The number of solutions of cos2$$\theta$$ = sin$$\theta$$ in (0, 2$$\pi$$) are

If $$y=\tan ^{-1}\left[\frac{1}{1+x+x^2}\right]+\tan ^{-1}\left[\frac{1}{x^2+3 x+3}\right], x>0$$, then $$\frac{d y}{d x}=$$

If $$z(2-i)=(3+i)$$, then $$z^{38}=$$, ( where $$z=x+i y$$)

The area bounded by the parabola $$y^2=x$$, the straight line $$y=4$$ and $$Y$$ axis is