A fair coin is tossed for a fixed number of times. If probability of getting 7 heads is equal to probability of getting 9 heads, then probability of getting 2 heads is

The region represented by the inequalities $$x \geq 6, y \geq 3,2 x+y \geq 10, x \geq 0, y \geq 0$$ is

IF $$A X=B$$, where $$A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right], X=\left[\begin{array}{l}x \\ y \\ z\end{array}\right], B=\left[\begin{array}{l}4 \\ 0 \\ 2\end{array}\right]$$, then $$2 x+y-z=$$

$$\int \frac{d x}{e^x+e^{-x}+2}=$$