An open tank with a square bottom, to contain 4000 cubic cm . of liquid, is to be constructed. The dimensions of the tank, so that the surface area of the tank is minimum, are

$$\int \operatorname{cosec}(x-a) \cdot \operatorname{cosec} x d x=$$

The contrapositive of the inverse of $\mathrm{p} \rightarrow(\mathrm{p} \rightarrow \mathrm{q})$ is

The area enclosed between the parabola $y^2=4 x$ and the line $y=2 x-4$ is