Question : If $x^2+ax+b$ is a perfect square, then which one of the following relations between $a$ and $b$ is true?

Option 1: $a^2=b$

Option 2: $a^2=4b$

Option 3: $b^2=4a$

Option 4: $b^2=a$

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

Option 1: $\frac{4a}{a^{2}+2}$

Option 2: $\frac{2a}{a^{2}+2}$

Option 3: $\frac{4a}{a^{2}+4}$

Option 4: $\frac{2a}{a^{2}+4}$

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 $x=3+2\sqrt{2}$, then $\frac{x^{6}+x^{4}+x^{2}+1}{x^{3}}$ is equal to:

Option 1: 216

Option 2: 192

Option 3: 198

Option 4: 204

Question : If $\frac{(a+b+c)}{2}=16$ and $2ab+2 bc+2ca=120$ ,then what is the value of $4a^2+4b^2+4c^2$?

Option 1: 2828

Option 2: 3368

Option 3: 3616

Option 4: 3056

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

Option 1: 1

Option 2: 27

Option 3: 0

Option 4: –27