$3.92 \, g$ of ferrous ammonium sulfate crystals are dissolved in $100 \, mL$ of water. During titration,$20 \, mL$ of this solution is required for complete oxidation by $18 \, mL$ of $KMnO_4$ solution. Calculate the weight of $KMnO_4$ in $1 \, L$ of the solution in grams.

In a conductometric titration,a small volume of titrant of higher concentration is added stepwise to a larger volume of titrate of much lower concentration,and the conductance is measured after each addition.
The limiting ionic conductivity ( $\Lambda ^0$ ) values (in $mS \ m ^2 \ mol ^{-1}$ ) for different ions in aqueous solutions are given below:

Ions	$Ag ^{+}$	$K ^{+}$	$Na ^{+}$	$H ^{+}$	$NO _3^{-}$	$Cl ^{-}$	$SO _4^{2-}$	$OH ^{-}$	$CH _3COO ^{-}$
$\Lambda _0$	$6.2$	$7.4$	$5.0$	$35.0$	$7.2$	$7.6$	$16.0$	$19.9$	$4.1$

For different combinations of titrates and titrants given in List-$I$,the graphs of 'conductance' versus 'volume of titrant' are given in List-$II$.

List-$I$	List-$II$
$(P)$ Titrate: $KCl$,Titrant: $AgNO _3$	$(1)$ Graph showing initial decrease then increase
$(Q)$ Titrate: $AgNO _3$,Titrant: $KCl$	$(2)$ Graph showing sharp decrease then sharp increase
$(R)$ Titrate: $NaOH$,Titrant: $HCl$	$(3)$ Graph showing slight decrease then increase
$(S)$ Titrate: $NaOH$,Titrant: $CH _3COOH$	$(4)$ Graph showing continuous increase
	$(5)$ Graph showing decrease then constant

Match each entry in List-$I$ with the appropriate entry in List-$II$ and choose the correct option.

If soap has a high alkali content,it irritates the skin. How can the amount of excess alkali be determined? What can be the source of excess alkali?

Solution $X$ contains $Na_2CO_3$ and $NaHCO_3$. $20 \ mL$ of $X$ when titrated using methyl orange indicator consumed $60 \ mL$ of $0.1 \ M \ HCl$ solution. In another experiment,$20 \ mL$ of $X$ solution when titrated using phenolphthalein consumed $20 \ mL$ of $0.1 \ M \ HCl$ solution. The concentrations (in $mol \ L^{-1}$) of $Na_2CO_3$ and $NaHCO_3$ in $X$ are respectively:

$10.0 \, mL$ of $Na_{2}CO_{3}$ solution is titrated against $0.2 \, M \, HCl$ solution. The following titre values were obtained in $5$ readings.
$4.8 \, mL, 4.9 \, mL, 5.0 \, mL, 5.0 \, mL$ and $5.0 \, mL$
Based on these readings,and convention of titrimetric estimation,the concentration of $Na_{2}CO_{3}$ solution is .... $mM$.
(Round off to the nearest integer)

$10.0 \, mL$ of $0.05 \, M \, KMnO_4$ solution was consumed in a titration with $10.0 \, mL$ of given oxalic acid dihydrate solution. The strength of given oxalic acid solution is $..... \times 10^{-2} \, g / L$ (Round off to the nearest integer).