Question : The ratio of the area of an equilateral triangle and that of its circumcircle is:

Option 1: $2\sqrt3:2\pi$

Option 2: $4:\pi$

Option 3: $3\sqrt3:4\pi$

Option 4: $7\sqrt2:2\pi$

Question : A circle is inscribed in an equilateral triangle and a square is inscribed in that circle. The ratio of the areas of the triangle and the square are:

Option 1: $\sqrt3:4$

Option 2: $\sqrt3:8$

Option 3: $3\sqrt3:2$

Option 4: $3\sqrt3:1$

Question : The perimeter of an equilateral triangle is 40 cm more than the length of each of its sides. What is the length of each side of this equilateral triangle?

Option 1: 10 cm

Option 2: 30 cm

Option 3: 15 cm

Option 4: 20 cm

Question : The longest side of the obtuse triangle is 7 cm and the other two sides of the triangle are 4 cm and 5 cm. Find the area of the triangle.

Option 1: $1 \sqrt{3} \mathrm{~cm}^2$

Option 2: $6 \sqrt{3} \mathrm{~cm}^2$

Option 3: $3 \sqrt{2} \mathrm{~cm}^2$

Option 4: $4 \sqrt{6} \mathrm{~cm}^2$

Question : A, B, and C are assigned to complete a work. If the ratio of time taken by A, B, and C is 4 : 3 : 6. Find the ratio of their efficiency.

Option 1: 3 : 4 : 2

Option 2: 4 : 3 : 6

Option 3: 3 : 4 : 6

Option 4: 4 : 6 : 8