${4 \over {1 + \sqrt 2 - \sqrt 3 }} = $
$2 + \sqrt 2 + \sqrt 6 $
$1 + \sqrt 2 + \sqrt 3 $
$3 + \sqrt 2 + \sqrt 3 $
None of these
If ${a^x} = bc,{b^y} = ca,\,{c^z} = ab,$ then $xyz$=
If ${x^y} = {y^x},$then ${(x/y)^{(x/y)}} = {x^{(x/y) - k}},$ where $k = $
Solution of the equation ${9^x} - {2^{x + {1 \over 2}}} = {2^{x + {3 \over 2}}} - {3^{2x - 1}}$
If ${\left( {{2 \over 3}} \right)^{x + 2}} = {\left( {{3 \over 2}} \right)^{2 - 2x}},$then $x =$
The square root of $\sqrt {(50)} + \sqrt {(48)} $ is