Combustion of glucose $$(\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6)$$ produces $$\mathrm{CO}_2$$ and water. The amount of oxygen (in $$\mathrm{g}$$) required for the complete combustion of $$900 \mathrm{~g}$$ of glucose is :

[Molar mass of glucose in $$\mathrm{g} \mathrm{~mol}^{-1}=180$$]

Molality $$(\mathrm{m})$$ of $$3 \mathrm{M}$$ aqueous solution of $$\mathrm{NaCl}$$ is : (Given : Density of solution $$=1.25 \mathrm{~g} \mathrm{~mL}^{-1}$$, Molar mass in $$\mathrm{g} \mathrm{~mol}^{-1}: \mathrm{Na}-23, \mathrm{Cl}-35.5$$)

The density of '$$x$$' $$\mathrm{M}$$ solution ('$$x$$' molar) of $$\mathrm{NaOH}$$ is $$1.12 \mathrm{~g} \mathrm{~mL}^{-1}$$, while in molality, the concentration of the solution is $$3 \mathrm{~m}$$ ( 3 molal). Then $$x$$ is

(Given : Molar mass of $$\mathrm{NaOH}$$ is $$40 \mathrm{~g} / \mathrm{mol}$$)

The number of moles of methane required to produce $$11 \mathrm{~g} \mathrm{~CO}_2(\mathrm{g})$$ after complete combustion is : (Given molar mass of methane in $$\mathrm{g} \mathrm{~mol}^{-1}: 16$$ )