Question : If $a \propto b, b \propto \frac{1}{c}$ and $c \propto d$, then the relation between $a$ and $d$ is:

Option 1: $a \propto \frac{1}{d}$

Option 2: $a \propto d$

Option 3: $a \propto d^2$

Option 4: $a \propto \sqrt{d}$

Question : If $\sin A=\frac{1}{2}$, then the value of $(\tan A+\cos A)$ is:

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

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

Option 3: $\frac{5}{2 \sqrt{3}}$

Option 4: $\frac{5}{3 \sqrt{3}}$

Question : If $a-\frac{1}{a}=4$, then the value of $a+\frac{1}{a}$ is:

Option 1: $5 \sqrt{5}$

Option 2: $4 \sqrt{5}$

Option 3: $2 \sqrt{5}$

Option 4: $3 \sqrt{5}$

Question : If $\sin (A-B)=\sin A \cos B–\cos A\sin B$, then $\sin 15°$ will be:

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

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

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

Option 4: $\frac{\sqrt{3}–1}{2\sqrt{2}}$

Question : If $\sin A=\frac{\sqrt{3}}{2}, 0<A<90^{\circ}$, then find the value of $2(\operatorname{cosec} A + \cot A)$.

Option 1: $2 \sqrt{3}$

Option 2: $\sqrt{3}$

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

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

Question : $7 \sin ^2 A+3 \cos ^2 A=4$, then find $\cot A$:

Option 1: $\sqrt{3}$

Option 2: $\sqrt{2}$

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

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