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:

$110 \, mL$ of $0.1 \, N \, HCl$ is titrated with $30 \, mL$ of $0.2 \, N \, NaOH$. The remaining titration is completed by adding $0.25 \, N \, KOH$ solution. What volume of $KOH$ in $mL$ is required?

$40 \ mL$ of a mixture of $CH_3COOH$ and $HCl$ (aqueous solution) is titrated against $0.1 \ M$ $NaOH$ solution conductometrically. Which of the following statements is correct?

Can titrations with $KMnO_4$ be performed in the presence of $HCl$? Why?

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

$20 \, mL$ of calcium hydroxide was consumed when it was reacted with $10 \, mL$ of an unknown solution of $H_2SO_4$. Also,$20 \, mL$ of a standard solution of $0.5 \, M$ $HCl$ containing $2$ drops of phenolphthalein was titrated with calcium hydroxide. The mixture showed a pink color when the burette displayed the value of $35.5 \, mL$,whereas the burette showed $25.5 \, mL$ initially. The concentration of $H_2SO_4$ is $..........M$ (Nearest integer).