Question : If $\sqrt{33}=5.745$, then the value of $\sqrt{\frac{3}{11}}$ is approximately.

Option 1: 1

Option 2: 0.5223

Option 3: 6.32

Option 4: 2.035

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 $\sin A-\cos A=\frac{\sqrt{3}-1}{2}$, 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 : If $\sin 2\theta=\frac{\sqrt{3}}{2}$, then what is the value of $\tan \theta$?

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

Option 2: $1$

Option 3: $\frac{1}{ \sqrt{3}}$

Option 4: $\sqrt{3}$

Question : If $\theta+\phi=\frac{\pi}{2}$ and $\sin\theta=\frac{1}{2}$, then the value of $\sin\phi$ is:

Option 1: $1$

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

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

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