Volume of $3\mathrm{M} \mathrm{NaOH}$ (formula weight $40 \mathrm{g} {\mathrm{mol}}^{-1}$ ) which can be prepared from $84 \mathrm{g}$ of $\mathrm{NaOH}$ is ____$\times {10}^{-1}{\mathrm{dm}}^3$.

A $6.50$ molal solution of $\mathrm{KOH}\left(\mathrm{aq}.\right)$ has a density of $1.89 \mathrm{g}{ \mathrm{cm}}^{-3}$. The molarity of the solution is $\mathrm{mol} {\mathrm{dm}}^{-3}$. (Round off to the Nearest Integer).

[Atomic masses: $\mathrm{K}:39.0 \mathrm{u}; \mathrm{O}:16.0 \mathrm{u}; \mathrm{H}:1.0 \mathrm{u}$]

Which of the following statements is true?

$1$) $200 \mathrm{mL}$ of $0.2 \mathrm{M}$ $\mathrm{NaOH}$ has a same number of moles of solute as $1000 \mathrm{mL}$ of $1 \mathrm{M} \mathrm{NaOH}$.
$2$) $200 \mathrm{mL}$ of $1 \mathrm{M} \mathrm{NaOH}$ has a same number of moles as $1000 \mathrm{mL}$ of $0.2 \mathrm{M} \mathrm{NaOH}$.
$3$) $100 \mathrm{mL}$ of $0.2 \mathrm{M} \mathrm{NaOH}$ has a same number of moles as $1000 \mathrm{mL}$ of $1 \mathrm{M} \mathrm{NaOH}$.
$4$) $2000 \mathrm{mL}$ of $0.2 \mathrm{M} \mathrm{NaOH}$ has a same number of moles as $1000 \mathrm{mL}$ of $1 \mathrm{M} \mathrm{NaOH}$.

The mole fraction of a solute in a $100$ molal aqueous solution ________ $\times {10}^{-2}.$

(Round off to the Nearest Integer).

[Given : Atomic masses: $\mathrm{H} :1.0 \mathrm{u}, \mathrm{O} :16.0 \mathrm{u}$]