${\lambda _4}$ is the wavelength of infrared rays.
$(b)$ The order of wavelengths in the electromagnetic spectrum is: ${\lambda _{X-rays}} < {\lambda _{UV}} < {\lambda _{IR}} < {\lambda _{Micro}}$.
Therefore,the ascending order is: ${\lambda _3} < {\lambda _2} < {\lambda _4} < {\lambda _1}$.
$(c)$ $(i)$ Microwaves are used in $RADAR$.
$(ii)$ $UV$ rays are used in $LASIK$ eye surgery.
$(iii)$ $X$-rays are used to detect fractures in bones.
$(iv)$ Infrared rays are used in optical communication.