Unsupervised domain adaptation (UDA) is a transfer learning technique utilized in deep learning. UDA aims to reduce the distribution gap between labeled source and unlabeled target domains by adapting a model through fine-tuning. Typically, UDA approaches assume the same categories in both domains. The effectiveness of transfer learning depends on the degree of similarity between the domains, which determines an efficient fine-tuning strategy. Furthermore, domain-specific tasks generally perform well when the feature distributions of the domains are similar. However, utilizing a trained source model directly in the target domain may not generalize effectively due to domain shift. Domain shift can be caused by intra-class variations, camera sensor variations, background variations, and geographical changes. To address these issues, we design an efficient unsupervised domain adaptation network for image classification and object detection that can learn transferable feature representations and reduce the domain shift problem in a unified network. We propose the guided transfer learning approach to select the layers for fine-tuning the model, which enhances feature transferability and utilizes the JS-Divergence to minimize the domain discrepancy between the domains. We evaluate our proposed approaches using multiple benchmark datasets. Our domain adaptive image classification approach achieves 93.2% accuracy on the Office-31 dataset and 75.3% accuracy on the Office-Home dataset. In addition, our domain adaptive object detection approach achieves 51.1% mAP on the Foggy Cityscapes dataset and 72.7% mAP on the Indian Vehicle dataset. We conduct extensive experiments and ablation studies to demonstrate the effectiveness and efficiency of our work. Experimental results also show that our work significantly outperforms the existing methods.