The following questions refer to an unknown molecule with the molecular formula C$5$H$602.$ A $\text{'}$H and $13$C NMR are provided.

$1.$ Calculate the hydrogen deficiency index for this compound. Show your work.

$2.$ The unknown molecule has two major absorptions in the infrared spectra. Identify these two absorptions$1698$ cm$1$

$3280$ cm$1$