Suppose that $\bar{p}, \bar{q}$ and $\overline{\mathrm{r}}$ are three non-coplanar vectors in $\mathbb{R}^3$. Let the components of a vector $\overline{\mathrm{s}}$ along $\overline{\mathrm{p}}, \overline{\mathrm{q}}$ and $\overline{\mathrm{r}}$ be 4,3 and 5 respectively. If the components of this vector $\overline{\mathrm{s}}$ along $(-\overline{\mathrm{p}}+\overline{\mathrm{q}}+\overline{\mathrm{r}}),(\overline{\mathrm{p}}-\overline{\mathrm{q}}+\overline{\mathrm{r}})$ and $(-\overline{\mathrm{p}}-\overline{\mathrm{q}}+\overline{\mathrm{r}})$ are $x$, $y$ and $z$ respectively, then the value of $2 x+y+z$ is

$\int \frac{x^4+x^2+1}{x^2-x+1} d x$ is equal to

If the curves $y^2=6 x, 9 x^2+\mathrm{b} y^2=16$ intersect each other at right angles, then the value of $b$ is

Let $\overline{\mathrm{a}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}$ and $\overline{\mathrm{b}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}$ If $\bar{c}$ is a vector such that $\bar{a} \cdot \bar{c}=|\bar{c}|$, $|\overline{\mathrm{c}}-\overline{\mathrm{a}}|=2 \sqrt{2}$ and the angle between $(\overline{\mathrm{a}} \times \overline{\mathrm{b}})$ and $\bar{c}$ is $60^{\circ}$, then the value of $|(\bar{a} \times \bar{b}) \times \bar{c}|$ is