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 $x+y+z=13,x^2+y^2+z^2=133$ and $x^3+y^3+z^3=847$, then the value of $\sqrt[3]{x y z}$ is:

Option 1: $8$

Option 2: $7$

Option 3: $-9$

Option 4: $-6$

Question : If $(\frac{x}{y})^{5a-3}=(\frac{y}{x})^{17-3a}$, then what is the value of $a$?

Option 1: –7

Option 2: –5

Option 3: 0

Option 4: 3

Question : If $x^4+x^2 y^2+y^4=133$ and $x^2-x y+y^2=7$, then what is the value of $xy$?

Option 1: 8

Option 2: 12

Option 3: 4

Option 4: 6

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