Electroencephalography (EEG) is the most used physiological measure to evaluate the cognitive state of a user efficiently. As EEG inherently suffers from a poor spatial resolution, features extracted from each EEG channel may not efficiently used for cognitive state assessment. In this paper, the EEG-based cognitive state assessment has been performed during the mental arithmetic experiment, which includes two cognitive states (task and rest) of a user. To obtain the temporal as well as spatial resolution of the EEG signal, we combined the Filter Bank Common Spatial Pattern (FBCSP) method and Long Short-Term Memory (LSTM)-based deep ensemble model for classifying the cognitive state of a user. Subject-wise data distribution has been performed due to the execution of a large volume of data in a low computing environment. In the FBCSP method, the input EEG is decomposed into multiple equal-sized frequency bands, and spatial features of each frequency bands are extracted using the Common Spatial Pattern (CSP) algorithm. Next, a feature selection algorithm has been applied to identify the most informative features for classification. The proposed deep ensemble model consists of multiple similar structured LSTM networks that work in parallel. The output of the ensemble model (i.e., the cognitive state of a user) is computed using the average weighted combination of individual model prediction. This proposed model achieves 87\% classification accuracy, and it can also effectively estimate the cognitive state of a user in a low computing environment.