The equation of the tangent to the curve $$y = 4x{e^x}$$ at $$\left( { - 1,{{ - 4} \over e}} \right)$$ is

The slope of the line through the origin which makes an angle of 30$$^\circ$$ with the positive direction of Y-axis measured anticlockwise is :

The domain of the function $$f(x)=\frac{1}{\sqrt{x+|x|}}$$ is

All the letters of the word 'ABRACADABRA' are arranged in different possible ways. Then the number of such arrangements in which the vowels are together is