The differential equation $$\frac{d y}{d x}=\frac{\sqrt{1-y^{2}}}{y}$$ determines a family of circles with :

Let $$\vec{a}, \vec{b}, \vec{c}$$ be unit vectors such that $$\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}$$. Which one of the following is correct?

Let $$\mathrm{ABCD}$$ be a quadrilateral with area 18 , with side $$\mathrm{A B}$$ parallel to the side $$\mathrm{C D}$$ and $$\mathrm{A B}=2 \mathrm{CD}$$. Let $$\mathrm{AD}$$ be perpendicular to $$\mathrm{AB}$$ and $$\mathrm{CD}$$. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is :

Let $$f(x)=\frac{x}{\left(1+x^{n}\right)^{1 / n}}$$ for $$n \geq 2$$ and $$g(x)=\underbrace{(f o f o \ldots . o f)}_{f \text { occurs } n \text { times }}(x)$$. Then $$\int x^{n-2} g(x) d x$$ equals :