CBSE Past Year MCQ Quiz

Assertion (A) : One of the particular solutions of the differential equation \(\frac{d y}{d x}=e^{x+y}\) can be \(e^{x}+e^{-y}=-2\).
Reason \((R): \quad \mathrm{e}^{\mathrm{x}}+\mathrm{e}^{-\mathrm{y}}=\mathrm{C}\) is the general solution of the differential equation \(\frac{d y}{d x}=e^{x+y}\).

\(\frac{d y}{d x}=F(x, y)\) will be a homogeneous differential equation for which of the following functions?
(i) \(\mathrm{F}(\mathrm{x}, \mathrm{y})=3 \mathrm{x}+2 \mathrm{y}\)
(ii) \(\mathrm{F}(\mathrm{x}, \mathrm{y})=\sin \frac{\mathrm{y}}{\mathrm{x}}+\log \mathrm{y}-\log \mathrm{x}\)
(iii) \(\mathrm{F}(\mathrm{x}, \mathrm{y})=\mathrm{e}^{\mathrm{y} / \mathrm{x}}+1\)
(iv) \(\mathrm{F}(\mathrm{x}, \mathrm{y})=\sqrt{\mathrm{x}^{2}+\mathrm{y}^{2}}-\mathrm{y}\)