Oxidation State of Central Metal Ion:
The brown ring complex is formed by the reaction of nitric oxide (NO) with ferrous chloride (FeCl2) in the presence of concentrated hydrochloric acid (HCl). The central metal ion in this complex is iron (Fe). To determine the oxidation state of the central metal ion, we need to consider the oxidation states of the other elements in the complex.

In the compound FeCl2, chlorine (Cl) has an oxidation state of -1 since it is a halogen. We can assign a variable "x" to the oxidation state of iron (Fe). The overall charge of the compound FeCl2 is 0, so the sum of the oxidation states must equal zero.

Fe(x) + 2(-1) = 0
x - 2 = 0
x = +2

Therefore, the oxidation state of the central metal ion (iron) in the brown ring complex is +2.

Magnetic Moment of Brown Ring Complex:
The magnetic moment of a compound is a measure of its ability to be influenced by an external magnetic field. It depends on the number of unpaired electrons present in the compound. To determine the magnetic moment of the brown ring complex, we need to consider the number of unpaired electrons on the central metal ion.

In the case of the brown ring complex, the central metal ion is Fe(II), which has a d6 electronic configuration. The electronic configuration of Fe(II) is [Ar] 3d6 4s0. According to Hund's rule, the electrons will first occupy separate orbitals with parallel spins before pairing up. Therefore, in the d6 configuration, there are 4 unpaired electrons.

The magnetic moment of a compound can be calculated using the formula:
Magnetic Moment (BM) = √(n(n+2))

Where n is the number of unpaired electrons.

Plugging in the value of n as 4, we get:
Magnetic Moment (BM) = √(4(4+2))
Magnetic Moment (BM) = √(4*6)
Magnetic Moment (BM) = √24
Magnetic Moment (BM) = 4.89898 BM (approximately 3.87 BM)

Therefore, the correct answer is option B: 1 and 3.87 BM.