Question : If $\sqrt7=2.646$, then the value of $\frac{1}{\sqrt{28}}$ up to three places of decimal is:

Option 1: 0.183

Option 2: 0.185

Option 3: 0.187

Option 4: 0.189

Question : If $\sin \theta = \frac{3}{11}$, then what is the value of $\cot \theta$?

Option 1: $\frac{3 \sqrt{7}}{11}$

Option 2: $\frac{4 \sqrt{7}}{11}$

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

Option 4: $\frac{3 \sqrt{7}}{28}$

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 : If $\sec \theta+\tan \theta=\frac{1}{\sqrt{3}}$, then the positive value of $\cot \theta+\cos \theta$ is:

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

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

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

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

Question : If $\sin A-\cos A=\frac{\sqrt{3}-1}{2}$, then the value of $\sin A\cdot \cos A$ is:

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

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

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

Option 4: $\frac{1}{\sqrt{3}}$

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