If $$y=4 x-5$$ is a tangent to the curve $$y^2=\mathrm{p} x^3+\mathrm{q}$$ at $$(2,3)$$, then $$\mathrm{p}-\mathrm{q}$$ is

If $$x=\sqrt{\mathrm{e}^{\sin ^{-1} t}}$$ and $$y=\sqrt{\mathrm{e}^{\cos ^{-1} t}}$$, then $$\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}$$ is

If $$\sum_\limits{r=1}^{50} \tan ^{-1} \frac{1}{2 r^2}=p$$ then $$\tan p$$ is

The value of $$\int \mathrm{e}^x\left(\frac{x^2+4 x+4}{(x+4)^2}\right) \mathrm{d} x$$ is :