A wire of length 20 units is divided into two parts such that the product of one part and cube of the other part is maximum, then product of these parts is

A particle is moving on a straight line. The distance $$\mathrm{S}$$ travelled in time $$\mathrm{t}$$ is given by $$\mathrm{S=a t^2+b t+6}$$. If the particle comes to rest after 4 seconds at a distance of $$16 \mathrm{~m}$$. from the starting point, then the acceleration of the particle is.

The equation of the tangent to the curve $$y = 4x{e^x}$$ at $$\left( { - 1,{{ - 4} \over e}} \right)$$ is

If $$f(x)=\log (\sin x), x \in\left[\frac{\pi}{6}, \frac{5 \pi}{6}\right]$$, then value of '$$c$$' by applying LMVT is