Question : If $\mathrm{A}=\cot 30^{\circ} \tan 60^{\circ}+\cot 60^{\circ} \tan 30^{\circ}$, then what is the value of A?

Option 1: $\frac{1}{ \sqrt{ 3}}$

Option 2: $\frac{10}{3}$

Option 3: $\frac{10}{ \sqrt{3}}$

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

Question : Find the value of $\cos 0^{\circ}+\cos 30^{\circ}-\tan 45^{\circ}+\operatorname{cosec} 60^{\circ}+\cot 90^{\circ}$.

Option 1: $\frac{7}{6 \sqrt{3}}$

Option 2: $\frac{\sqrt{3}}{6}$

Option 3: $\frac{7}{6}$

Option 4: $\frac{7}{2 \sqrt{3}}$

Question : The value of the expression $\left[\operatorname{cot} 1^{\circ} \cdot \operatorname{cot} 2^{\circ} \cdot \operatorname{cot} 3^{\circ} \cdot \operatorname{cot} 4^{\circ} \cdot \operatorname{cot} 5^{\circ} \ldots . \operatorname{cot} 178^{\circ} \cdot \operatorname{cot} 179^{\circ}\right]$ is:

Option 1: $1235$

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

Option 3: $1$

Option 4: $0$

Question : If $\sqrt{3} \tan ^2 \theta-4 \tan \theta+\sqrt{3}=0$, then what is the value of $\tan ^2 \theta+\cot ^2 \theta$?

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

Option 2: $\frac{10}{3}$

Option 3: $3$

Option 4: $\frac{6}{5}$

Question : If $\tan(5\theta-10^\circ)=\cot(5\varphi+20^\circ)$, then the value of $(\theta+\varphi)$ is:

Option 1: $16^\circ$

Option 2: $18^\circ$

Option 3: $15^\circ$

Option 4: $20^\circ$