Representation and classification of Electroencephalography (EEG) brain signals are critical processes for their analysis in cognitive tasks. Particularly, extraction of discriminative features from raw EEG signals, without any pre-processing, is a challenging task. Motivated by nuclear norm, we observed that there is a significant difference between the variances of EEG signals captured from the same brain region when a subject performs different tasks. This observation lead us to use singular value decomposition for computing dominant variances of EEG signals captured from a certain brain region while performing a certain task and use them as features (nuclear features). A simple and efficient class means based minimum distance classifier (CMMDC) is enough to predict brain states. This approach results in the feature space of significantly small dimension and gives equally good classification results on clean as well as raw data. We validated the effectiveness and robustness of the technique using four datasets of different tasks: fluid intelligence clean data (FICD), fluid intelligence raw data (FIRD), memory recall task (MRT), and eyes open / eyes closed task (EOEC). For each task, we analyzed EEG signals over six (06) different brain regions with 8, 16, 20, 18, 18 and 100 electrodes. The nuclear features from frontal brain region gave the 100% prediction accuracy. The discriminant analysis of the nuclear features has been conducted using intra-class and inter-class variations. Comparisons with the state-of-the-art techniques showed the superiority of the proposed system.