Question : If $\sqrt[2]{0.014\times0.14x}=0.014\times0.14\sqrt[2]{y}$, then find the value of $\frac{x}{y}$?

Option 1: 0.000196

Option 2: 0.00196

Option 3: 0.0196

Option 4: 0.196

Question : If $x=\frac{1}{2+\sqrt{3}}$ and $y=\frac{1}{2-\sqrt{3}},$ then the value of $8xy(x^{2}+y^{2})$ is:

Option 1: 196

Option 2: 290

Option 3: 112

Option 4: 194

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

Option 1: 950

Option 2: 730

Option 3: 650

Option 4: 970

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 $x^2+\frac{1}{x^2}=\frac{7}{4}$ for $x>0$; then what is the value of $x+\frac{1}{x}$?

Option 1: $2$

Option 2: $\frac{\sqrt{15}}{2}$

Option 3: $\sqrt{5}$

Option 4: $\sqrt{3}$

Question : If $x^2+\frac{1}{x^2}=\frac{7}{4}$ for $x>0$, what is the value of $(x^3+\frac{1}{x^3})$?

Option 1: $\frac{3\sqrt{3}}{5}$

Option 2: $\frac{3\sqrt{15}}{5}$

Option 3: $\frac{3\sqrt{15}}{8}$

Option 4: $\frac{3\sqrt{5}}{8}$