Option (B) is correct. I and IV are equivalent.
$¬∀x(P(x)) \equiv ∃x(¬P(x))$ [De morgan's Law]
Alternate approach:
Let's take an example.
Let $P(x)\implies$ Student $x$ is pass
$I \implies$ Not all students are pass. (which means "Some students are fail")
$II\implies$There does not exist a student who is pass. (which means "Every student is fail")
$III \implies$There does not exist a student who is not pass (which means "Every student is pass")
$IV\implies$Some students are not pass. (which means "Some students are fail")
I and IV are equivalent.