If $$\vec{a}, \vec{b}, \vec{c}$$ are three non-zero vectors, no two of them are collinear, $$\vec{a}+2 \vec{b}$$ is collinear with $$\vec{c}, \vec{b}+3 \vec{c}$$ is collinear with $$\vec{a}$$, then $$\vec{a}+2 \vec{b}$$ is

If $$|z-2+i| \leq 2$$, then the difference between the greatest and least value of $$|z|$$ is ________, $$(\mathrm{i}=\sqrt{-1})$$

A box contains 100 tickets numbered 1 to 100 . A ticket is drawn at random from the box. Then the probability, that number on the ticket is a perfect square, is

If $$\int \frac{\sqrt{1-x^2}}{x^4} \mathrm{~d} x=\mathrm{A}(x)\left(\sqrt{1-x^2}\right)^{\mathrm{m}}+\mathrm{c}$$ for a suitable chosen integer $$\mathrm{m}$$ and a function $$\mathrm{A}(x)$$, where $$\mathrm{c}$$ is a constant of integration, then $$(\mathrm{A}(x))^{\mathrm{m}}$$ equals