In household appliances,which waves are used to operate remote control switches?

$A$ monochromatic source of light operating at $15 \text{ kW}$ emits $2.5 \times 10^{22} \text{ photons/s}$. The region of an electromagnetic spectrum to which the emitted electromagnetic radiation belongs to . . . . . . . (Take $h = 6.6 \times 10^{-34} \text{ J}\cdot\text{s}$ and $c = 3 \times 10^8 \text{ m/s}$).

The correct order of electromagnetic waves with increasing frequency is

Match List-$I$ (Wavelength range of electromagnetic spectrum) with List-$II$ (Method of production of these waves) and select the correct option from the options given below the lists:

List-$I$	List-$II$
$(1)$ $700\, nm$ to $1\, mm$	$(i)$ Vibration of atoms and molecules
$(2)$ $1\, nm$ to $400\, nm$	$(ii)$ Inner shell electrons in atoms moving from one energy level to a lower level
$(3)$ $< 10^{-3}\, nm$	$(iii)$ Radioactive decay of the nucleus
$(4)$ $1\, mm$ to $0.1\, m$	$(iv)$ Magnetron valve

If ${\lambda _v}$,${\lambda _x}$,and ${\lambda _m}$ represent the wavelengths of visible light,$X$-rays,and microwaves respectively,then:

Electromagnetic waves of wavelength ranging from $100 \text{ Å}$ to $400 \text{ Å}$ come under which region?