At the risk of making a mountain out of a molehill....
This thread has been posted for some months now, but it appears that the contributors to this post have not taken into account the fact that 2-butanol possesses a chiral center, which renders the methylene protons (CH3-CHaHb-CHOH-CH3) diastereotopic.
Thus, protons Ha and Hb are expected to display (often only slightly) different chemical shifts. Protons Ha and Hb are mutually coupled and are expected to display Jgem coupling in addition to the Jvic coupling that each proton displays due to spin-spin interactions with adjacent CH3 and CH(OH) protons.
However, it is possible that the difference between chemical shifts of Ha and Hb becomes vanishingly small under the conditions (solvent, concentration, temperature) at which the proton NMR spectrum of 2-butanol has been obtained. This situation represents an example of "accidental degeneracy", and the spectrum would simplify accordingly, thereby permitting the type of first order analysis that the question appears to presuppose.
Additionally, in order to arrive at Choice C ("pentet") as the answer to the question, one also must assume that the magnitude of vicinal coupling between degenerate CH2 protons and the adjacent CH3 group in 2-butanol turns out accidentally to be the same as that between CH2 and the adjacent CH(OH) proton.
A complete proton NMR spectrum of 2-butanol can be viewed by visiting the SDBS online website; reference: 1H NMR Spectrum No. SBDS-507 c/o
http://sdbs.db.aist.go.jp/