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 : Which of the following is a true statement?

Option 1: Two similar triangles are always congruent.

Option 2: Two similar triangles have equal areas.

Option 3: Two triangles are similar if their corresponding sides are proportional.

Option 4: Two polygons are similar if their corresponding sides are proportional.

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

Question : If $x=\frac{\sqrt{5}-\sqrt{4}}{\sqrt{5}+\sqrt{4}}$ and $y=\frac{\sqrt{5}+\sqrt{4}}{\sqrt{5}-\sqrt{4}}$ then the value of $\frac{x^2-x y+y^2}{x^2+x y+y^2}=$?

Option 1: $\frac{361}{363}$

Option 2: $\frac{341}{343}$

Option 3: $\frac{384}{387}$

Option 4: $\frac{321}{323}$