When a beam of white light passes through a region of very fine dust particles, the colour of light that scatters the most in that region is :

As per the NCERT chapter (Section 10.6.1, Tyndall Effect), when a beam of light strikes fine particles such as dust, smoke or air molecules suspended in the atmosphere, the path of the beam becomes visible because the light is scattered by these particles — this is the Tyndall effect. The chapter explicitly states: "The colour of the scattered light depends on the size of the scattering particles. Very fine particles scatter mainly blue light while particles of larger size scatter light of longer wavelengths." Since very fine dust particles are much smaller than the wavelength of visible light, they scatter shorter-wavelength light (blue) far more effectively than longer-wavelength light, consistent with the reasoning given for why the clear sky is blue (blue light, having a shorter wavelength than red, is scattered about $1.8$ times more strongly by fine particles). Hence option (C) blue is correct.

Why the other options are wrong:

• (A) red: The chapter states red light has a wavelength about $1.8$ times that of blue light, and it is precisely because of this longer wavelength that red light is scattered the least, not the most, by fine particles (this is also why danger signal lights are red — the chapter notes "red is least scattered by fog or smoke").
• (B) orange: Orange lies closer to the red end of the visible spectrum (longer wavelength than blue/violet), so like red it is scattered less by fine particles than blue light is.
• (D) yellow: Yellow also has a longer wavelength than blue and is scattered less strongly by very fine particles; it is not the colour associated with maximum scattering by fine dust in the chapter's explanation.