Find the value$(s)$ of $P$ for which the given quadratic equation $3x^{2}-5x+P=0$ has equal roots.

If $x^{4} + \frac{1}{x^{4}} = 119$,then the value of $x^{3} - \frac{1}{x^{3}}$ is

If one of the roots of the equation ${x^2} + ax + 3 = 0$ is $3$ and one of the roots of the equation ${x^2} + ax + b = 0$ is three times the other root,then the value of $b$ is equal to

Solve the given two equations and select the correct answer from the given options.
$I.$ $\sqrt{25} x + \sqrt{16} y = 41$
$II.$ $\sqrt{16} x + \sqrt{25} y = 40$

If $x-\sqrt{3}-\sqrt{2}=0$ and $y-\sqrt{3}+\sqrt{2}=0,$ then the value of $(x^{3}-20\sqrt{2})-(y^{3}+2\sqrt{2})$ is:

Solve the given two equations and select the correct answer from the given options.
$I. x = \sqrt{1764}$
$II. y^2 = 1764$