For the following questions answer them individually
A square and a regular hexagon are drawn such that all the vertices of the square and the hexagon are on circle of radius r cm. The ratio of area of the square and the hexagon is
A solid cylinder has the total surface area 231 sq.cm. If its curved surface area is $$\frac{2}{3}$$ of the total surface area, then the volume of the cylinder is
The lateral surface area of frustum of a right circular cone,if the area of its base is $$16 \pi cm^2$$ and the diameter of circular upper surface is 4 cm and slant height 6 cm, will be
The diameter of a sphere is twice the diameter of another sphere, The surface area ofthefirst sphere is equal to the volume of the second sphere, The magnitude of the radius ofthefirst sphereis
A right circular cylinder having diameter 21 cm & height 38 cm is full of ice cream. The ice cream is to be filled in cones of height 12 cm and diameter 7 cm having a hemispherical shape on the top. The numberof such conesto befilled with ice cream is
The Simplified value of $$Â \left(1 - \frac{2xy}{x^2 + y^2}\right) \div \left(\frac{x^3 - y^3}{x - y} - 3xy\right)$$ is
If $$a + b + c = 0$$ then the value of $$\frac{1}{(a + b)(b + c)} + \frac{1}{(b + c)(c + a)} + \frac{1}{(c + a)(a + b)}$$ is
If $$x = \frac{\sqrt{5} + 1}{\sqrt{5} - 1} and y = \frac{\sqrt{5} - 1}{\sqrt{5} + 1}$$, the value of $$\frac{x^2 + xy + y^2}{x^2 - xy + y^2}$$ is
If $$\left(x - \frac{1}{x}\right)^2 = 3$$, then the value of $$x^6 + \frac{1}{x^6}$$ equals
