Question : What is the length (in cm) of the transverse common tangent between two circles with radii 6 cm and 4 cm, given that the distance between their centres is 14 cm?

Option 1: $2 \sqrt{6}$

Option 2: $4 \sqrt{6}$

Option 3: $5 \sqrt{6}$

Option 4: $3 \sqrt{6}$

Question : The radius of circle A is twice that of circle B and the radius of circle B is twice that of circle C. Their area will be in the ratio:

Option 1: 16 : 4 : 1

Option 2: 4 : 2 : 1

Option 3: 1 : 2 : 4

Option 4: 1 : 4 : 16

Question : The radii of two circles are 5 cm and 3 cm. The distance between their centre is 24 cm. Then the length of the transverse common tangent is:

Option 1: $16$ cm

Option 2: $15\sqrt{2}$ cm

Option 3: $16\sqrt{2}$ cm

Option 4: $15$ cm

Question : The radius of a hemisphere is twice that of a sphere. What is the ratio of the total surface area of the hemisphere and sphere?

Option 1: 3 : 1

Option 2: 12 : 1

Option 3: 4 : 1

Option 4: 6 : 1

Question : Three cars travelled a distance in the ratio 1 : 2 : 3. If the ratio of the time of travel is 3 : 2 : 1, then the ratio of their speed is:

Option 1: 3 : 9 : 1

Option 2: 1 : 3 : 9

Option 3: 1 : 2 : 4

Option 4: 4 : 3 : 2