Phenolphthalein is used as an indicator for the titration of sodium hydroxide solution against a standard solution of oxalic acid. The colour change that is observed at an alkaline pH close to the equivalence point during this titration is:

$25 \ mL$ of the given $HCl$ solution requires $30 \ mL$ of $0.1 \ M$ sodium carbonate solution. What is the volume of this $HCl$ solution required to titrate $30 \ mL$ of $0.2 \ M$ aqueous $NaOH$ solution? .............. $mL$

In the titration of potassium permanganate $(KMnO_4)$ against ferrous ammonium sulphate $(FAS)$ solution,dilute sulphuric acid $(H_2SO_4)$ but not nitric acid $(HNO_3)$ is used to maintain an acidic medium,because:

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.

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

$10.0 \, mL$ 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)