Algebra Test for SSC CGL

If $a^3 + b^3 = 405$ and $a + b = 9$, then the value of $ab$ is

If $x^2 + 4y^2 = 53$ and $x - 2y = 5$, then what is the value of $x^3 - 8y^3$?

Simplify $(x - y + z)^2 - (x - y - z)^2$.

If $x^2 + \frac{1}{x^2} = 7$, then the value of $x^3 + \frac{1}{x^3}$ where $x > 0$ is equal to:

If $a^2 + b^2 = 65$ and $ab = 8$, with $a > b > 0$, then find the value of $a^2 - b^2$.

If $X^{y^z}=1$, $Y^{z^x}=125$ and $Z^{y^x}=243$ (x, y and z are natural numbers), then what is the value of $9x + 10y - 18z$?

If $x + y + z = 18$, $xyz = 81$ and $xy + yz + zx = 90$, then the value of $x^3 + y^3 + z^3 + xyz$ is:

If $x^4+\frac{1}{x^4} = 727$, $x>1$, then what is the value of $\left(x-\frac{1}{x}\right)$?

If $a^2 + b^2 + c^2 = 6.25$ and $(ab + bc + ca) = 0.52$, what is the value of $(a + b + c)$, if $(a + b + c) < 0$?

If $27(x + y)^3 - 8(x - y)^3 = (x + 5y)(Ax^2 + By^2 + Cxy)$, then what is the value of $(A + B - C)$?