NIMCET 2022 — Mathematics PYQ

\mathbf{x} ^{\mathrm{m} }\times \mathbf{y} ^{\mathrm{n} }> ( \mathbf{x} + \mathbf{y} ) ^{\mathrm{m+ n}}
     m$\log x+$n\log y>(m+n$)\log ($x+y)
     differentiate w.r.t. x
$$\begin{array}{rlr}& amp;\frac{m}{x}+\frac{n}{y}\frac{dy}{dx}=\frac{m+n}{x+y}\left(1+\frac{dy}{dx}\right)& \\ & amp;\frac{dy}{dx}(\frac{n}{y}-\frac{m+a}{x+v})=\frac{m+n}{x+y}-\frac{m}{x}& \\ & amp;\frac{dy}{dx}\left(\frac{nx+ny-my-ny}{y(x+y)}\right)=\frac{mx+nx-mx-my}{x(x+y)}& \\ & amp;\frac{dy}{dx}& gt;\left(\frac{nx-my}{nx-my}\right)\frac{y}{x}\\ & amp;\frac{dy}{dx}=\frac{y}{x}(\mathsf{d})& \end{array}$$