  We have carried out tilt magnetic field (B) studies of the \nu=12/5
fractional quantum Hall state in an ultra-high quality GaAs quantum well
specimen. Its diagonal magneto-resistance Rxx shows a non-monotonic dependence
on tilt angle (\theta). It first increases sharply with increasing \theta,
reaches a maximal value of ~ 70 ohms at \theta ~ 14^o, and then decreases at
higher tilt angles. Correlated with this dependence of Rxx on \theta, the 12/5
activation energy (\Delta_{12/5}) also shows a non-monotonic tilt dependence.
\Delta_{12/5} first decreases with increasing \theta. Around \theta = 14^{o},
\Delta_{12/5} disappears as Rxx becomes non-activated. With further increasing
tilt angles, \Delta_{12/5} reemerges and increases with \theta. This tilt B
dependence at \nu=12/5 is strikingly different from that of the well-documented
5/2 state and calls for more investigations on the nature of its ground state.
