Question : If $2 x+3 y=9$ and $x y=3$, what is $8 x^3+27 y^3?$

Option 1: $235$

Option 2: $244$

Option 3: $243$

Option 4: $234$

Question : Simplify the given expression $\frac{(x^3-y^3)(x+y)}{x^2+x y+y^2}$.

Option 1: $x - y$

Option 2: $x^2-y^2$

Option 3: $x + y$

Option 4: $x^2+y^2$

Question :  If $x^2+\frac{1}{x^2}=7$, then what is the value of $x^3+\frac{1}{x^3}$?

Option 1: 9

Option 2: 18

Option 3: 27

Option 4: 36

Question : If ${x^2+y^2+z^2=2(x+z-1)}$, then the value of $x^3+y^3+z^3$ is equal to:

Option 1: 6

Option 2: 1

Option 3: 2

Option 4: 8

Question : If $x=\operatorname{cosec \theta}-\sin\theta$ and $y=\sec\theta-\cos\theta$, then the relation between $x$ and $y$ is:

Option 1: $x^{2}+y^{2}+3=1$

Option 2: $x^{2}y^{2}\left ( x^{2}+y^{2}+3 \right )=1$

Option 3: $x^{2}\left ( x^{2}+y^{2}-5 \right )=1$

Option 4: $y^{2}\left ( x^{2}+y^{2}-5 \right )=1$

Question : If 8% of $x$ = 4% of $y$, then 20% of $x$ is:

Option 1: 10% of $y$

Option 2: 16% of $y$

Option 3: 40% of $y$

Option 4: 80% of $y$