Question : If $x=\sqrt3+\frac{1}{\sqrt3}$, then the value of $(x-\frac{\sqrt{126}}{\sqrt{42}})(x-\frac{1}{x-\frac{2\sqrt3}{3}})$ is:

Option 1: $\frac{5\sqrt3}{6}$

Option 2: $\frac{2\sqrt3}{3}$

Option 3: $\frac{5}{6}$

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

Question : The base of a right pyramid is an equilateral triangle of side $10\sqrt3$ cm. If the total surface area of the pyramid is $270\sqrt3$ sq. cm. its height is:

Option 1: $12\sqrt3$ cm

Option 2: $10$ cm

Option 3: $10\sqrt3$ cm

Option 4: $12$ cm

Question : The value of $3\frac{1}{2} - [2\frac{1}{4}+ 1\frac{1}{4} - \frac{1}{2}(1\frac{1}{2}-\frac{1}{3} -\frac{1}{6})]$ is:

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

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

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

Option 4: $9\frac{1}{2}$

Question : If the sides of an equilateral triangle are increased by 1 metre, then its area is increased by $\sqrt3$ sq. metre. The length of any of its sides is:

Option 1: $2$ metres

Option 2: $\frac{5}{2}$ metres

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

Option 4: $\sqrt3$ metres

Question : If $\sqrt{a}=3b$, then $\frac{a}{b^2}$ is equal to:

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

Option 2: $6$

Option 3: $\frac{1}{9}$

Option 4: $9$