To match the given List I (EM-Wave) with List II (Wavelength Range), we need to understand the typical wavelength ranges associated with each type of electromagnetic (EM) wave mentioned in List I.

Here's the matching based on known wavelength ranges:

• Infra-red: Infrared radiation lies between the visible and microwave portions of the electromagnetic spectrum. The wavelength range for infrared is typically from about 700 nm (nanometers) to 1 mm (millimeter), which means it matches with option (III) - 1 mm to 700 nm.


• Ultraviolet: Ultraviolet (UV) light sits between visible light and X-rays along the electromagnetic spectrum, with wavelengths shorter than visible light but longer than X-rays. The typical wavelength range for UV light is from 400 nm down to 10 nm, so it matches with option (II) - 400 nm to 1 nm (even though the strict lower bound should be 10 nm, this is the closest option provided).


• X-rays: X-rays have a wavelength range shorter than UV rays and longer than gamma rays, typically ranging from 10 nm down to 0.01 nm (or $$10^{-2}$$ nm). Thus, X-rays match with option (IV) - 1 nm to $$10^{-3}$$ nm, as this is the closest range provided that fits the typical scope of X-ray wavelengths.


• Gamma rays: Gamma rays have the shortest wavelength on the electromagnetic spectrum, with wavelength less than 10 picometers (pm), which equates to less than $$10^{-3}$$ nm. This corresponds to option (I) - $$<10^{-3}$$ nm.

So, based on the above analysis, the correct option for the matching would be:

• (A)-(III)


• (B)-(II)


• (C)-(IV)


• (D)-(I)

Therefore, the correct answer is Option B: (A)-(III), (B)-(II), (C)-(IV), (D)-(I).