If $\mathrm{f}(x)=(1+x)\left(1+x^2\right)\left(1+x^4\right)\left(1+x^8\right)$, then $f^{\prime}(1)=$

$$\int_\limits{0.2}^{3.5}[x] \mathrm{d} x=$$ (where $[x]=$ greatest integer not greater than $x$ )

Let $\mathrm{p}, \mathrm{q}$ and r be the statements

$\mathrm{p}: \mathrm{X}$ is an equilateral triangle

$\mathrm{q}: \mathrm{X}$ is isosceles triangle

r: q $\vee \sim p$,

then the equivalent statement of $r$ is

The bacteria increase at the rate proportional to the number of bacteria present. If the original number N doubles in 8 hours, then the number of bacteria in 24 hours will be