GATE EC 2015 Question Paper (31-Jan-2015) (Shift 1)

The solution of the differential equation $\frac{{\mathrm{d}}^2\mathrm{y}}{\mathrm{d}{\mathrm{t}}^2}+2\frac{\mathrm{dy}}{\mathrm{dt}}+\mathrm{y}=0$ with $\mathrm{y}\left(0\right)={\mathrm{y}}^{\prime }\left(0\right)=1$ is

A vector P is given by $\vec{\mathrm{P}}={\mathrm{x}}^3\mathrm{y}{\vec{\mathrm{a}}}_{\mathrm{x}}-{\mathrm{x}}^2{\mathrm{y}}^2{\vec{\mathrm{a}}}_{\mathrm{y}}-{\mathrm{x}}^2\mathrm{yz}{\vec{\mathrm{a}}}_{\mathrm{z}}$ . Which one of the following statements is TRUE?

Which one of the following graphs describes the function

f(x) = e${}^{-x}$ (x² + x + 1) ?

The maximum area (in square units) of a rectangle whose vertices lie on the ellipse x² + 4y² = 1 is ____________________.

The damping ratio of a series RLC circuit can be expressed as