The equation of a circle with origin as a center and passing through an equilateral triangle whose median is of length $$3$$$$a$$ is :

The area bounded by the curves $$y = \ln x,y = \ln \left| x \right|,y = \left| {\ln {\mkern 1mu} x} \right|$$ and $$y = \left| {\ln \left| x \right|} \right|$$ is :

The solution of the equation $$\,{{{d^2}y} \over {d{x^2}}} = {e^{ - 2x}}$$

The order and degree of the differential equation
$$\,{\left( {1 + 3{{dy} \over {dx}}} \right)^{2/3}} = 4{{{d^3}y} \over {d{x^3}}}$$ are