The value of the integral $\int\limits_{\frac{\pi}{6}}^{\frac{\pi}{3}}\left(\frac{4-\operatorname{cosec}^2 x}{\cos ^4 x}\right) d x$ is :

Let $\mathrm{A}=\{1,2,3,4,5,6\}$. The number of one-one functions $f: \mathrm{A} \rightarrow \mathrm{A}$ such that $f(1) \geq 3, f(3) \leq 4$ and $f(2)+f(3)=5$, is $\_\_\_\_$ .

Two players A and B play a series of games of badminton. The player, who wins 5 games first, wins the series. Assuming that no game ends in a draw, the number of ways, in which player A wins the series is $\_\_\_\_$ .

If the sum of the coefficients of $x^7$ and $x^{14}$ in the expansion of $\left(\frac{1}{x^3}-x^4\right)^n, x \neq 0$, is zero, then the value of $n$ is $\_\_\_\_$ .