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Question:

When a user opens a web browser and sees a page that looks drastically different from her typical home page, what kind of attack is she likely to be facing? She also saw that her default search engine had been changed to a third-party search engine that she had never heard of?

A browser redirection
Explaination

It's likely that your browser has been hijacked by malware if you notice that your browser has been altered or that the results of a search come from a third-party site.