The splitting pattern expected to be observed in the nmr spectrum, for the hydrogens indicated by the arrow is e. doublet. Therefore , e. doublet is correct.
The hydrogens indicated by the arrow in the structure are chemically equivalent, meaning they have the same chemical environment.
As a result, they will resonate at the same chemical shift value in the NMR spectrum.
However, they are also magnetically equivalent, meaning they have the same number of neighboring protons with the same coupling constant.
This means that their NMR signal will be split into a doublet with a splitting of 2J.
The other answer choices are incorrect:
A pentet is a multiplet with five peaks, which would be observed if the protons were coupled to four adjacent protons.
A singlet is a single peak, which would be observed if the protons were not coupled to any other protons.
A triplet is a multiplet with three peaks, which would be observed if the protons were coupled to two adjacent protons.
A quartet is a multiplet with four peaks, which would be observed if the protons were coupled to three adjacent protons