Question : If $2x+3y=16$ and $xy=9$, then find the value of $8x^3+27y^3$.

Option 1: 1980

Option 2: 2980

Option 3: 1504

Option 4: 2189

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 $( x^{3}-y^{3}):( x^{2}+xy+y^{2})=5:1$ and $( x^{2}-y^{2}):(x-y)=7:1$, then the ratio $2x:3y$ equals:

Option 1: $4:1$

Option 2: $2:3$

Option 3: $4:3$

Option 4: $3:2$

Question : If 4x² + y² = 40 and xy = 6, then find the value of 2x + y.

Option 1: 6

Option 2: 8

Option 3: 5

Option 4: 4

Question : If $(4 y-\frac{4}{y})=13$, find the value of $(y^2+\frac{1}{y^2})$.

Option 1: $12 \frac{11}{16}$

Option 2: $10 \frac{9}{16}$

Option 3: $12 \frac{9}{16}$

Option 4: $8 \frac{9}{16}$

Question : If $x=1+\sqrt{2}+\sqrt{3}$, then the value of $(2x^4-8x^3-5x^2+26x-28)$ is:

Option 1: $2\sqrt{2}$

Option 2: $3\sqrt{3}$

Option 3: $5\sqrt{5}$

Option 4: $6\sqrt{6}$