If $$\alpha, \beta$$ and $$\gamma$$ are the cube roots of $$P,(P<0)$$, then for any $$x, y$$ and $$z$$ which does not make denominator zero, the expression $$\frac{x \alpha+y \beta+z \gamma}{x \beta+y \gamma+z \alpha}$$ equals to

If $$x+\frac{1}{x}=1$$ and $$p=x^{4000}+\frac{1}{x^{4000}}$$ and $$q$$ is the digit at unit place in the number $$2^{2 n}+1$$, then the value of $$(p+q)$$ is equal to

Let $$z_k=\cos \left(\frac{2 k \pi}{10}\right)+i \sin \left(\frac{2 k \pi}{10}\right) ; k=1,2, \ldots \ldots \ldots$$ 9, then $$\frac{1}{10}\left\{\left|1-z_1\right|\left|1-z_2\right| \ldots .\left|1-z_a\right|\right\}$$ equals to

The condition in order that $$Z_1, Z_2, Z_3$$ are vertices of an isosceles triangle right angled at $$z_2$$, is