The value of ${{15} \over {\sqrt {10} + \sqrt {20} + \sqrt {40} - \sqrt 5 - \sqrt {80} }}$ is
$\sqrt 5 (5 + \sqrt 2 )$
$\sqrt 5 (2 + \sqrt 2 )$
$\sqrt 5 (1 + \sqrt 2 )$
$\sqrt 5 (3 + \sqrt 2 )$
If ${a^{x - 1}} = bc,{b^{y - 1}} = ca,{c^{z - 1}} = ab,$then $\sum {(1/x) = } $
${{{{[4 + \sqrt {(15)} ]}^{3/2}} + {{[4 - \sqrt {(15)} ]}^{3/2}}} \over {{{[6 + \sqrt {(35)} ]}^{3/2}} - {{[6 - \sqrt {(35)} ]}^{3/2}}}} = $
The number of integers $q , 1 \leq q \leq 2021$, such that $\sqrt{ q }$ is rational, and $\frac{1}{ q }$ has a terminating decimal expansion, is
If ${x^{x\root 3 \of x }} = {(x\,.\,\root 3 \of x )^x},$ then $x =$
Solution of the equation ${4.9^{x - 1}} = 3\sqrt {({2^{2x + 1}})} $ has the solution