If ${a^{1/x}} = {b^{1/y}} = {c^{1/z}}$ and ${b^2} = ac$ then $x + z = $
$y$
$2y$
$2xyz$
None of these
If ${x^{x\root 3 \of x }} = {(x\,.\,\root 3 \of x )^x},$ then $x =$
If ${2^x} = {4^y} = {8^z}$ and $xyz = 288,$ then ${1 \over {2x}} + {1 \over {4y}} + {1 \over {8z}} = $
${{12} \over {3 + \sqrt 5 - 2\sqrt 2 }} = $
$\root 4 \of {(17 + 12\sqrt 2 )} = $
The rationalising factor of ${a^{1/3}} + {a^{ - 1/3}}$ is