Question : The areas of a circle and a square are the same. The ratio of the side of the square to the radius of the circle is:

Option 1: $2\pi :1$

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

Option 3: $\sqrt{\pi}:1$

Option 4: $1:\pi$

Question : A square and a regular hexagon are drawn such that all the vertices of the square and the hexagon are on a circle of radius $r$ cm. The ratio of area between the square and the hexagon is:

Option 1: $3: 4$

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

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

Option 4: $1:\sqrt{2}$

Question : ABCD is a square inscribed in a circle of radius $r$. Then the total area (in square units) of the portions of the circle lying outside the square is:

Option 1: $\pi (r^{2}-4)$

Option 2: $2\pi (r ^{2}-1)$

Option 3: $\pi^{2} r(r-7)$

Option 4: $r^{2}(\pi -2)$

Question : In a circle of radius 3 cm, two chords of length 2 cm and 3 cm lie on the same side of a diameter. What is the perpendicular distance between the two chords?

Option 1: $\frac{4 \sqrt{3}-3 \sqrt{2}}{2}$ cm

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

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

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

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