Identify the product formed when ethyl benzene reacts with nitric acid.

The vectors $$\overrightarrow{\mathrm{AB}}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{k}}$$ and $$\overrightarrow{\mathrm{AC}}=5 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}$$ are the sides of a triangle $$\mathrm{ABC}$$. The length of the median through $$\mathrm{A}$$ is

The principal solutions of $$\cot x=\sqrt{3}$$ are

The area of the region included between the parabolas $$y^2=8 x$$ and $$x^2=8 y$$, is