IPMAT Rohtak 2019 (QA) PYQs

$\sqrt{2+\sqrt{3}} \times \sqrt{2+\sqrt{2+\sqrt{3}}} \times \sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}} \times \sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}$ is equal to

The greatest number among $2^{300}$, $3^{200}$, $4^{100}$, $2^{100} + 3^{100}$ is

If $2^{x+y} = 4^{x-y} = \sqrt{32}$, then $xy =$ ___.