Finding an optimal subspace of bands that has the most expressive power for classifying hyperspectral image has been very challenging task due to its insufficient number of training pixels with respect to large number of bands. Feature reduction is considered a promising solution in this type of task. However, it is very hard to select an optimal feature reduction technique which is effective as well as computationally efficient in case of hyperspectral image classification. Moreover, it becomes challenging when the number of training pixels of a class is not sufficient. In this paper, we have rigorously studied some feature selection techniques for reducing spectral dimension by considering all the classes in hyperspectral image on a benchmark data set. We have projected that this study will be very supportive for further study on band selection and hyperspectral image classification.