Question : Simplify the following:
$7\left(\cot 11^{\circ} \cot 13^{\circ} \cot 19^{\circ} \cot 29^{\circ} \cot 61^{\circ} \cot 71^{\circ} \cot 77^{\circ} \cot 79^{\circ}\right)$

Option 1: 7

Option 2: – 7

Option 3: – 1

Option 4: 1

Question : The value of the following is:
$\frac{\left (\tan20^{\circ} \right )^{2}}{\left (\operatorname{cosec70^{\circ}} \right )^{2}}+\frac{\left (\cot20^{\circ} \right )^{2}}{\left (\sec70^{\circ} \right )^{2}}+2\tan15^{\circ}  \tan45^{\circ} \tan75^{\circ}$

Option 1: $1$

Option 2: $4$

Option 3: $3$

Option 4: $2$

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 : The value of the following is:
$\left ( \frac{\sin47^{\circ}}{\cos43^{\circ}} \right )^{2}+\left ( \frac{\cos43^{\circ}}{\sin47^{\circ}} \right )^{2}-4\cos^{2}45^{\circ}$

Option 1: $-1$

Option 2: $0$

Option 3: $1$

Option 4: $\frac{1}{2}$

Question : Solve: $\left(1+\frac{5}{6}+\frac{7}{8}+\frac{11}{12}\right) \div\left(\frac{3}{4}-\frac{5}{8}\right)$

Option 1: 29

Option 2: 39

Option 3: 19

Option 4: 49

Question : Evaluate the given expression: $\cos ^2 36^{\circ}+\cos 54^{\circ} \cdot \sin 36^{\circ}+\left(\frac{\tan 26^{\circ}}{\cot 64^{\circ}}\right)$

Option 1: 4

Option 2: 3

Option 3: 1

Option 4: 2