Question : If $36 : 81 :: x : 63$, then what is the value of $x$?

Option 1: 30

Option 2: 31

Option 3: 28

Option 4: 29

Question : If $x^2-5 x+1=0$, then the value of $\frac{x^6+x^4+x^2+1}{5 x^3}=?$

Option 1: 30

Option 2: 25

Option 3: 23

Option 4: 28

Question : If $x^{3}-y^{3}=81$ and $x-y=3$, what is the value of $x^{2}+y^{2}$?

Option 1: 18

Option 2: 21

Option 3: 27

Option 4: 36

Question : If $x=\sqrt[3]{28}, y=\sqrt[3]{27}$, then the value of $x+y-\frac{1}{x^{2}+xy+y^{2}}$ is:

Option 1: 8

Option 2: 7

Option 3: 6

Option 4: 5

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

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: –1

Question : If $x^2-xy+y^2=2$ and $x^4+x^2y^2+y^4=6$, then the value of $(x^2+xy+y^2)$ is:

Option 1: 1

Option 2: 12

Option 3: 3

Option 4: 36