The correct option is C what you do with your personal life - object of a preposition
A noun clause is a dependent clause that functions as a noun. It usually
begins with what, whatever, whom, that and other such relative
pronouns. A noun clause can act as a subject, object, predicate
nominative or object of a preposition, in a sentence.
A noun, noun
phrase or a noun clause that comes after a preposition (to, for, with,
etc.) is called an object of that preposition.
Option A is correct
because "what you do with your personal life" is a noun clause, where "what" is a relative
pronoun, "you" is the subject and "do" is the verb. This clause is the
object of the preposition "in".
Option B is incorrect because "your personal life" is not a clause, but a phrase.
Option C is incorrect because "We have no interest" is not a noun clause; a noun clause usually begins with a relative pronoun and functions as a noun, they do not contain the main verb "have" as a part of them.
Option D is incorrect because it is apart of the noun clause, not the entire clause. (The subject and relative pronoun are missing.)