$A$ 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?

If $\omega$ is a complex cube root of unity,then $\sin \left\{\left(\omega^{10}+\omega^{23}\right) \pi-\frac{\pi}{4}\right\}$ is equal to

The reagent used in the Wolff-Kishner reduction is

An iron load of $2 \ kg$ is suspended in air from the free end of a sonometer wire of length $1 \ m$. $A$ tuning fork of frequency $256 \ Hz$ is in resonance with $\frac{1}{\sqrt{7}}$ times the length of the sonometer wire. If the load is immersed in water,the length of the wire in metres that will be in resonance with the same tuning fork is (Specific gravity of iron $= 8$)

Let $z = \cos \theta + i \sin \theta$. Then the value of $\sum_{m=1}^{15} \operatorname{Im}(z^{2m-1})$ at $\theta = 2^{\circ}$ is

Kangaroo rat is found in .........