Master Spectroscopy with 13CH3OH: Correct Statements Explained

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Indicate those of the following statements that are correct for the compound 13CH3OH
(The 13 in front of C is supposed to indicate carbon-13)

a. The carbon-13 spectrum will be a 1:2:1 triplet.
b. The proton NMR spectrum will be a 1:1 doublet and a broad singlet.
c. The broad singlet in the proton spectrum is due to the exchange of protons among methanol molecules.
d. Because of the oxygen, the IR spectrum will have a strong band around 1750 cm-1.
e. This compound will absorb in the visible region, and will therefore be coloured.
f. The mass spectrum should have a peak at mass 15.

Can someone explain to me which statement(s) are correct?

Thanks
 
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What do you know about 13-C NMR spectroscopy? Heteronuclear decoupling?
Tell us what you know about 1-H NMR.
What about IR spectroscopy? Do alcohols have a strong absorption at 1750 cm-1?
Any visible chromophores in methanol?
What fragment might have mass = 15? Is it a likely fragment for methanol?