Question : What is the number of common tangents that can be drawn to two circles that touch each other externally?

Option 1: 2

Option 2: 4

Option 3: 3

Option 4: 1

Question : A, B, and C are three points such that AB = 9 cm, BC = 11 cm, and AC = 20 cm. The number of circles passing through points A, B, and C is:

Option 1: 2

Option 2: 0

Option 3: 1

Option 4: 3

Question : If two circles do not touch or intersect each other and one does not lie inside the other, then find the number of common tangents.

Option 1: 5

Option 2: 4

Option 3: 2

Option 4: 3

Question : If basis points are defined so that 1% is equal to 100 basis points, by how many basis points is 82.5% greater than 62.5%?

Option 1: 0.2

Option 2: 20

Option 3: 200

Option 4: 2000

Question : Two equal circles intersect so that their centres and the points at which they intersect form a square of side 1 cm. The area (in cm²) of the portion that is common to the circle is:

Option 1: $\frac{\pi }{4}$

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

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

Option 4: $(\sqrt{2}-1)$