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: $0$

Question : If $\sec A=\frac{9}{4}$, then what is the value of $\cot A$?

Option 1: $\frac{4}{\sqrt{65}}$

Option 2: $\frac{9}{\sqrt{65}}$

Option 3: $\frac{\sqrt{65}}{9}$

Option 4: $\frac{\sqrt{65}}{4}$

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 : Evaluate $\sqrt{20}+\sqrt{12}+\sqrt[3]{729}-\frac{4}{\sqrt{5}-\sqrt{3}}-\sqrt{81}:$

Option 1: $\sqrt{2}$

Option 2: $\sqrt{3}$

Option 3: $0$

Option 4: $2\sqrt{2}$

Question : The value of $x$ in the expression $\tan^{2}\frac{\pi }{4}-\cos^{2}\frac{\pi }{3}=x\sin\frac{\pi }{4}\cos\frac{\pi }{4}\tan\frac{\pi }{3}$ is:

Option 1: $\frac{2}{\sqrt{3}}$

Option 2: $\frac{3\sqrt{3}}{4}$

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

Option 4: $\frac{\sqrt{3}}{2}$