Assertion (A) Order of the differential equations of a family of circles with constant radius is two.

Reason (R) An algebraic equation having two arbitrary constants is general solution of a second order differential equation.

If $$l$$ and $$m$$ are order and degree of a differential equation of all the straight lines at constant distance of $$P$$ units from the origin, then $$l m^2+l^2 m=$$

If $$2 x-y+C \log (|x-2 y-4|)=k$$ is the general solution of $$\frac{d y}{d x}=\frac{2 x-4 y-5}{x-2 y+2}$$, then $$C=$$

By eliminating the arbitrary constants from $$y=(a+b) \sin (x+c)-d e^{x+e+f}$$, then differential equation has order of