The solution of the differential equation $x^2 \dfrac{dy}{dx} - xy = 1$ is...

If $\bar{a}$ and $\bar{b}$ are unit vectors and $\theta$ ($0 < \theta < \pi$) is the angle between them, then the value of $\dfrac{|\bar{a} + \bar{b}|}{|\bar{a} - \bar{b}|}$ is equal to...

If ABCDEF is a regular hexagon and $\overline{AB} + \overline{AC} + \overline{AD} + \overline{AE} + \overline{AF} = p\overline{AD} = q\overline{AO}$, where O is the center of the hexagon, then the values of $p$ and $q$ respectively are

The vector $\bar{r}$ whose magnitude is $3\sqrt{2}$ units and which makes angles of $\dfrac{\pi}{4}$ and $\dfrac{\pi}{2}$ with the positive y- and z-axes respectively is....