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The number of signals in NMR shows the different types of protons present.

The multiplicity shows how many hydrogen atoms are present in the next carbon atom.Multiplicity is an important part of the NMR spectra as it shows how many protons are present in the next carbon atom.

As the molecule contain a center of symmetry so, the signals of one-half part of the molecule are equal to another half.

Signals and multiplicity in hexane (a)

So, the number of signals shown by the molecule is 3. The ${\text{-CH}}_{\text{3}}$molecule shows triplet, while the ${\text{-CH}}_{\text{2}}$ next to methyl group shows sextet and the 3rd${\text{-CH}}_{\text{2}}$ shows triplet.

As all the ${\text{-CH}}_{\text{2}}$groups have a different environment hence, they show different signals. Therefore, the given molecule shows 3 signals.

Signals and multiplicity in (b)

The ${\text{-CH}}_{\text{2}}$group next to $\mathbf{I}$ and $\mathbf{Br}$ shows triplet, while the middle ${\text{-CH}}_{\text{2}}$ group couples with four hydrogen shows quintet.

As the molecule contain a center of symmetry so, the signals of one-half part of the molecule are equal to another half.

So, the number of signals shown by the molecule is 2.

Signals and multiplicity in (c)

The middle group couples with four hydrogens hence, shows a quintet, while the ${\text{-CH}}_{\text{2}}$group next to chlorine shows triplet.

As all the ${\text{-CH}}_{\text{2}}$ groups have a different environment hence, they show different signals. Therefore, the given molecule shows 3 signals.

Signals and multiplicity in (d)

The middle ${\text{-CH}}_{\text{2}}$group shows the quartet, $\text{-CH}$group shows triplet, while ${\text{-CH}}_{\text{2}}$group next to iodine shows triplet.