This work investigated two different machine learning techniques: Cascade Learning and Deep Learning, to find out which algorithm performs better to detect the number plate of vehicles registered in Bangladesh. To do this, we created a dataset of about 1000 images collected from a security camera of Independent University, Bangladesh. Each image in the dataset were then labelled manually by selecting the Region of Interest (ROI). In the Cascade Learning approach, a sliding window technique was used to detect objects. Then a cascade classifier was employed to determine if the window contained object of interest or not. In the Deep Learning approach, CIFAR-10 dataset was used to pre-train a 15-layer Convolutional Neural Network (CNN). Using this pre-trained CNN, a Regions with CNN (R-CNN) was then trained using our dataset. We found that the Deep Learning approach (maximum accuracy 99.60% using 566 training images) outperforms the detector constructed using Cascade classifiers (maximum accuracy 59.52% using 566 positive and 1022 negative training images) for 252 test images.