$510 \ mg$ of a liquid on vaporisation in Victor Mayer's apparatus displaces $510 \ cm^3$ of dry air (at $NTP$). The molecular weight of the liquid is:

$5 \ g$ of $NaOH$ was dissolved in deionized water to prepare a $450 \ mL$ stock solution. What volume (in $mL$) of this solution would be required to prepare $500 \ mL$ of $0.1 \ M$ solution?
Given: Molar Mass of $Na$,$O$,and $H$ is $23$,$16$,and $1 \ g \ mol^{-1}$ respectively.

The volume of $0.04 \ M$ aqueous solution of $HNO_3$ required to neutralize $50 \ mL$ of $0.01 \ M$ aqueous solution of $Ba(OH)_2$ is (Assume complete neutralization). (in $mL$)

$20 \ mL$ of methane is completely burnt using $50 \ mL$ of oxygen. The volume of the gas left after cooling to room temperature is (in $mL$)

How many milliliters of water must be added to $10 \, mL$ of $10 \, N \, HNO_3$ to convert it into $0.1 \, N \, HNO_3$?

$0.53 \ g$ of $Na_2CO_3$ has been dissolved in $100 \ mL$ of a sodium carbonate solution. The normality of the solution will be