The novel coronavirus 2019 (COVID-19) is a respiratory syndrome that resembles pneumonia. The current diagnostic procedure of COVID-19 follows reverse-transcriptase polymerase chain reaction (RT-PCR) based approach which however is less sensitive to identify the virus at the initial stage. Hence, a more robust and alternate diagnosis technique is desirable. Recently, with the release of publicly available datasets of corona positive patients comprising of computed tomography (CT) and chest X-ray (CXR) imaging; scientists, researchers and healthcare experts are contributing for faster and automated diagnosis of COVID-19 by identifying pulmonary infections using deep learning approaches to achieve better cure and treatment. These datasets have limited samples concerned with the positive COVID-19 cases, which raise the challenge for unbiased learning. Following from this context, this article presents the random oversampling and weighted class loss function approach for unbiased fine-tuned learning (transfer learning) in various state-of-the-art deep learning approaches such as baseline ResNet, Inception-v3, Inception ResNet-v2, DenseNet169, and NASNetLarge to perform binary classification (as normal and COVID-19 cases) and also multi-class classification (as COVID-19, pneumonia, and normal case) of posteroanterior CXR images. Accuracy, precision, recall, loss, and area under the curve (AUC) are utilized to evaluate the performance of the models. Considering the experimental results, the performance of each model is scenario dependent; however, NASNetLarge displayed better scores in contrast to other architectures, which is further compared with other recently proposed approaches. This article also added the visual explanation to illustrate the basis of model classification and perception of COVID-19 in CXR images.