The language $L=\{x^ny^n \text{such that }n\geq 1\}$ has following set of strings:
$L=(xy,xxyy,xxxyyy…….\infty)$
1) $E\rightarrow xEy \mid xy$: This grammar can generate all possible string which is generated by language $L.$
Following strings can be generated by the above grammar: $xy,xxyy,xxxyyy….\infty$
so this option is correct.
2) $xy\mid x^+xyy^+$: the minimum length of the string that can be generated by this regular expression is $xy$. it can generate all the string which is generated by language $L$ but it can also generate additional string which is not generated by language $L$ such as $xxxyy,xxyyy$. these are invalid strings for language $L.$
so this option is wrong here.
3) $x^+y^+$: this regular expression generate strings like $xy,xxy,xyy,xxxy,xyyy….\infty$ which is not generated by language $L.$
so this option is also wrong.
$\therefore \text{Option A is correct.}$