Question : What is the fourth proportional of $3 \sqrt{5}, 5 \sqrt{8}$, and $3 \sqrt{10}$?

Option 1: $10 \sqrt{5}$

Option 2: $40 \sqrt{2}$

Option 3: $30$

Option 4: $20$

Question : Which of the following is true?

Option 1: $\sqrt 5 + \sqrt 3 > \sqrt 6 + \sqrt 2$

Option 2: $\sqrt 5 + \sqrt 3 < \sqrt 6 + \sqrt 2$

Option 3: $\sqrt 5 + \sqrt 3 = \sqrt 6 + \sqrt 2$

Option 4: $(\sqrt 5 + \sqrt 3 ) (\sqrt 6 + \sqrt 2 )= 1$

Question : The ratio of three numbers is 6 : 5 : 9. If 20% of the first number is 30, then what would be 50% of the difference between the third and second numbers?

Option 1: 40

Option 2: 50

Option 3: 30

Option 4: 45

Question : If $x=(\sqrt{6}-1)^{\frac{1}{3}}$, then the value of $\left(x-\frac{1}{x}\right)^3+3\left(x-\frac{1}{x}\right)$ is:

Option 1: $\frac{2 \sqrt{6}-6}{5}$

Option 2: $\frac{4 \sqrt{6}-6}{5}$

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

Option 4: $\frac{4 \sqrt{3}-6}{5}$

Question : If $x=\frac{4\sqrt{15}}{\sqrt{5}+\sqrt{3}}$, the value of $\frac{x+\sqrt{20}}{x–\sqrt{20}}+\frac{x+\sqrt{12}}{x–\sqrt{12}}$ is:

Option 1: $1$

Option 2: $2$

Option 3: $\sqrt{3}$

Option 4: $\sqrt{5}$