determine the number of grams of solute needed to make 1.05 mole solution of HNO3 in 2.00Kg ofH2O

Answer 1

I am not familiar with a mole solution. You could mean 1.05 molAR or 1.05 molAL. I suspect you mean 1.05 molal.
molality = moles/kg solvent.
Plug in molality and kg solvent and calculate moles.
Then use moles = grams/molar mass to calculate grams HNO3.
Post your work if you get stuck.