Solution:

Given:
Molality (m) = 3.0 mol/kg
Density = 1.110 g/mL

To find:
Molarity (M) of the solution

Molality (m) is defined as the number of moles of solute per kilogram of solvent.
Molality (m) = moles of solute / mass of solvent in kg

We know that the molar mass of NaOH is 40 g/mol.

Step 1: Calculation of mass of solute (NaOH)
The molality is given as 3.0 mol/kg. Let's assume the mass of the solvent is 1 kg.
Therefore, the moles of solute (NaOH) = molality x mass of solvent = 3.0 mol/kg x 1 kg = 3.0 mol

Step 2: Calculation of volume of solution
The density is given as 1.110 g/mL. Let's assume the volume of the solution is V mL.
Therefore, the mass of the solution = density x volume of solution = 1.110 g/mL x V mL = 1.110V g

Since the mass of the solution is equal to the mass of the solute plus the mass of the solvent, we can write:
mass of the solution = mass of solute (NaOH) + mass of solvent

1.110V g = 3.0 mol x 40 g/mol + mass of solvent

Step 3: Calculation of mass of solvent
Rearranging the equation, we get:
mass of solvent = 1.110V g - 3.0 mol x 40 g/mol

Step 4: Calculation of molarity
Molarity (M) is defined as the number of moles of solute per liter of solution.
Molarity (M) = moles of solute / volume of solution in L

Since the volume of the solution is given in mL, we need to convert it to L.
1 L = 1000 mL
Therefore, volume of solution in L = V mL / 1000 = V/1000 L

Using the equation for molarity, we can substitute the values we calculated:
Molarity (M) = 3.0 mol / (V/1000 L)

Since the answer choices are given in 3 decimal places, we need to round the molarity to the nearest thousandth.

Therefore, the molarity of the solution is given by option (D) 2.973 M.