Solve the given two equations and select the correct option.
$I.$ $x^{3} - 468 = 1729$
$II.$ $y^{2} - 1733 + 1564 = 0$

Find the combined product of $(a^{4}+b^{4})(a^{2}+b^{2})(a+b)(a-b)$.

If $x=332, y=333, z=335,$ then the value of $x^{3}+y^{3}+z^{3}-3xyz$ is

If $\alpha$ and $\beta$ are the roots of the equation $2x^2 - 3x + 4 = 0$,then the equation whose roots are $\alpha^2$ and $\beta^2$ is

If $\alpha$ and $\beta$ are the roots of $ax^2 + bx + c = 0$ and $\alpha + \beta$,$\alpha^2 + \beta^2$,and $\alpha^3 + \beta^3$ are in $G.P.$,where $\Delta = b^2 - 4ac$,then:

If $\lambda \in R$ is such that the sum of the cubes of the roots of the equation $x^2 + (2 - \lambda) x + (10 - \lambda) = 0$ is minimum,then the magnitude of the difference of the roots of this equation is