(C) The $n^{th}$ term of an $A.P.$ is given by $T_{n} = a + (n-1)d$.Given $T_{7} = 12$ and $T_{12} = 72$.The common difference $d$ can be calculated u

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(C) The $n^{th}$ term of an $A.P.$ is given by $T_{n} = a + (n-1)d$.Given $T_{7} = 12$ and $T_{12} = 72$.The common difference $d$ can be calculated using the formula $d = \frac{T_{n} - T_{m}}{n - m}$.Substituting the values: $d = \frac{T_{12} - T_{7}}{12 - 7}$.$d = \frac{72 - 12}{5}$.$d = \frac{60}{5} = 12$.Therefore,the common difference $d$ is $12$.