If $\theta$ is the angle between vectors $\vec{a}$ and $\vec{b}$ and $|\vec{a} \times \vec{b}| = |\vec{a} \cdot \vec{b}|$,then $\theta$ is equal to

An optical fibre communication system works on a wavelength of $1.3 \mu m$. The number of subscribers it can feed if a channel requires $20 \text{ kHz}$ is:

$A$ solution which is $10^{-3} \ M$ each in $Mn^{2+}$,$Fe^{2+}$,$Zn^{2+}$ and $Hg^{2+}$ is treated with $10^{-16} \ M$ sulphide ion. If the $K_{sp}$ of $MnS$,$FeS$,$ZnS$ and $HgS$ are $10^{-15}$,$10^{-23}$,$10^{-20}$ and $10^{-54}$ respectively,which one will precipitate first?

Element having highest $I.P.$ value is

Two objects of masses $200 \text{ g}$ and $500 \text{ g}$ possess velocities $10 \hat{i} \text{ m/s}$ and $(3 \hat{i} + 5 \hat{j}) \text{ m/s}$ respectively. The velocity of their centre of mass in $\text{m/s}$ is:

Which of the following is a dihydric alcohol?