question_answer

If the ratio of the sums of \[{{\mathbf{m}}^{\mathbf{2}}}\] and \[{{\mathbf{n}}^{\mathbf{2}}}\] of an AP is \[{{\mathbf{m}}^{\mathbf{3}}}:\text{ }{{\mathbf{n}}^{\mathbf{3}}}\], the of its \[{{\mathbf{m}}^{\mathbf{2}}}\] and \[{{\mathbf{n}}^{\mathbf{2}}}\] terms is ______

A) \[\frac{2{{m}^{2}}+mn}{2{{n}^{2}}+mn}\]   

B)                                \[\frac{2{{m}^{2}}+mn-1}{2{{n}^{2}}+mn-1}\]

C) \[\frac{{{m}^{2}}+mn-2}{{{n}^{2}}+mn-2}\]    

D)        \[\frac{2{{m}^{2}}+mn+1}{2{{n}^{2}}+mn+1}\]

E) None of these