Step-by-step Solution:

1. Analyze the given compound: The compound is [Fe(H₂O)₅NO]SO₄. This is the well-known complex formed in the 'brown ring test' for nitrate ions. The complex ion is [Fe(H₂O)₅NO]²⁺ and the counter-ion is the sulfate ion, SO₄²⁻.

2. Determine the oxidation state of Iron (Fe) in the complex ion: Let the oxidation state of Fe be x. The water molecule (H₂O) is a neutral ligand, so its charge is 0. In this specific complex, the nitrosyl ligand (NO) is considered as a nitrosonium ion (NO⁺), which carries a +1 charge. This is a common convention for the brown ring complex in coordination chemistry. The overall charge of the complex ion is +2. We can set up the equation for the sum of charges: $x + 5(0) + 1(+1) = +2$ $x + 1 = +2$ $x = +1$ So, the oxidation state of iron in this complex is +1.

3. Determine the electronic configuration of the Fe⁺¹ ion: The atomic number of Iron (Fe) is 26. The electronic configuration of a neutral Fe atom is [Ar] 3d⁶ 4s². When it forms the Fe⁺¹ ion, it loses one electron, resulting in the configuration [Ar] 3d⁷.

4. Evaluate Statement 2: The Fe in [Fe(H₂O)₅NO]SO₄ has three unpaired electrons. To find the number of unpaired electrons (n), we can use the experimentally determined magnetic moment (μ) of the complex, which is approximately 3.87 Bohr Magnetons (B.M.). The spin-only magnetic moment is given by the formula: $μ = \sqrt{n(n+2)} \text{ B.M.}$ Substituting the experimental value: $3.87 = \sqrt{n(n+2)}$ Squaring both sides: $(3.87)² ≈ 15 = n(n+2)$ $n² + 2n - 15 = 0$ Solving this quadratic equation by factoring: $(n+5)(n-3) = 0$ Since the number of unpaired electrons (n) cannot be negative, we have n = 3. This means the Fe⁺¹ ion in the complex has three unpaired electrons. Therefore, Statement 2 is True.

5. Evaluate Statement 1: [Fe(H₂O)₅NO]SO₄ is paramagnetic. Paramagnetism is a property of materials that are weakly attracted to a magnetic field. This property arises from the presence of unpaired electrons in the atoms or ions of the material. As determined in the previous step, the complex ion [Fe(H₂O)₅NO]²⁺ contains 3 unpaired electrons. Because it has unpaired electrons, the compound is paramagnetic. Therefore, Statement 1 is True.

6. Analyze the relationship between the two statements: Statement 1 states that the compound is paramagnetic. Statement 2 states that the central metal ion has three unpaired electrons. The very definition of paramagnetism is linked to the presence of unpaired electrons. The existence of three unpaired electrons is the direct physical reason for the compound's paramagnetic behavior. Thus, Statement 2 provides the correct explanation for Statement 1.

7. Conclusion: Both Statement 1 and Statement 2 are true, and Statement 2 is the correct explanation for Statement 1. This corresponds to option A.