Question : The value of $\frac{\sqrt{72}\times \sqrt{363}\times \sqrt{175}}{\sqrt{32}\times \sqrt{147}\times \sqrt{252}}$ is:

Option 1: $\frac{55}{42}$

Option 2: $\frac{45}{56}$

Option 3: $\frac{45}{28}$

Option 4: $\frac{55}{28}$

Question : The value of ($\sin 45^\circ+\cos 45^\circ$) is___________.

Option 1: $\frac{2}{\sqrt{2}}$

Option 2: $\frac{1}{\sqrt{2}}$

Option 3: $1$

Option 4: ${\sqrt{2}}$

Question : The value of $\frac{1}{1+\sqrt{2}+\sqrt{3}}+\frac{1}{1-\sqrt{2}+\sqrt{3}}$ is:

Option 1: $\sqrt{2}$

Option 2: $\sqrt{3}$

Option 3: $1$

Option 4: $4(\sqrt{3}+\sqrt{2})$

Question : If $\sqrt{\frac{\mathrm{a}}{\mathrm{b}}}=\frac{8}{3}-\sqrt{\frac{\mathrm{b}}{\mathrm{a}}}$ and $a-b=10$, then the value of $ab$ is:

Option 1: $32 \frac{1}{7}$

Option 2: $32 \frac{3}{7}$

Option 3: $32 \frac{4}{7}$

Option 4: $32 \frac{2}{7}$

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

Option 1: $\sqrt{3}$

Option 2: $3\sqrt{3}$

Option 3: $16\sqrt{3}$

Option 4: $2\sqrt{3}$

Question : The simplified value of $\frac{3\sqrt 2 }{\sqrt3 + \sqrt6} - \frac{4 \sqrt 3 }{\sqrt{6}+ \sqrt {2}} + \frac{\sqrt 6}{\sqrt{3}+ \sqrt 2}$ is:

Option 1: $\sqrt 2$

Option 2: $\frac{1}{\sqrt2}$

Option 3: $\sqrt 3- \sqrt 2$

Option 4: $0$