Find the value of $x^{3}+y^{3}+z^{3}-3xyz$,when $x+y+z=16$ and $xy+yz+zx=78$.

Solve the given two equations and select the correct answer from the given options.
$I.$ $\sqrt{1225} x + \sqrt{4900} = 0$
$II.$ $(81)^{1/4} y + (343)^{1/3} = 0$

Solve the given two equations and select the correct answer from the given options.
$I.$ $\frac{12 \times 4}{x^{4/7}} - \frac{3 \times 4}{x^{4/7}} = x^{10/7}$
$II.$ $y^3 + 783 = 999$

Roots of $ax^2 + b = 0$ are real and distinct if

The equation $x^{(3/4)(\log_2 x)^2 + (\log_2 x) - 5/4} = \sqrt{2}$ has

If the cost price of an article is $79 \frac{2}{7} \%$ of the marked price and there is a discount of $Rs. \,68$ on the marked price,resulting in a profit of $20 \%$,find the cost price (Quantity $I$) and compare it with a given value (Quantity $II = 1200$).