Statement I: Picric acid is 2, 4, 6-trinitrophenol, not 2, 4, 6-trinitrotoluene.
Statement II: Phenol-2, 4-disulphuric acid is treated with concentrated HNO$_3$ to produce picric acid.
The question involves assessing the correctness of two statements related to the chemical compound 'picric acid'. Let's analyze both statements one by one:
Based on the examination of each statement:
Therefore, the most appropriate answer is: Statement I is incorrect but Statement II is correct.