Question : If $(x-\frac{1}{x})^2=\sqrt3$, then the value of $(x^6+\frac{1}{x^6})$ equals:

Option 1: 90

Option 2: 100

Option 3: 110

Option 4: 120

Question : Rs. 900 is divided among A, B, and C. The division is such that $\frac{1}{2}$ of A's money =$\frac{1}{3}$ of B's money =$\frac{1}{4}$ of C's money. Find the amounts (in Rs.) received by A, B, and C.

Option 1: 300, 400, and 200

Option 2: 350, 450, and 100

Option 3: 200, 300, and 400

Option 4: 400, 150, and 350

Question : If $\frac{1}{6}$ of $x$ – $\frac{7}{2}$ of $\frac{3}{7}$ equals to $(-\frac{7}{4})$, then the value of $x$ is:

Option 1: –1.5

Option 2: –3

Option 3: –2.5

Option 4: 6

Question : The value of $4 \div 12$ of $[3 \div 4$ of $\{(4-2) \times 6 \div 2\}]-2 \times 6 \div 8+3$ is:

Option 1: $4 \frac{1}{6}$

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

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

Option 4: $7 \frac{1}{6}$

Question : What will be the value of $\sin 10^{\circ}- \frac{4 }{ 3} \sin ^3 10^{\circ}?$

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

Option 2: $\frac{1}{6}$

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

Option 4: $\frac{\sqrt{3}}{6}$