A point moves along the arc of parabola $y=2 x^2$. Its abscissa increases uniformly at the rate of 2 units $/ \mathrm{sec}$. At the instant, the point is passing through ( 1,2 ), its distance from origin is increasing at the rate of

The equation of the normal to the curve $y=x \log x$, which is parallel to the line $2 x-2 y+3=0$, is

The function $\mathrm{f}(x)=2 x^3-6 x+5$ is an increasing function, if

A square plate is contracting at the uniform rate $3 \mathrm{~cm}^2 / \mathrm{sec}$, then the rate at which the perimeter is decreasing, when the side of the square is 15 cm , is