Which reagent is commonly used in titration to determine the hardness of water?

Consider the following statements about manganate and permanganate ions. Identify the correct statements:
$(A)$ The geometry of both manganate and permanganate ions is tetrahedral.
$(B)$ The oxidation states of $Mn$ in manganate and permanganate are $+7$ and $+6$, respectively.
$(C)$ Oxidation of $Mn(II)$ salt by peroxodisulphate gives manganate ion as the final product.
$(D)$ Manganate ion is paramagnetic and permanganate ion is diamagnetic.
$(E)$ Acidified permanganate ion reduces oxalate, nitrite and iodide ions.
Choose the correct answer from the options given below:

Two persons of equal height are carrying a long uniform wooden beam of length $l$. They are at distances $\frac{l}{5}$ and $\frac{l}{3}$ from the nearest ends of the rod. The ratio of the normal reaction at their heads is:

The joint equation of the lines passing through the origin and trisecting the first quadrant is . . . . . .

The equation of the normal to the curve $y^4=ax^3$ at $(a, a)$ is

An oil drop having a mass $4.8 \times 10^{-13} ~kg$ and charge $2.4 \times 10^{-18} ~C$ stands still between two charged horizontal plates separated by a distance of $1 ~cm$. If now the polarity of the plates is changed,the instantaneous acceleration of the drop is: $(g = 10 ~ms^{-2})$ (in $~ms^{-2}$)