Question : If $(x-y)=3$, then what is the value of $(x^3-y^3-9xy)$?

Option 1: $3$

Option 2: $9$

Option 3: $18$

Option 4: $27$

Question : What will be the value of $x^{3}+y^{3}+z^{3}-3xyz$, when $x+y+z=9$ and $x^{2}+y^{2}+z^{2}=31?$

Option 1: 27

Option 2: 3

Option 3: 54

Option 4: 9

Question : If $x^2+8 y^2+12 y-4 x y+9=0$, then the value of $(7 x+8 y)$ is:

Option 1: –33

Option 2: 9

Option 3: 33

Option 4: –9

Question : If $x^2 = y+z$, $y^2=z+x$, $z^2=x+y$, then the value of $\frac{1}{x+1}+\frac{1}{y+1}+\frac{1}{z+1}$ is:

Option 1: –1

Option 2: 1

Option 3: 2

Option 4: 4

Question : If $\frac{x}{4 y}=\frac{3}{4}$ then, the value of $\frac{2 x+3 y}{x–2 y}$ is:

Option 1: 7

Option 2: 9

Option 3: 6

Option 4: 8

Question : If $x= 19$ and $y= 18$, then the value of $\frac{x^{2}+y^{2}+xy}{x^{3}-y^{3}}$ is:

Option 1: 1

Option 2: 37

Option 3: 324

Option 4: 361