Group theory is often used by chemists as an aid in the interpretation of IR spectra. For example, there are four NH bonds in NH₄⁺ and four stretching modes are possible. There is the possibility that several vibrational modes occur at the same frequency, and hence are degenerate. A quick glance at the character table will tell if degeneracy is possible. 

(a) In the case of the tetrahedral NH4+ ion, is it necessary to consider the possibility of degeneracies? 

(b) Are degeneracies possible in any of the vibrational modes of NH2D₂⁺?