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

$A$ $100 \ mL$ solution of $0.1 \ N \ HCl$ was titrated with $0.2 \ N \ NaOH$ solution. The titration was discontinued after adding $30 \ mL$ of $NaOH$ solution. The remaining titration was completed by adding $0.25 \ N \ KOH$ solution. The volume of $KOH$ required for completing the titration is $..... \ mL$

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.

Given below are two statements:
Statement $I$: In the oxalic acid vs $KMnO_4$ (in the presence of dil. $H_2SO_4$) titration,the solution needs to be heated initially to $60^{\circ}C$,but no heating is required in Ferrous Ammonium Sulphate $(\text{FAS})$ vs $KMnO_4$ titration (in the presence of dil. $H_2SO_4$).
Statement $II$: In oxalic acid vs $KMnO_4$ titration,the initial formation of $MnSO_4$ takes place at high temperature,which then acts as a catalyst for the further reaction. In the case of $\text{FAS}$ vs $KMnO_4$,heating oxidizes $Fe^{2+}$ into $Fe^{3+}$ by oxygen of air and error may be introduced in the experiment.
In the light of the above statements,choose the correct answer from the options given below:

When $10 \ mL$ of an aqueous solution of $Fe^{2+}$ ions was titrated in the presence of dil $H_{2}SO_{4}$ using diphenylamine indicator,$15 \ mL$ of $0.02 \ M$ solution of $K_{2}Cr_{2}O_{7}$ was required to get the end point. The molarity of the solution containing $Fe^{2+}$ ions is $X \times 10^{-2} \ M$. The value of $x$ is $....$ (Nearest integer)

Why in the redox titration of $KMnO_4$ vs oxalic acid,do we heat the oxalic acid solution before starting the titration?