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In this paper classification of mental task-root Brain-Computer Interfaces (BCI) is being investigated, as those are a dominant area of investigations in BCI and are of utmost interest as these systems can be augmented life of people having severe disabilities. The BCI model's performance is primarily dependent on the size of the feature vector, which is obtained through multiple channels. In the case of mental task classification, the availability of training samples to features are minimal. Very often, feature selection is used to increase the ratio for the mental task classification by getting rid of irrelevant and superfluous features. This paper proposes an approach to select relevant and non-redundant spectral features for the mental task classification. This can be done by using four very known multivariate feature selection methods viz, Bhattacharya's Distance, Ratio of Scatter Matrices, Linear Regression and Minimum Redundancy & Maximum Relevance. This work also deals with a comparative analysis of multivariate and univariate feature selection for mental task classification. After applying the above-stated method, the findings demonstrate substantial improvements in the performance of the learning model for mental task classification. Moreover, the efficacy of the proposed approach is endorsed by carrying out a robust ranking algorithm and Friedman's statistical test for finding the best combinations and comparing different combinations of power spectral density and feature selection methods.