Radius of gyration of a body depends on

If $(x, y, z)$ is an arbitrary point lying on a plane $P$ which passes through the points $(42, 0, 0)$,$(0, 42, 0)$,and $(0, 0, 42)$,then the value of the expression $3 + \frac{x-11}{(y-19)^2(z-12)^2} + \frac{y-19}{(x-11)^2(z-12)^2} + \frac{z-12}{(x-11)^2(y-19)^2} - \frac{x+y+z}{14(x-11)(y-19)(z-12)}$ is:

$A$ solid cylinder $30 \ cm$ in diameter at the top of an inclined plane $2.0 \ m$ high is released and rolls down the incline without loss of energy due to friction. Its linear speed at the bottom is .......... $m/s$.

The scientist who classified plants based on their habitat is .........

The value of $\sqrt{42+\sqrt{42+\sqrt{42+\ldots}}}$ is equal to:

$A$ parallel beam of light is incident on a system of two convex lenses of focal lengths $f_1 = 20\, cm$ and $f_2 = 10\, cm$. What should be the distance between the two lenses so that the rays after refraction from both the lenses emerge as a parallel beam?........$cm$