In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways, in which none of the students sits on the allotted seat, is _________.

Let a line $$l$$ pass through the origin and be perpendicular to the lines

$$l_{1}: \vec{r}=(\hat{\imath}-11 \hat{\jmath}-7 \hat{k})+\lambda(\hat{i}+2 \hat{\jmath}+3 \hat{k}), \lambda \in \mathbb{R}$$ and

$$l_{2}: \vec{r}=(-\hat{\imath}+\hat{\mathrm{k}})+\mu(2 \hat{\imath}+2 \hat{\jmath}+\hat{\mathrm{k}}), \mu \in \mathbb{R}$$.

If $$\mathrm{P}$$ is the point of intersection of $$l$$ and $$l_{1}$$, and $$\mathrm{Q}(\propto, \beta, \gamma)$$ is the foot of perpendicular from P on $$l_{2}$$, then $$9(\alpha+\beta+\gamma)$$ is equal to _____________.

The mean of the coefficients of $$x, x^{2}, \ldots, x^{7}$$ in the binomial expansion of $$(2+x)^{9}$$ is ___________.

If $$a$$ and $$b$$ are the roots of the equation $$x^{2}-7 x-1=0$$, then the value of $$\frac{a^{21}+b^{21}+a^{17}+b^{17}}{a^{19}+b^{19}}$$ is equal to _____________.