The area bounded by the parabola $$y^2=4 a x$$ and its latus-rectum $$x=a$$ is

If $$y=\log \sqrt{\tan x}$$, then the value of $$\frac{d y}{d x}$$ at $$x=\frac{\pi}{4}$$ is

If $$\mathrm{x}=\mathrm{a}\left(\mathrm{t}-\frac{1}{\mathrm{t}}\right)$$ and $$\mathrm{y}=\mathrm{b}\left(\mathrm{t}+\frac{1}{\mathrm{t}}\right)$$, then $$\frac{\mathrm{dy}}{\mathrm{dx}}=$$

Out of 7 consonants and 4 vowels, the number of words consisting of 3 consonants and 2 vowels are