If ${ }^{n+4} C_{n+1}-{ }^{n+3} C_n=15(n+2)$, then $n=$

The correct simplified circuit diagram for the logical statement $[\{\mathrm{q} \wedge(\sim \mathrm{q} \vee \mathrm{r})\} \wedge\{\sim \mathrm{p} \vee(\mathrm{p} \wedge \sim \mathrm{r})\}] \vee(\mathrm{p} \wedge \mathrm{r})$ Where $p, q, r$ represents switches $s_1, s_2, s_3$ respectively.

$$ \mathop {\lim }\limits_{n \to \infty }\left[\frac{1}{1-n^4}+\frac{8}{1-n^4}+\ldots \ldots \ldots \ldots .+\frac{n^3}{1-n^4}\right]= $$

If $f(\theta)=\cos \theta_1 \cdot \cos \theta_2 \cdot \cos \theta_3$ .............. $\cos \theta_n$, then $\tan \theta_1+\tan \theta_2+\tan \theta_3+$. ............ $+\tan \theta_{\mathrm{n}}=$