The value of $\sqrt {[12 - \sqrt {(68 + 48\sqrt 2 )} ]} = $
$2 + \sqrt 2 $
$2 - \sqrt 2 $
$\sqrt 2 - 1$
None of these
If ${2^x} = {4^y} = {8^z}$ and $xyz = 288,$ then ${1 \over {2x}} + {1 \over {4y}} + {1 \over {8z}} = $
If ${a^x} = {(x + y + z)^y},{a^y} = {(x + y + z)^z}$, ${a^z} = {(x + y + z)^x},$ then
If ${a^x} = {b^y} = {(ab)^{xy}},$ then $x + y = $
$\root 4 \of {(17 + 12\sqrt 2 )} = $
$\sqrt {(3 + \sqrt 5 )} - \sqrt {(2 + \sqrt 3 )} = $