Question : The value of $\frac{1}{4-\sqrt{15}}-\frac{1}{\sqrt{15}-\sqrt{14}}+\frac{1}{\sqrt{14}-\sqrt{13}}-\frac{1}{\sqrt{13}-\sqrt{12}}+\frac{1}{\sqrt{12}-\sqrt{11}}-\frac{1}{\sqrt{11}-\sqrt{10}}+\frac{1}{\sqrt{10}-3}-\frac{1}{3-\sqrt{8}}$ is:

Option 1: $2-2 \sqrt{2}$

Option 2: $4+2 \sqrt{2}$

Option 3: $4-2 \sqrt{2}$

Option 4: $2+2 \sqrt{2}$

Question : If the LCM and the HCF of two numbers are 12 and 2 respectively, then find the mean proportional of these numbers.

Option 1: $2 \sqrt{6}$

Option 2: $\sqrt{14}$

Option 3: $2$

Option 4: $\sqrt{6}$

Question : Two concentric circles of radii 15 cm and 13 cm are given. Find the length of the chord of the larger circle which touches the smaller circle.

Option 1: $22\sqrt{7}$

Option 2: $8\sqrt{14}$

Option 3: $4\sqrt{14}$

Option 4: $12\sqrt{7}$

Question : The arithmetic mean of the following numbers
1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7 is:

Option 1: 4

Option 2: 5

Option 3: 14

Option 4: 20

Question : The mean proportion between 7 and 112 is:

Option 1: 42

Option 2: 28

Option 3: 21

Option 4: 14