In this situation is 12 weeks test is conclusive?

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Any virus, for that matter, once is presented in a infective dose, will be detected by the human immune system, and that will result in production of antibodies. And with regard to HIV, this will be seen by 12 weeks after exposure.

In case, of direct inoculation of the HIV virus into the blood stream, as via cuts, injections, etc, this will occur much sooner.

In case of any other form of exposure, most individuals would develop antibodies within 12 weeks after exposure.