Let $2 \sin ^2 x+3 \sin x-2>0$ and $x^2-x-2<0$. ( $x$ is measured in radians). The $x$ lies in the interval

If $\mathrm{A} \equiv(1,-1,0), \mathrm{B} \equiv(0,1,-1)$ and $\mathrm{C} \equiv(-1,0,1)$, then the unit vector $\overline{\mathrm{d}}$ such that $\overline{\mathrm{a}}$ and $\overline{\mathrm{d}}$ are perpendiculars and $\overline{\mathrm{b}}, \overline{\mathrm{c}}, \overline{\mathrm{d}}$ are coplanar is

A bullet is shot horizontally and its distance S cm at time t second is given by $\mathrm{S}=1200 \mathrm{t}-15 \mathrm{t}^2$, then the distance covered by the bullet when it comes to the rest, is

If $|z|=1$ and $w=\frac{z-1}{z+1}$ (where $\left.z \neq-1\right)$, then $\operatorname{Re}(w)$ is