Question : What is the third proportion of $2 \sqrt{3}$ and $6 \sqrt{5}$?

Option 1: $50 \sqrt{6}$

Option 2: $40 \sqrt{3}$

Option 3: $20 \sqrt{6}$

Option 4: $30 \sqrt{3}$

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 : Two circles of radii 15 and 18 cm touch each other externally. What is the length (in cm) of the direct common tangent to the two circles?

Option 1: $18 \sqrt{6}$

Option 2: $12 \sqrt{15}$

Option 3: $30 \sqrt{6}$

Option 4: $6 \sqrt{30}$

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 : The fourth proportional to 6, 8, and 12 is:

Option 1: 15

Option 2: 12

Option 3: 18

Option 4: 16