We present an angular power spectrum analysis of the 2 Micron All Sky Survey ( 2MASS ) full release extended source catalogue . The main sample used includes 518 576 galaxies below an extinction-corrected magnitude of K _ { s } = 13.5 and limited to |b| > 20 ^ { \circ } . The power spectrum results provide an estimate of the galaxy density fluctuations at extremely large scales , r \sim < 1000 h ^ { -1 } Mpc . We compare this with mock predictions constructed from the \Lambda CDM Hubble Volume mock catalogue . We find that over the range 1 \leq l \leq 100 the 2MASS C _ { l } is steeper than that for the Hubble Volume model . However , in the linear regime ( l \leq 30 ) there is good agreement between the two . We investigate in detail the effects of possible sources of systematic error . Converting linear power spectrum predictions for the form of the three-dimensional matter power spectrum , P ( k ) , and assuming a flat CDM cosmology , a primordial n _ { s } =1 spectrum and negligible neutrino mass , we perform fits to the galaxy angular power spectrum at large linear scales ( l \leq 30 , corresponding to r \sim > 50 h ^ { -1 } Mpc ) . We obtain constraints on the galaxy power spectrum shape of \Gamma _ { eff } = 0.14 \pm 0.02 , in good agreement with previous estimates inferred at smaller scales . We also constrain the galaxy power spectrum normalisation to ( \sigma _ { 8 } b _ { K } ) ^ { 2 } = 1.36 \pm 0.10 ; in combination with previous constraints on \sigma _ { 8 } we infer a K _ { s } -band bias of b _ { K } =1.39 \pm 0.12 . We are also able to provide weak constraints on \Omega _ { m } h and \Omega _ { b } / \Omega _ { m } . These results are based on the usual assumption that the errors derived from the Hubble Volume mocks are applicable to all other models . If we instead assume that the error is proportional to the C _ { l } amplitude then the constraints weaken ; for example it becomes more difficult to reject cosmologies with lower \Gamma _ { eff } .