Olefins can be hydrogenated by

In $\triangle ABC$,$(a+b+c)\left(\tan \frac{A}{2}+\tan \frac{B}{2}\right)$ is equal to

$A$ bucket filled with water is tied to a rope of length $0.5 ~m$ and is rotated in a circular path in a vertical plane. The minimum velocity it should have at the lowest point of the circle so that the water does not spill is,$(g = 10 ~m/s^2)$.

Cork cambium is a

If $4x^2 - 5xy + y^2 = 0$ represents a pair of lines with slopes $m_1$ and $m_2$,then the value of $|m_1 - m_2|$ equals

Let the vectors $\overline{a}, \overline{b}, \overline{c}$ be such that $|\overline{a}|=2, |\overline{b}|=4$ and $|\overline{c}|=4$. If the projection of $\overline{b}$ on $\overline{a}$ is equal to the projection of $\overline{c}$ on $\overline{a}$ and $\overline{b}$ is perpendicular to $\overline{c}$,then the value of $|\overline{a}+\overline{b}-\overline{c}|$ is