We determine the upper critical field $mu_0 H_{c2}(T_c)$ of non-centrosymmetric superconductor $Y_2 C_3$ using two distinct methods: the bulk magnetization M(T) and the tunnel-diode oscillator (TDO) based impedance measurements. It is found that the upper critical field reaches a value of 30T at zero temperature which is above the weak-coupling Pauli paramagnetic limit. We argue that the observation of such a large $mu_0 H_{c2}(0)$ in $Y_2 C_3$ could be attributed to the admixture of spin-singlet and spin-triplet pairing states as a result of broken inversion symmetry.
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