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
The equation $\sqrt {(x + 1)} - \sqrt {(x - 1)} = \sqrt {(4x - 1)} $, $x \in R$ has
If ${2^x} = {4^y} = {8^z}$ and $xyz = 288,$ then ${1 \over {2x}} + {1 \over {4y}} + {1 \over {8z}} = $
If $a = \sqrt {(21)} - \sqrt {(20)} $ and $b = \sqrt {(18)} - \sqrt {(17),} $ then
If $x + \sqrt {({x^2} + 1)} = a,$ then $x =$
If ${\left( {{2 \over 3}} \right)^{x + 2}} = {\left( {{3 \over 2}} \right)^{2 - 2x}},$then $x =$