Aqueous NaOH solution is labelled as 10% by weight. Mole fraction of the solute in it is

Concentration of NaOH is 10% w/w. Let there be 100 g of solution, then moles of NaOH in 10 g. 

$\mathrm{Moles}=\frac{10}{40}=0.25 \mathrm{mol}$

Mass of water in solution:

$100 \mathrm{g}-10 \mathrm{g}=90 \mathrm{g}$

Moles of water:

$\mathrm{Moles}=\frac{90}{18}=5 \mathrm{mol}$

Mole fraction of NaOH:

$\frac{\mathrm{Moles} \mathrm{of} \mathrm{NaOH}}{\mathrm{Moles} \mathrm{of} \mathrm{NaOH}+\mathrm{Moles} \mathrm{of} \mathrm{water}}=\frac{0.25 \mathrm{mol}}{5.25 \mathrm{mol}}=0.0476$