Question : If the ratio of the area of two similar triangles is $\sqrt{3}:\sqrt{2}$, then what is the ratio of the corresponding sides of the two triangles?

Option 1: 9 : 4

Option 2: 3 : 2

Option 3: $\sqrt[3]{3}: \sqrt[3]{2}$

Option 4: $\sqrt[4]{3}: \sqrt[4]{2}$

Question : If the ratio of corresponding sides of two similar triangles is $\sqrt{5}: \sqrt{7},$ then what is the ratio of the area of the two triangles?

Option 1: $\sqrt[3]{5}: \sqrt{7}$

Option 2: $25: 49$

Option 3: $\sqrt{5}: \sqrt{7}$

Option 4: $5: 7$

Question : If $x=\sqrt{–\sqrt{3}+\sqrt{3+8 \sqrt{7+4 \sqrt{3}}}}$ where $x > 0$, then the value of $x$ is equal to:

Option 1: 3

Option 2: 4

Option 3: 1

Option 4: 2

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

Option 1: 2

Option 2: 4

Option 3: 6

Option 4: 8

Question : If $\cos 21^{\circ}=\frac{x}{y}$, then $(\operatorname{cosec21^{\circ}}-\cos 69^{\circ})$ is equal to:

Option 1: $\frac{x^{2}}{y\sqrt{y^{2}-x^{2}}}$

Option 2:

$\frac{y^{2}}{x\sqrt{y^{2}-x^{2}}}$

Option 3:

$\frac{y^{2}}{x\sqrt{x^{2}-y^{2}}}$

Option 4: $\frac{x^{2}}{y\sqrt{x^{2}-y^{2}}}$