The novel Coronavirus, declared as a pandemic by WHO, has caused a health crisis and disrupted the daily course of the people globally. The effectiveness of Chest X-ray (CXR) in the differentiation of COVID from non-COVID has exhorted us to propose a diagnostic model based on deep features. This paper proposes a diagnostic framework to diagnose COVID-19 from Chest X-rays (CXR). Further Grad-CAM visualizations are shown to get a visual interpretation for the predicted images. We validated the performance of the proposed diagnostic model using the area under the curve (AUC), accuracy, precision, recall, F1-score and geometric mean (G-mean). Few popular machine learning models such as random forest, dense neural network, support vector machine (SVM), twin SVM (TWSVM), extreme learning machine (ELM), random vector functional link (RVFL) and kernel ridge regression (KRR) have been selected for diagnosing the COVID cases. The deep features are extracted by transfer learning. Grad-CAM visualizations are presented for the predicted images. We have achieved the best AUC score of 0.98 on TWSVM classifier on the feature vector extracted by ResNet50 architecture. The feature vector extracted from ResNet50 outperforms all other CNN architecture rank wise based on AUC. The experimental outcome indicates the efficiency of the proposed diagnostic framework.