The curve $$y=a x^3+b x^2+c x+5$$ touches $$X$$-axis at $$P(-2,0)$$ and cuts $$Y$$-axis at a point $$Q$$, where its gradient is 3, then

The area of the region bounded by the curve $$y=2 x-x^2$$ and X-axis is

The equation of a line with slope $$-\frac{1}{\sqrt{2}}$$ and makes an intercept of $$2 \sqrt{2}$$ units on negative direction of $$y$$-axis is

If $$\mathrm{\frac{3+2i}{1+i}=\frac{1}{2}(x+iy)}$$, then x $$-$$ y =