The function $y=\frac{\log x}{x^3}$ is strictly increasing function for

The curve $4 y=3 x^4-2 x^2$ attains ----------- at the points $x=-\frac{1}{\sqrt{3}}$ and $x=\frac{1}{\sqrt{3}}$

$x=a(\theta+\sin \theta)$ and $y=a(1-\cos \theta)$ represents the equation of a curve. If $\theta$ changes at a constant rate $k$ then the rate of change of the slope of the tangent to the curve at $\theta=\frac{\pi}{3}$ is

Quadrilateral PQRS is inscribed inside a rectangle of dimensions $10 \mathrm{~cm} \times 8 \mathrm{~cm}$. The value of ' $x$ ', if the area of the quadrilateral is minimum is