No browser supports all Unicode, or is required for this. Specifications do not require all characters or any particular subset of them to be displayed properly. This would be almost impossible to do, because no font can span all Unicode, and even combining public fonts does it.
Thus, the question should be rephrased in terms of font support for specific characters. In addition, you should use font-family ads that make reasonable efforts to use appropriate fonts. The reason is that browsers still have difficulty returning the font: they do not always automatically find the appropriate font for backup if the declared fonts or the default browser font do not contain a specific character.
Using a downloadable font (web font) may be part of the answer, but it will probably be redundant if you just want to use multiple icons. For a text written in Devanagari, its probably the best approach; the only commonly installed font that supports it is Arial Unicode MS, and people who don't have Microsoft Office installed probably didn't receive it. Therefore, consider using, for example, either FreeSans or FreeSerif from GNU Freefont as a downloadable font via @font-face .
General information on the topic: Guidelines for using special characters in HTML .
Jukka K. Korpela
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