Question : Let $\sqrt[3]{a}=\sqrt[3]{26}+\sqrt[3]{7}+\sqrt[3]{63}$. Then:

Option 1: $a<729$ but $a>216$

Option 2: $a<216$

Option 3: $a>729$

Option 4: $a = 729$

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 : If $\theta$ is an acute angle and $\sin \theta \cos \theta=2 \cos ^3 \theta-\frac{1}{4} \cos \theta$, then the value of $\sin \theta$ is:

Option 1: $\frac{\sqrt{15}-1}{8}$

Option 2: $\frac{\sqrt{15}-1}{4}$

Option 3: $\frac{\sqrt{15}+1}{4}$

Option 4: $\frac{\sqrt{15}-1}{2}$

Question : If $a=\frac{1}{a-\sqrt{6}}$ and $(a>0)$, then the value of $\left(a+\frac{1}{a}\right)$ is:

Option 1: $\sqrt{6}$

Option 2: $\sqrt{10}$

Option 3: $\sqrt{15}$

Option 4: $\sqrt{7}$

Question : If $\sin(A+B)=\sin A\cos B+\cos A \sin B$, then the value of $\sin75°$ is:

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

Option 2:

$\frac{\sqrt{2}+1}{2\sqrt{2}}$

Option 3:

$\frac{\sqrt{3}+1}{2\sqrt{2}}$

Option 4:

$\frac{\sqrt{3}+1}{2}$