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The disease has no cure, till now, except for the prior diagnosis. The present study aims for classifying the MRI scans of two datasets OASIS and ADNI into 2 categories: binary and multi-classification. To achieve the objective, the EfficientNetB0 architecture of deep learning is fine-tuned by adding three dense layers on the top of the network. The swish activation function is used in the inner dense layers added. The dropout and batch normalization layers are also added for dealing with the problem of overfitting. This architecture offers high accuracy and high efficiency compared to other pre-trained networks. The model is assessed on various performance measures and outperformed the state of art techniques. For the OASIS dataset, the best testing accuracy for binary classification is 93.10% with a 0.01 learning rate. The sensitivity is 95.93%, specificity is 90.08%, false-negative rate is 4.07, the false-positive rate is 9.92 and the F1-score is 93.48%. The best testing accuracy of multi-classification is 84.50% with a 0.001 learning rate. For the ADNI dataset, the best testing accuracy is 96.08% with a learning rate of 0.001. The sensitivity is 94.74%, specificity is 99.32%, false-negative rate is 5.26, the false-positive rate is 0.68 and the f1-score is 97.16%. The best testing accuracy of multi-classification is 98.10 with a 0.01 learning rate. 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