The rationalising factor of $2\sqrt 3 - \sqrt 7 $ is
$\sqrt 3 + \sqrt 7 $
$2\sqrt 3 + \sqrt 7 $
$\sqrt 3 + 2\sqrt 7 $
None of these
If ${a^x} = {(x + y + z)^y},{a^y} = {(x + y + z)^z}$, ${a^z} = {(x + y + z)^x},$ then
If $x = 3 - \sqrt {5,} $ then ${{\sqrt x } \over {\sqrt 2 + \sqrt {(3x - 2)} }} = $
Number of Solution of the equation ${(x)^{x\sqrt x }} = {(x\sqrt x )^x}$ are
If ${a^x} = {b^y} = {(ab)^{xy}},$ then $x + y = $
If $x + \sqrt {({x^2} + 1)} = a,$ then $x =$