Question : If $x+y+z=0$, then what is the value of $\frac{x^2}{3z}+\frac{y^3}{3xz}+\frac{z^2}{3x}$?

Option 1: $0$

Option 2: $xz$

Option 3: $y$

Option 4: $3y$

Question : If $(x+y):(x-y)=11:1$, find the value of $(\frac{5x+3y}{x-2y})$.

Option 1: $\frac{45}{4}$

Option 2: $\frac{4}{45}$

Option 3: $-\frac{45}{4}$

Option 4: $-\frac{4}{45}$

Question : The graphs of the equations
$4 x+\frac{1}{3} y=\frac{8}{3}$ and $\frac{1}{2} x+\frac{3}{4} y+\frac{5}{2}=0$ intersect at a point P. The point P also lies on the graph of the equation:

Option 1: $x + 2y - 5 = 0$

Option 2: $3x - y - 7 = 0$

Option 3: $x - 3y - 12= 0$

Option 4: $4x - y + 7= 0$

Question : If $xy(x+y)=m$, then the value of $(x^3+y^3+3m)$ is:

Option 1: $\frac{m^3}{xy}$

Option 2: $\frac{m^3}{(x+y)^3}$

Option 3: $\frac{m^3}{x^3y^3}$

Option 4: $mx^3y^3$

Question : If $x+y+z=0$, then what is the value of $\frac{\left (3y^{2}+x^{2}+z^{2} \right )}{\left (2y^{2}-xz \right)}$?

Option 1: $2$

Option 2: $1$

Option 3: $\frac{3}{2}$

Option 4: $\frac{5}{3}$